George Em Karniadakis - US grants

An essential process in many industrial systems is the transfer of heat from a surface to a flowing fluid stream with a minimum dissipation cost. As a result of the critical role that efficient heat transport plays in applications, several heat transfer enhancement techniques have been devised in the past. A common form of transport enhancement is flow destabilization via cylindrical eddy-promoters placed inside a channel. Previous studies suggest that appropriate destabilization of the flow in the laminar regime results in increasing transport rates up to 500 percent. In this work, the transitional and turbulent flow regime, mostly encountered in engineering practice, will be studied. Destabilization should be applied at the naturally stable scales of motion, i.e. excitation of the -near-the-wall viscous sublayer. The work will include both Direct Numerical Simulation (DNS), as well as companion detailed experiments. The numerical simulations are based on spectral element methods that combine high-accuracy, as well as flexibility in handling complex geometries. The experiments are chosen to allow a maximum overlay with the numerical data in measuring time lines and fluid particle paths of velocity and temperature fields. Experimental techniques include flow visualization via hydrogen bubble, schlieren photography, and laser-sheet scanning techniques. The research will have a direct impact on the development of innovative heat exchanger systems. At the same time, it will underline the potential of DNS as a very powerful tool in gaining deep understanding and obtaining detailed results for transport processes. The companion experiments will provide a basis for the validation of the computations.

An Engineering Research Equipment Grant is to be utilized in obtaining a computer workstation and associated equipment for research in computational fluid dynamics. Fluid flow and heat transfer are being modeled by this investigator in three-dimensional complex geometries, aimed at control of drag and enhancement of heat transfer. The capability of the investigator will be greatly enhance with this equipment.

This research involves numerical modeling of flow near a surface containing riblets, or corrugations alligned in the flow direction, to ascertain the basic mechanisms behind their drag-reducing capability, and also development of a new numerical scheme for dealing with flow over rough surfaces. In the second thrust a spectral element method is to be coupled to a Cellular Automata (CA) model very close to the surface to create a faster and more accurate method for the numerical prediction of flow over complex surfaces. The research results should provide both physical insight into the drag-reducing properties of structured surfaces, as well as superior numerical codes for modeling complex surface flow.

A systematic procedure for computer- aided studies of largescale engineering systems combining complex spatial structure with nonlinear dynamics behavior will be developed. A general methodology is developed, interfacing direct simulations, model reduction, and modern stability and bifurcation algorithms. This procedure will be validated on a number of representative engineering problems in complex geometries, involving and reaction phenomena. More specifically, high-order direct simulations based on spectral element discretizations will be combined with the Proper Orthogonal Decomposition method, in order to extract a small number of global modes governing the behavior of spatially extended systems. A Galerkin weighted residual formulation employing these global modes yields low-dimensional accurate dynamic models, which can subsequently be used to analyze spatial and temporal system behavior, including stability and transition to time-periodic and chaotic states. The proposed methodology can be expected to become a standard powerful computational tool for studying the dynamic behavior of realistic engineering systems. Furthermore, the low-dimensional engineering models resulting from this methodology will be useful in a wide variety of applications, from modeling and analysis, to design, prediction and control of spatially extended systems.

9413819 Karniadakis A research group at Brown University, working on aspects of high performance architectures for computational science, will use ARI funds to purchase a state-of-the-art parallel computer for researches involved in: (1) Parallel Algorithims Paradigms; (2) Parallel Methods for Hyperbolic Problems; (3) Parallel Methods for Incompressible Flows.

Advancing our understanding in a wide range of scientific and engineering fields require the solution of the fluid equations over a very large range of densities and physical scales. These problems, which are not soluble on the current generation of computers, can be solved with the new generation of massively parallel high performance computers using object oriented languages and are likely to form one of the most important scientific applications of these machines. The MAE and Astrophysics departments at Princeton are at the forefront of research into the development of numerical algorithms and computer technology to utilize the next generation of machines in this effort. The engineering and scientific goals are the applications to aerodynamics (the design of airplanes, cars and ships); to turbulence research; and to structure formation in the universe. Progress in these different application areas requires a continuing research effort toward the development of algorithms amenable to parallel processing, automatic grid adaption, coloring schemes for domain decomposition of an arbitrary unstructured tetrahedral grid, and implementation of efficient message passing algorithms to reduce the communication costs on distributed memory architectures. These problems are generic, and not specific to a particular field of application. It is felt that a multi-disciplinary approach to the study of such problems would greatly benefit the training of students and enhance the effective use of high performance computing in research. The MAE and Astrophysics departments have collaborated in this effort in the past, and will continue to do so in the future. We request support for five graduate students to be trained in the design of algorithms for the numerical solution of partial differential equations using massively parallel computer platforms and the application of complex hydrocodes to engineering and physics problems ranging from turbulence research in aerodyna mics to the evolution of cosmological structure.

ABSTRACT CTS-9417520 George Karniadakis A three-dimensional numerical model will be formulated, programmed, and carried out to predict the unsteady velocity, vorticity, and temperature fields in the wake behind a heated circular cylinder. The proposed numerical model more correctly accounts for the three-dimensionality of the flow, and comparisons with the results of more traditional approaches will be made. Comparisons for validity will also be made with the experimental measurements of a co-funded project.

Brown University has received a Major Research Instrumentation Award for the acquisition of a virtual reality display system (a CAVE), a graphics computer to provide synchronized output to the CAVE, and a large shared-memory computer interconnected to the graphics computer via a high speed link. This equipment will form the core of a shared research computing environment at Brown University. Connectivity to resources available at federally funded computing laboratories will be provided through vBNS connection at Brown. A large array of computer and computational science research projects drawn from computer science, chemistry, cognitive and linguistic sciences, geological sciences, mathematics, and physics will be utilizing the proposed equipment. The research projects range over scientific visualization conducted by the Brown Graphics Group in collaboration with the NSF Science and Technology Center for Graphics and Visualization, interactive graphics in computational fluid mechanics at the Center for Fluid Mechanics, geophysical research on earthquake mechanics using numerical modeling, and condensed matter physics. The equipment will be used by graduate students for research and by undergraduate students in over a dozen courses in at least six different science departments, as well for honors thesis projects. In addition, new course units and new interdisciplinary courses in topics such as computational science, neural networks, and medical imaging will be developed to take advantage of this powerful new facility. Ongoing work by undergraduates that could take advantage of this equipment include projects that span departments such as computational steering, scientific visualization, interaction techniques for immersive virtual reality, and the creation of immersive interactive teaching tools.

9809815 Karniadakis A new class of projection methods, the Discontinuous Galerkin Methods (DGM), has been developed recently and has found its use very quickly in such diverse applications as aeroacoustics, semi-conductor device simulation, turbomachinery, turbulent flows, materials processing, MHD and plasma simulations, and image processing. While there has been a lot of interest from mathematicians, physicists and engineers in DGM, only scattered information is available and there has been no prior effort in organizing and publishing the existing volume of knowledge on this subject. The authors of this proposal plan to organize the first international symposium on DGM with equal emphasis on the theory, numerical implementation, and applications. They plan to publish a book to serve as the first reference on this subject with both review articles and state-of-the-art contributions presented at the symposium. The Symposium will include both invited papers as well as other contributions in order to encourage wider participation especially from young scientists and under-represented minorities.

ABSTRACT

Proposal Number: CTS 9901732

Principal Investigator: G. Karniadakis

This award, in conjunction with award 9903346, is to support an investigation into the flow around and the heat transfer from tube banks. Turbulent heat transfer from tube banks depends strongly on the specific geometric configuration employed, and is influenced substantially by the flow-induced vibrations that the tubes may be subject to. In particular, the recent use of high strength materials has produced more slender structures, which are more susceptible to vibration. Existing models for predicting heat transfer and flow-induced vibrations are semi-empirical and even the most sophisticated ones depend critically on time-dependent coefficients, which are difficult to measure. In this work a model is proposed that exhibit some of the complexity of turbulent heat transfer in flexible cylinder arrays but in a simplified setting. Evidence from experimental and direct numerical simulation studies has shown that despite their complexity this type of coupled systems exhibit low-dimensionality and can be modeled effectively using dynamical systems techniques motivated by the theory of approximate inertial manifolds using nonlinear Galerkin models based on hierarchical modes extracted from numerical and experimental data bases using the ``method of snapshots". These models, in addition to the overall force coefficients and Nusselt number, provide detailed spatio-temporal description of the velocity and temperature fields. The experimental and numerical data bases will be obtained at one representative value of Peclet number using DPIV/T measurements and dynamic spectral simulations developed in a previous NSF grant. More specifically, the objective of this renewal grant is two-fold: First, to develop new experimental and simulation tools that will enable high temporal and spatial resolution of general flow/heat-structure interaction problems. Second, to construct reduced dynamical models that retain the spatio-temporal complexity of the full systems and predict accurately the mean and fluctuating quantities of interest.

Visualization of Multi-valued Scientific Data: Applying Ideas from Art and Perceptual Psychology

This is a multi-disciplinary research project to discover new visualization tools for interacting with and understanding multi-valued volumes of scientific data and the physical phenomena they measure. The tools will be developed and evaluated in close collaboration with scientists in three disciplines: neurobiologists studying neural development and disease via biological imaging, computational flow researchers studying blood flow through arteries, and geographers using remote sensing for environmental monitoring and resource management. We will factor out common patterns from the problems in these multiple disciplines to develop interaction metaphors and visualization techniques that are generalizable and widely applicable.

This project develops new visualization evaluation methodologies, an area that has only begun to be addressed. And it compares the effectiveness of visualization applications in several interactive and static computing and display environments including a 4-wall Cave, a 40'x40' virtual environment with a head mounted display, stereo head-tracked workbenches, desktop workstations, paper, and 3D rapid-prototyping output. Immersive environments will be studied
because the value of these non-traditional working environments has not been established and because they present an opportunity to explore fundamentally different interaction metaphors. Comparisons will be performed for both interactive and static cases with appropriate technology determined for each application.

This project brings together experience from art and perceptual psychology for inspiration. Through several centuries, artists have evolved a tradition of techniques to create visual representations for particular communication goals. Art history provides a language for understanding that knowledge. We will draw inspiration from painting, sculpture, drawing, and graphic design and apply these techniques to the scientific problems.

Beyond inspiration, perceptual psychology also brings a second set of knowledge to bear on scientific visualization problems. Evaluating the effectiveness of visualization methods is difficult because, not only are the goals difficult to define and codify, tests that evaluate them meaningfully are difficult to design and execute. These evaluations are akin to evaluating how the human perceptual system works. Perceptual psychologists have been developing experiments for understanding perception for decades, and they will help develop methodology and expertise for evaluating visualization methods in close collaboration with biologists, fluids researchers, geographers, artists, and computer scientists.

While many of the individual components of this project are important alone, the collaborative aspects are the most notable. Mining ideas from art and perception will suggest unusually innovative visualization ideas. The application of new visualization techniques and collaboration with researchers in other fields will provide us with a unique opportunity to validate the techniques and ensure that they are responsive to the needs of the scientific problems. Because the techniques will be developed with application to multiple disciplines, they are likely to find further application within these and other disciplines. The assembled team brings strengths in all of the disciplines and has already demonstrated a track record of collaborative work.

The broader impact of the proposed research lies not only in the information technology arena, where new methods will help scientists in many disciplines to more effectively interact with and understand their data and gain insight about the physical phenomena they represent, but also in the specific scientific domains we will study. The study of blood flow could lead to improved understanding of and treatment for cardiovascular pathologies. An understanding of early neural development could enable new therapies for birth defects, genetic disorders, and other diseases. Remote sensing advances could provide more effective resource monitoring and permit widespread improvements in global quality of life.

EIA-0218142
George E. Karniadakis
Brown University

ITR/DDDAS Generalized Polynomial Chaos: Parallel Algorithms for Modeling and Propagating Uncertainty in Physical and Biological Systems

The applications we target are prototype problems in bioengineering and in nanotechnology. The coupled nature of such problems and the many parameters involved provide a good testbed for evaluating the performance of the new algorithms at resolutions from 0.1 to 1 billion degrees-of-freedom. The sources of uncertainty may be caused by incomplete knowledge or fluctuations in boundary or initial conditions, geometric domain, transport coefficients, mechanical properties, and other external forcing or volumetric sources.

The proposed work will have significant and broad impact as it will establish a composite error bar in large-scale simulations and will enable numerical stochastic approaches to large-scale simulations of physical and biological systems. It will also benefit many other fields including climate and network/web traffic modeling, where current uncertainty modeling approaches are inadequate. Stochastically simulated responses can serve as sensitivity analysis that could potentially guide experimental work and dynamic instrumentation.

The PI's will collaborate to develop and validate new stochastic approaches in order to incorporate and propagate uncertainty in direct numerical simulations and reduced-order models of convective heat transfer. The uncertainty may be associated with free stream turbulence, thermal boundary conditions, geometric roughness or even transport coefficients and source terms. On the simulation side, they will employ the generalized polynomial chaos approach -- an extension of Norbert Wiener's pioneering ideas but with enhanced robustness and efficiency. It employs a correspondence between probability distribution functions and polynomial functional representations. On the experimental side, they will use DPIV (Digital Particle Image Velocimetry) and DPIT (Digital Particle Image Thermometry) to measure accurately probability distributions functions. The emphasis of the experiments will be on analyzing uncertainties associated with boundary conditions.
The proposed work will have broad impact as it will set the foundations of data assimilation and rigorous sensitivity analysis of convective heat transfer. The proposed approach will affect fundamentally the way new experiments are designed and the type of questions that may be addressed, while the interaction between simulation and experiment will become more meaningful and more dynamic. This, in turn, will find its way in the design of heat transfer equipment and will provide a rigorous reliability framework. On the education front, the new knowledge will contribute towards understanding nonlinear systems subject to noise, fundamentals in stochastic dynamics, data assimilation, and design under uncertainty. The PI's plan to incorporate these new ideas in engineering and applied mathematics courses that they teach at Caltech and Brown University.
The award has been funded by the Thermal Transport and Thermal Processing Program of the Chemical and Transport Systems Division, and it is part of a joint program involving Sandia National Laboratory and the NSF in the area of "Engineering Sciences for Modeling, Simulation, Decision-Making and Emerging Technologies.

The investigators propose to organize the next International Conference on "Spectral And High-Order Methods (ICOSAHOM'04)" on June 21-25 2004 at Brown University. The algorithmic themes addressed in this conference are many and new, and attract most leading researchers in spectral methods, h-p finite elements, ENO schemes, high-order finite differences, and wavelets. There are nine confirmed keynote speakers (selected by voting by the scientific committee), four of whom are from USA, and two are women. The topics they will cover are: wavelets, h-p finite elements, singular solutions, electromagnetics, non-Newtonian flows, inverse problems, uncertainty, ocean modeling, fast solvers, and high-order finite differences.

Spectral and high-order methods have become increasingly important in diverse and important applications as aeroacoustics, electromagnetics and optics, ocean and climate modeling. These methods continue to grow in importance as a simulation tool and attract global attention. The proposed conference, part of a long series, continues to be the main meeting where such methods are discussed and new and exciting applications displayed. Furthermore, emphasis is traditionally placed on involving many young researchers as well as underrepresented minorities and women. As a new thing, the conference will conclude with a round-table discussion consisting of a mix of invited speakers, minisymposia organizers, and researchers from national labs and industry. The objective is to discuss and report to NSF the open issues and future algorithmic and application trends of high-order and other discretization methods and their potential in applications of national interest.

This project is to discover new distributed simulation, visualization, and analysis tools for interacting with and understanding multi-valued volumes of scientific data and the biological phenomena they measure. The tools will be developed and evaluated in close collaboration with biologists studying three independent flow-related problems: coronary artery lesion and thrombus formation, the mechanisms and evolution of bat flight, and the mechanism and evolution of fish propulsion and maneuvering.

The work includes advancing basic scientific understanding in the three biological application areas. In addition, the experimental methodology of acquiring 3D motion and flow data using 3D Digital Particle Image Velocimetry (DPIV) and high-speed video will advance the state of the art for studying flow interactions with other biological and man-made systems and may be used for prediction, risk-assessment and decision-making.

The simulation and modeling work to address the biological problems will create new simulation methods for coupling unsteady flow and structure calculations, new methods for incorporating uncertainty into unsteady simulation results, new methods for combining unsteady experimental and simulation data to facilitate comparisons between them, and new methods for filling in gaps in unsteady experimental data.

Abstract
CTS-0326702
M. Maxey, Brown University

Controlled manipulation of super-paramagnetic beads can lead to formation of self-assembled structures suitable for use as micro-optical filters, in DNA separation, or for exploring new concepts in micro- and nanofabrication, especially in three-dimensions. The evidence to date has come from experiments where magneto-rheological (MR) fluids with micron-size beads subject to external magnetic fields form columnar chains that have a regular distribution and spacing. The process is fully reversible and has been found to avoid the difficulties associated with electro-rheological fluids. Recent advances have been made, through laboratory demonstrations, of how particles can be manipulated in microchannels for cell sorting, cell removal or to fabricate new pumps, valves and mixers.

While the experiments have demonstrated some of the intriguing properties of MR fluids, their full potential remains to be developed. In this proposal, we aim to simulate and study the fundamental properties of MR fluids and resulted self-assembled structures, and to also investigate new designs and optimum performance of prototype colloidal microdevices. In a broader context we propose new ways of fabricating microdevices without the use of lithography. We will consider two different classes of problems, the first involving tens of paramagnetic microspheres whereas the second involving thousands.

To this end, we will employ a hierarchical simulation methodology that performs best in a certain range of parameters in terms of both accuracy and computational complexity. It will include new stochastic techniques to represent Brownian noise; geometric roughness or other uncertainties associated with the boundary conditions, particle size and interaction forces. Specifically, we will employ direct numerical simulations based on high-order discretizations and three different formulations: (1) the arbitrary Lagrangian Eulerian (ALE), (2) the distributed Lagrangian multiplier method (DLM), and (3) the force-coupling method (FCM). The stochastic contributions will be modeled spectrally using the recently developed generalized polynomial chaos method.

The first primary goal of the project is to develop and evaluate the proposed simulation methodology for colloidal microdevices. We will then apply it to design micropumps, microvalves and other microdevices such as mixers and sorters, and optimize their performance. We will also investigate new concepts in fabricating three-dimensional microdevices. The second goal is to study the formation of self-assembled structures such as chains, or arrays of chains, from a suspension of micron-scale and sub-micron paramagnetic beads.
Brownian motion plays a significant role for smaller particles, and the relative strength of the magnetic field is an underlying parameter, together with void fraction, channel geometry and any imposed fluid flow. The dynamic characteristics for time-varying magnetic fields or a nonuniform patterning of the field will be considered.

The broader research impact of this work is great as it addresses for the first time simulation of magneto-rheological fluids in many different configurations. The possibility to target and precisely control the electro-optical as well as the mechanical properties of microstructures in a dynamic way using external fields will open new horizons in microfluidics research and will suggest new protocols in micro- and nanofabrication. Self-assembled magnetic matrices can find a large range of applications for the separation of DNA and other intermediate-size objects. Self-assembly of colloids can be used in a bottom-up approach to the fabrication of nanosystems and three-dimensional microsystems.

The broader education impact is also great in that the proposed work will contribute to fundamental understanding of properties of MR fluids, self-assembly processes, and new nanotechnology applications. Self-assembly processes occur at all scales from molecular (crystals) to the planetary scale (weather system), and this universality will attract the curiosity of young minds. We expect to attract undergraduate and graduate students with diverse scientific backgrounds to be involved in this project. We also plan to inform the broader community through demonstrations and visualizations, and we will enhance Brown's ARTEMIS program in educating and inspiring young women on issues of nanotechnology and computational science.
The previous NSF grant of the lead PI supported two African-American female PhD students.

ABSTRACT

The Division of Applied Mathematics at Brown University is acquiring research computing equipment dedicated to support of research in the mathematical sciences. The main items to be purchased include: (1) high-bandwidth low-cost storage optimized for use with the Lustre file system and existing Linux clusters, (2) high-speed network components to support trunked-ethernet communications between the compute nodes, storage, and graphics systems, (3) high-end Linux client PCs for data analysis and visualization, and (4) a small computer experimental facility to support collection and analysis of neural spike-train data for the mathematical modeling and statistical analysis of biological vision. The computing equipment will be used to carry out the research of NSF-sponsored projects in numerical methods for partial differential equations, mathematical modeling in brain science, and statistical procedures in experimental neuroscience.

The research in applied mathematics is closely tied to applications in engineering, physics, and the life sciences. The NSF-sponsored research focuses on development of new mathematical and statistical methods designed for the application areas. For example, some of the work on computational methods for engineering is motivated by the need to design stealth aircraft. Also, the research on new statistical methods is needed for the advancement of brain science, to understand how information is encoded in neural spike trains. The computer equipment provided by this grant is crucial for the ability of faculty and students to create these new mathematical and statistical methodologies.

In numerical simulations of fluid flows, just as in experiments, we often question the accuracy of the results, and we construct error bars that reflect the numerical accuracy of the solution. In many cases, however, there exists a much larger error associated with the fact that the physical parameters, the geometry, and the operating conditions of the simulated flow are not precisely known. With the computational fluid dynamics field reaching now some degree of maturity, we naturally pose the more general question of how to model uncertainty and stochastic input mathematically, and how to develop new algorithms that will yield simulation results that reflect accurately the propagation of uncertainty. To this end, the Monte Carlo approach can be employed but it is computationally expensive and it is only used as the last resort.

In this grant we develop a new approach similar to high-order finite element methods but instead decomposing the random domain. Specifically, we extend the pioneering ideas of Norbert Wiener in generalized Fourier series -- the so-called polynomial chaos expansion -- and apply it locally to each random element. The resulting system of governing equations forms a set of coupled modified flow equations, which are deterministic and thus can be solved with standard numerical methods. Comparisons with the Monte Carlo method show that the new method is faster by a factor of 100 to 1000 on the average. We propose to document systematically this method and use it to study in detail important problems in high-speed flows and in modeling blood flow in the human arterial tree. The proposed approach will affect fundamentally the way we design new experiments and the type of questions that we can address, while the interaction between simulation and experiment will become more meaningful and more dynamic. This, in turn, will find its way into the design of flow systems equipment and will provide a rigorous reliability framework.

We plan to involve graduate and undergraduate students in the current research and we will develop a specific initiative to attract pre-college female students to mathematics and computational science.

It is now well established that platelet aggregation is not only important for primary hemostasis but, when exaggerated, can also lead to the formation of occlusive thrombi, which form at sites of atherosclerotic plaque rupture, resulting in a heart attack, stroke or sudden death. Platelets are micron-size cells - smaller than red blood cells - and when activated they become adhesive for other activated platelets and they adhere to the vessel wall. Their strong interaction with nano-size proteins at the sub-endothelium matrix activates and reshapes them from passively traveling discoids to active spiny spheres. The length and time scales characterizing such interactions as well as platelet-blood flow interactions span several orders of magnitude.

We propose a multiscale modeling methodology with focus on flow-modulated phenomena such as platelet adhesion and aggregation at the micron-scale, and including nanoscale effects representing the main protein interactions. We will develop an integrated approach by coupling multiscale representations of blood flow, ranging from a quasi 1D transient flow in compliant vessels at the largest scale, to unsteady 3D flows in curved and flexing vessels at the mm range, to multi micron-scale thrombus formation at a fissure in the lumen of such a vessel with an atherosclerotic plaque, to changes over short times (seconds and minutes) in the behavior of platelet structure, receptors and bonds in a developing thrombus-wall interaction. To this end, we will develop a new mesoscopic numerical method that bridges the gap between atomistic phenomena and large-scale phenomena to seamlessly connect length scales from 10 nm to a few mm. The new simulation approach will be validated systematically against experiments of varying biological and computational complexity.

We also propose to establish a virtual center for multiscale modeling in order to provide modelers and experimentalists with quantitative information about molecular and cellullar processes that can be incorporated into simplified models. To this end, we plan to organize a workshop on multiscale modeling of biological processes during the second year of the proposed project. In our outreach program, we plan to engage pre-college women from the Providence area in computer and computational sciences. This will involve lectures by our medical collaborators as well as interactive learning at Brown's virtual immersive visualization facility.

The potential impact of this work is great as it provides a new simulation capability for studying biomolecular interactions in blood vessels, organs and the entire arterial tree in a few hours instead of days or even weeks on a supercomputer. This, in turn, will allow fundamental studies at the molecular and cellular level and interaction with macroscales not currently possible with existing methodologies.

PIs: George Karniadakis (Brown University), Steven Dong (Purdue University) and
Nicholas Karonis (Northern Illinois University)
Number: CI-TEAM Proposal 0636336
Title: CI-TEAM Implementation Project: Collaborative Research: Training Simulation
Scientists in Advanced Cyberinfrastructure Tools and Concepts
Project Abstract:

Harnessing the most powerful open computational resources of the nation as integrated by the TeraGrid (TG) and its future extensions will enable otherwise infeasible discoveries in simulation science, in general, and in life sciences, in particular, as well as presenting an unprecedented opportunity to share this unique scientific achievement with our nation's students and educators. Our demonstration of using effectively TG resources in performing the first cross-site simulations and visualizations of the human arterial tree has created great enthusiasm among faculty and their students who are interested in accessing this new simulation environment. As developers and users of some of the most advanced tools in computational science today, we want to make these tools available to the wider scientific community, to train the trainers, and to engage postdocs, graduate and undergraduate students as well as high school students and their teachers in this effort. Our goal is to lower barriers to the use of TG simulations and our objectives are to: (1) mobilize the biomechanics research community, (2) train a new generation of simulation scientists, and (3) inspire young students to become tomorrow's leaders in inter-disciplinary simulation science. To this end, we will implement a biomechanics gateway on the TG and establish it as the main platform and simulation framework for further developments and biomedical research. The framework we have developed for the human arterial tree can serve as the common thread in integrating a number of large biological endeavors into a coherent and exciting future research direction and in developing effective new training methods.

Broader Impact: The software implemented in this project will be open source and will be distributed to all TG users, facilitating a transition in computational biology from traditional computing to grid computing on the TG with potentially unlimited scalability. The new simulation environment will be critical in educating and training a new generation of inter-disciplinary scientists to be comfortable in using advanced software tools and concepts across many disciplines. New courses developed in this project, on grid computing, multiscale biological modeling, and scientific visualization in immersive interactive environments will better prepare future generations of scientists and engineers and educators in the use and development of cyberinfrastructure. We will work with community colleges in the Chicago area to train their faculty. This project also promotes engaging students, especially undergraduates, of diverse groups in inter-disciplinary projects, and in outreach activities engaging high school students, especially women and minorities.

This project is building on an existing undergraduate major in Applied Mathematics - Biology by providing an immersive research experience in applied mathematics and biology for undergraduates in their junior and senior years. Student teams, drawn from both applied mathematics and biology backgrounds, are working on joint projects in physiology and in genomics. The projects, all active research areas of the investigators, cover the human circulation and the multi-scale dynamics that regulate blood flow, from the arterial level to the dynamics of individual blood cells in maintaining hemostasis; the dynamics of cells and cellular organisms; and the molecular biology of genes and gene function. Students work with faculty advisors and alongside graduate students and post-doctoral associates, participating in regular research meetings and seminars as well as a monthly group meeting for all the project participants. Students also participate in submission of papers for conference presentation or journal publication. The project work is coordinated with recently introduced courses and mentoring of the students and it is drawing together undergraduate students and faculty to work on innovative and challenging problems.

Intellectual Merit and Education: There has been an explosion in recent years in the quantified analysis of biological systems that requires a new look at how we educate undergraduates. This project meets the need to provide them with a background in mathematics and biological science that will prepare them as a new generation for future graduate level programs. There have been major advances in multi-scale simulations and scientific computing - both continuum and atomistic, dynamical systems, and the statistical methods applied to genomics and gene expression networks. Much of this is still only accessible to graduate students yet the excitement surrounding the topics they encompass are powerful motivations for engaging undergraduate students in research.

Broader Impact: The development of new courses, research projects and the formulation of the Applied Mathematics-Biology concentration will be valuable resources that will be shared with others in the NSF-UBM program and more generally through web-based links. The undergraduate students are also able to participate in an established outreach program for local high school students, sharing with them their experience and motivation.

This proposal will demonstrate a software infrastructure specialized to study of cerbrovasculature. The problem is of great societal importance and is typical of a number of multiscale multiphysics problems encountered in multiple branches of science. The investigators will focus in this project on:
? Scalable Continuum Models using their highly accurate hp adaptive spectral element code NEKTAR,
? Stochastic Continuum/Atomistic Modeling (LAMMPS-DPD);
? Multi-Level Parallelism, and, finally an effort to make computing across multiple grids by doing a pilot of TeraGrid-DEISA Grid Computing.

The investigators propose to participate in organizing the next ICOSAHOM (International Conference on Spectral And High-Order Methods) on June 22-26 2009 at the Norwegian University of Science and Technology (NTNU) in Trondheim, Norway. They have been working in this field for several decades and have been active participants in all past ICOSAHOM meetings. Selected papers from the proceedings will be published as a special issue in a archival journal. They also plan to produce a report for the funding agency that will provide feedback from a round-table discussion we plan to organize. The theme of this round-table discussion will be the future algorithmic trends and applications of numerical methods and what is the role of high-order methods. Also, their transition to computer codes that will be used for the simulation needs of the national labs and in industry will be discussed, especially in the context of petaflop applications. To this end, they plan to invite researchers with advanced computing expertise and also have interest on high-order accuracy to participate in this panel. The invited and contributed talks will contain new theoretical and applications results of spectral and high-order methods which had not been published yet. Spectral and high-order methods have become increasingly important in diverse applications as aeroacoustics, electromagnetics, ocean modeling, seismology, energy, non-Newtonian flows, nonlinear optics, plasma dynamics, and uncertainty quantification. New developments in the last few years have addressed issues of complex geometry, high-speed flows, fast solvers for large-scale simulations, reduced order modeling, and stochastic modeling.

NSF has invested heavily in computer hardware in their last three decades in par with the rapid growth of computer industry. However, simultaneous advances are required in the development of algorithms and software in order to make effective use of the new computer resources. This conference will advance the state-of-the-art in algorithms of high accuracy that are required in order to produce credible simulation results. In addition to the senior researchers invited, we plan to sponsor young researchers, postdocs and PhD students, especially from under-represented minorities, in order to educate a new cadre of simulation scientists in these methods. Today, high-order accuracy (at least second-order) is a requirement for publishing archival work in engineering journals, and the planned panel discussion is expected to have great impact in the engineering community. In addition, the important issue of numerical versus modeling accuracy and issues related to Verification and Validation will be discussed.

DESCRIPTION (provided by applicant): Project Summary/Abstract The objective of this project is to develop a unified and validated multiscale modeling methodology for two diseases with serious hematological disorders: celebral malaria (CM) and sickle-cell (SS) anemia. The common clinical symptom of both diseases is obstruction in the microcirculation caused primarily by loss of deformability of red blood cells (RBCs) and increased cytoadhesion. Both diseases are characterized by multiscale phenomena, spanning at least four orders of magnitude in length scale with corresponding disparity in the temporal scale. Moreover, the local vaso-oclusions occurring in CM and SS strongly affect blood flow and oxygen transport at the global organ scale as well. Building on recent progress in modeling RBCs at the spectrin level and cell-aggregation processes and taking advantage of available petaflop-level computing resources, we propose a parallel multiscale methodology to model CM and SS and use it as a predictive tool for quantitatively assessing the severity of these diseases. This will form a general simulation platform for adding further complexity in future studies, e.g., incorporating more biochemical details or studying other hemolytic disorders. Predictability of multiscale models requires quantifying uncertainty, and, to this end, we will incorporate polynomial chaos methods to model and propagate parametric uncertainties through the multiscale system. In addition, to validate the new methodology, microfluidic experiments, optical tweezers measurements and 3D phase microscopy will be used to test different aspects of the conceptual and numerical modeling under different conditions. The specific contributions of this project include: (1) Development of fine- and coarse-grained RBC models in CM (cytoskeleton dynamics) and SS (oxygen transport and polymerization) using molecular dynamics (MD), partial differential equations (PDEs), and mean-field theory. (2) Characterization of infected RBCs and sickle cells at different developmental stages using optical non-invasive means. (3) Modeling of flow and rheology in small vessels. Flow modeling will be based on the "triple-decker"1 - a new algorithm that we have developed for interfacing seamlessly MD, mesoscopic dynamics, and the Navier-Stokes equations. For mesoscopic dynamics we will employ the dissipative particle dynamics (DPD) method, a particularly effective simulation approach for complex fluids. We plan to disseminate our models and software tools, including the general-purpose triple-decker algorithm, via web-based repositories, existing public openware sites, summer schools, and through the MSM consortium. 1 http://www.cfm.brown.edu/crunch/IMAG/FedosovK08.pdf PUBLIC HEALTH RELEVANCE: We propose to develop a unified multiscale modeling methodology for two diseases with serious hematological disorders: celebral malaria (CM) and sickle-cell (SS) anemia. We will model the increase in stiffness of the deformable red blood cells and the adhesion processes involved and correspondingly blood flow in capillaries and arterioles, modeling multiscale phenomena across more than four orders of magnitude in spatio-temporal scales.

CBET - 0852948
Karniadakis



Many microfluidic, synthetic-materials, and biomedical applications often need to model multiscale flow phenomena across several orders of magnitude in spatio-temporal scales from near-wall subdomains but also the outer flow over long simulation times. The goal of this project is to develop a validated methodology for simulating multiscale flow phenomena over functionalized surfaces with a biomedical focus. To this end, the PIs propose a "triple-decker" flow model based on interfacing seamlessly a mesoscopic method (dissipative particle dynamics or DPD) to molecular dynamics (MD) on one side and incompressible Navier-Stokes (NS) equations on the other side. The novelty of the PIs' approach is the use of a mesoscopic layer between NS and MD--unlike previous approaches-- to facilitate a smooth transition from the atomistic to the continuum regime. Their preliminary results for simple fluids show the great potential of this method. Here the PIs propose fundamental new developments to make the method applicable to complex fluids and to flows over functionalized surfaces including polymer brushes, where an assembly of polymer chains tethered by one end to a surface creates a surface with specialized properties. The large theoretical and experimental works on this topic, starting with the work of de Gennes, will act as a testbed to validate the proposed methodology and evaluate its efficiency and then model cytoadhesion over protein-coated surfaces using the polymer brushes as model of cell surface. The objective here is to develop a molecularly based adhesive dynamics model to complement existing mechanistic macromodels for multiparticle adhesive dynamics. Specifically, the PIs will simulate the binding of malaria-infected red blood cells (RBCs) to functionalized walls, as was done in recent microfluidic experiments, in essence mimicking cytoadhesion in arterioles and capillaries. The triple-decker (MD-DPD-NS) approach is general and can be applied to simple and complex fluids in microfluidic or biomedical applications but also in more classical applications, e.g., control of wall shear stress using surfactants or hydrophobic surfaces. DPD, first popularized in Europe, is a very effective method for modelng both complex fluids and soft matter but has not yet been adapted widely in USA, and the proposed work will contribute to its further use and development. More broadly, this work on polymer brushes can be used in a wide range of industrial applications in oil recovery, automotive lubrication, colloid stabilization, and in tailoring surface properties. The PIs will disseminate their models and the triple-decker codes as open source codes via existing external open source websites. They will organize seminar-courses open to all students at Brown University focused on multiscale modeling and applications. In addition, undergraduate students, through Brown's UTRA (Undergraduate Teaching and Research Assistantships) program, will be involved in the research projects, either during the academic year or the summer. The PIs also plan outreach activities for inner-city high school students in a partnership with the MET school, where Brown students will be tutoring MET high school students in physics and mathematics in close collaboration with MET school teachers.

This study is cofunded by the CBET, CMMI, and DMS divisions.

Proposal #: CNS 09-23393
PI(s): Laidlaw, David H.; Hesthaven, Jan S.; Karnadiakis, George E.; van Dam, Andries
Institution: Brown University
Providence, RI 02912-9002
Title: MRI/Dev.: Next-Generation Interactive Virtual-Reality Display Environment for Science

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).



Project Proposed:
This project, developing a world-class interactive large-field-of-view 95 megapixel immersive virtual-reality environment, aims at creating a novel, demonstrably useful, rich, and expressive interaction, visualization, and analysis that truly leverage the human visual and motor systems in Virtual Reality (VR).
This work intends to help accelerate scientific work, research into innovative visualization methods for accelerating science in the future, and even leverage the fundamental advantages of immersive large-field-of-view visualization and body-centric human-computer interaction. Two decades of research have established the value of immersive displays as a research tool in many scientific domains and has also identified a set of currently unmet needs that block application of such displays to new problems and domains. These needs encompass high display resolution, brightness, contrast, and size; fast, responsive tracking with high accuracy and low latency; ease of use in working with new kinds of data; and reliability. Although a few multi-million dollar systems exist that may be able to address these needs, these few systems do not match the proposed display?s color gamut, small physical space requirement, and lower replication cost. The system is expected to support more natural and effective interaction with data than the current 3D point-and-click wand driven CAVEsTM by maximally utilizing as appropriate full-body, motion-captured user interactions and gestures. More display information will be made accessible to the human visual system with less user effort by matching, or exceeding the perceptual qualities of a modern LCD monitor. An immersive stereo display will be integrated with the perceptual resolution of a desktop display and superior brightness and contrast. Integration of software tools for creating virtual-reality applications quickly will address ease-of-use and reliability. The new tools are expected to be simple, support a spectrum of displays, and provide rich support for gestural interaction. A monitoring process to identify potential problems among the interacting hardware and software components will be put in place to identify and address problems before instruments are delayed. Users of the system include planetary geologists, systems biologists, brain scientists, cell and molecular biologists, biologists studying animal motion (including flight), fluid dynamicists, bioengineers studying arterial hemodynamics, visual designers developing interactive techniques for scientists, digital literary artists, and visualization and interaction researchers. Within interaction research, experiments using the system are expected to establish the appropriate level of display technology (e.g., resolution, interactivity, or stereographic display) needed for different classes of scientific analysis. The techniques, monitoring system, and software environment will be distributed on SourceForge to respectively help accelerate scientific progress nationwide, for developing multi-display applications, and for ensuring reliability.

Broader Impacts: While educating many students, the instrument is expected to enable new advances in all of the scientific disciplines of the users listed above, including a better understanding of the workings of cells and genes and proteins they contain (which could consequently improve quality of life broadly), behavior of fluids in arteries and around moving animals, animal locomotion (which could lead to improved biomimetic locomotive, floating, or flying vehicles), the wiring of the human brain, how it affects human capabilities, and how it can degrade; and Mars. The efforts are likely to produce a new generation of scientists who can better analyze research problems using scientific visualization, computer scientists more cognizant of scientists? analytical needs, and artists and designers who can accelerate the design process for immersive scientific visualization tools.

The PI proposes to develop new effectrive methods for solving stochastic partial differential equations (SPDEs). In particular, the PI will address two outstanding issues in polynomial chaos (PC) methods for modeling uncertainty in computer simulations of physical and biological systems. The first one is related to treating effectively many stochastic dimensions while the second one is related to modeling accurately white noise. Such problems arise in applications with small relative correlation length or large number of independent random parameters. The two approaches are complementary to each other as problems with very small correlation length can be effectively modeled by white noise processes.The new ideas are the use of ANOVA decomposition and the introduction of proper weighted Wiener chaos
spaces and stochastic convolution products. ANOVA provides a hierarchical functional decomposition that exploits the effective dimensionality of the system. This type of dimension-wise decomposition can effectively break the curse of dimensionality in certain approximation problems in which the effective dimensionality is much lower than the nominal dimensionality. In preliminary work, the PI has demonstrated the effectiveness of the new approach in approximating efficiently problems with more than 500 dimensions.

The proposed work will have significant and broad impact as it will set rigorous foundations in uncertainty quantification, data assimilation and sensitivity analysis for many physical and biological systems. For example, in computational fluid dynamics, it will establish a robust and efficient framework to endow simulations with a composite error bar that goes beyond numerical accuracy and includes uncertainties in operating conditions, the physical parameters, and the domain.The proposed work is transformative as it will make stochastic simulations the standard rather than the exception. It will also affect fundamentally the way new experiments are designed and the type of questions that can be addressed, while the interaction between simulation and experiment will become more meaningful and more dynamic.
The PI plans to incorporate these new ideas in engineering and applied mathematics courses at Brown. Sponsored graduate and undergraduate students will be involved in this research and will interact with
all senior personnel that includes several international visitors. The PI will work closely with undergraduate students who are involved with outreach activities through two very effective organizations at Brown that target women in science and engineering and also middle school students. He also plans outreach activities for inner-city high schools by developing along with the teachers computer-based interactive math learning strategies. Preliminary results working with the MET school have been very encouraging, and the PI plans to expand this activity nationwide.

Future petaflop simulations of realistic biological and physical systems will necessarily involve concurrent multiscale modeling. This project will address fundamental mathematical, algorithmic and software issues for simulating a human brain vascular model, the first of its kind, consisting of 100 large 3D arteries (Macrovascular Network, MaN), 10 million arterioles (Mesovascular Network,MeN) and one billion capillaries (Microvascular Network, MiN). The three-level MaN-MeN-MiN integration offers a general platform for developing hybrid deterministic-stochastic systems, scalable algorithms, and scalable multiscale software to handle coupling between heterogeneous PDEs and also between continuum and atomistic formulations. Building upon their initial work on the human arterial tree and the new brain imaging data, PIs propose image-based 3D Navier-Stokes simulations for fully resolving MaN, coupled to subpixel stochastic simulations of MeN and MiN to complete the closure. Project will implement an MPI/UPC hybrid model to exploit the strengths of both programming paradigms: the high scalability and rich functionality for process control in MPI, and the low communication overhead for small messages and fine-grain parallelism in UPC. We will further seek to integrate multi-threading into the MPI/UPC model, especially for dynamic refinement. The main software advancement will be the development of MPIg tailored for multiscale applications, like the MaN-MeN-MiN problem, on a single or multiple petaflop platforms. Several open issues associated with co-processing and visualization of petabyte-size data will be also addressed.


Broader Impact: This work will contribute to Computational Mathematics (interfacing heterogeneous PDEs, and also PDEs-atomistic systems); to Computer Science (development of UPC/MPI, multiscale MPIg, and increased leverage of vendor-supplied MPI in MPIg); and Bioengineering (biomechanics gateway to simulate brain pathologies). This proposal is transformative in that it shifts the computational paradigm to a new level (orders of magnitude above the state-of-the-art) that will allow, for first time, realistic simulations of cerebrovasculature in health and disease. The validated algorithms for peta°op computing we propose are of general interest for use in many multiscale biological and physical applications, including vascular trees of all living organisms and also in simulations of nuclear reactors and other power/chemical plants. The new simulation environment, with the human brain as a backdrop, will be critical in training a new generation of inter-disciplinary scientists to be comfortable in using multiscale mathematics and scalable software tools for extreme computing. Project will engage postdocs, graduate, undergraduate and high school students. We will use 3D immersive/interactive visualizations as an opportunity to educate students about simulation, predictability, and other issues of computer science, engineering, and applied mathematics. Outreach activities will involve female students from middle and high schools and students from the special MET high schools.

New theory and corresponding numerical algorithms are proposed for addressing fundamental open questions in stochastic modeling of physical and biological systems, e.g., the curse-of-dimensionality, the lack of regularity and the long-time integration of stochastic systems. Such problems arise in applications involving processes with small relative correlation length or large number of random parameters, and for time-dependent nonlinear systems subject to uncertainty. The new equations are formulated in terms of the time-evolution of the joint probability density function (PDF) between the system's response and the stochastic excitation. In particular, functional integral methods are employed to determine new types of linear deterministic partial differential equations satisfied by the joint response-excitation PDF associated with the stochastic solution of nonlinear stochastic ordinary and partial differential equations. So far the theory is complete for nonlinear and for quasilinear first-order stochastic PDEs subject to random boundary conditions, random initial conditions or random forcing terms. For higher-order equations, such the stochastic wave equation or the Oberbeck-Boussinesq thermal convection equations, it is proposed to develop a new PDF method based on differential constraints for the PDF of the solution. It is proposed to investigate the theoretical and numerical effectiveness of this new approach for high-dimensional random systems, such as random flows subject to high-dimensional random boundary or initial conditions in bounded domains.

Stochastic modeling and uncertainty quantification are important new directions in computational mathematics that will enable accurate predictions of physical and biological phenomena,in critical applications such as climate, energy and the design of new products. The proposed work will have significant and broad impact as it will set new rigorous foundations in uncertainty quantification, data assimilation and sensitivity analysis for many physical and biological systems. It will affect fundamentally the way we design new experiments and the type of questions that we can address, while the interaction between simulation and experiment will become more meaningful and more dynamic. This work will also aid in educating a new cadre of simulation scientists in this metadiscipline at the interface of computational mathematics and probability theory.

DESCRIPTION (provided by applicant): The objective of this project is to develop a validated multiscale modeling methodology for quantifying the biophysical characteristics of sickle cell disease (SCD) -- a hematological disorder that affects tens of thousands of people in US with one in every 500 African-American births resulting in a child with SCD. The pathogenesis of SCD results from (1) irregular red blood cell (RBC) shapes due to hemoglobin polymerization inside the RBCs; (2) stiffening of the RBC membrane; and (3) adhesion of sickle RBCs to the endothelium and the other blood cells. The combination of these phenomena results in vaso-occlusive events or crises responsible for the majority of morbidity and mortality associated with SCD but little is certain about the proximal causes or the circumstances in which they occur. The spatio-temporal scales involved in accurately modeling SCD blood flow and vaso-occlusion span at least four orders of magnitude, hence new numerical methods are needed to simulate such multiscale phenomena. We present a general methodology based on 3D dissipative particle dynamics (DPD) to model flow and soft matter seamlessly, i.e., RBCs and other blood cells, blood plasma, cytosol, hemoglobin polymerization, and adhesive dynamics. DPD can be interfaced with molecular dynamics (MD) and with continuum-based description (e.g. Navier-Stokes) based on the triple-decker algorithm we have developed in order to capture molecular details or for computational efficiency in simulating large arteries or networks, respectively. We adopt the same approach here that has proven very effective in our previous work on malaria, namely that models for single RBCs (healthy or sickled), informed and validated from comprehensive single-cell measurements, will be used to predict the collective dynamics and rheology of SCD blood flow. We also present a systematic experimental plan, using microfluidics, nanomechanics and advanced optical techniques, to validate the various stages of the development of our models by targeting individual scales as well as interactions between scales. We will extend the first generation of models to study different modalities of existing and experimental therapeutic interventions for SCD, including simple transfusion, fetal hemoglobin (HbF) induction by hydroxyurea, and RBC hydration. Predictability of multiscale models requires quantifying uncertainty, and, to this end, we will incorporate polynomial chaos methods to model and propagate parametric uncertainties through the multiscale system. We plan to disseminate our models, software tools, and experimental data including the general-purpose triple-decker algorithm, via web-based repositories, existing public open-ware sites, tutorials and through the MSM consortium.

The workshop, "Modeling, Analysis, and Numerics for Nonlocal Applications", will take 11-15 December 2017 in Sante Fe, New Mexico; information is at the website: sites.google.com/site/manna2017abq. The focus of this workshop is on non-local mathematical models, a topic of increasing interest in several diverse scientific and engineering applications related to, as an example, material science, biology, and environmental studies. Non-local calculus and the corresponding models have emerged as a powerful tool for modeling multi-scale phenomena, including overlapping microscopic and macroscopic scales. In the computational mathematics community, two relatively separate groups of researchers (i.e., the "fractional derivatives" and the "non-local operators" communities) are concurrently working on the analysis and simulation of these relevant problems. One of the main goals of this workshop is to unite these separate communities providing significant benefit from their interaction and opportunity to exchange their recent progress and results on the topic. Central to the workshop is also the involvement of students or young researches, not necessarily already engaged in non-local research, who will have the opportunity to interact and learn from worldwide experts. The main topics that will be addressed are the analysis and improvement of such non-local models and their efficient simulation by means of cutting-edge algorithms on the newest computer architectures.

Non-local operators provide a new framework to overcome limitations that are present in classical PDE-based models. This workshop is designed to facilitate the exchange of information between the (tempered) fractional calculus and non-local vector calculus and the establishment of connections between them; this will lead to the design of new improved non-local models and will facilitate their analysis and simulation. As a result, the workshop will lead to new research in applications of national interest such as subsurface flow simulations, energy storage systems, contaminant transport, polymer and complex fluid flow, material failure and damage, or any applications in complex systems and disordered media that exhibit anomalous transport and diffusion. The goals and objectives of the workshop include establishing synergies between participants working on fractional PDEs with those working on general non-local integral models; maximizing both the breadth and depth of the information imparted to and exchanged among participants; providing researchers at all career stages with the opportunity to present their state-of-the-art results or to learn from experts in the field; and identifying the most important needs and most potentially fruitful avenues for future non-local related research and related applications. This will be facilitated by the discussion session at the end of each day that will focus on a review of the recent past and near-future directions of research in each area.

The operation of current power systems depend on deterministic and static models, which are not suitable for analyzing smart power grids due to the increasing large-volume of data collected by the grids and sensors and the need to integrate intermittent renewable resources and dynamic load compositions. Large uncertainty in the model prediction is problematic as it does now allow careful planning, and failure to identify large fluctuations and possible instabilities could endanger the reliable operation of the power grid. Hence, it is crucial to incorporate new monitoring capabilities realized by new tools such as machine learning and predictive multi-rate modeling in modeling the smart grid. Classical methods that deal with uncertainty lead to inefficient solutions as they are too slow to converge to a solution and hence they cannot be used effectively for real-time control of power grids. This difficulty stems from the requirement of sampling the very complex power grid thousands of times in order to arrive to a reasonably accurate solution. The goal of this project is to establish significant advances in research and education in the development of machine learning and real-time predictive modeling of power systems, with particular focus on the smart grid.

Machine learning and real-time predictive modeling have received increasing attention in recent years. Extensive research effort has been devoted to these topics, and novel numerical methods have been developed to efficiently deal with sensor data and complex engineering systems. Both machine learning and real-time predictive modeling enable us to better extract the useful information from available sensor data and make critical decision in real time with the presence of uncertainties. For example, solar and wind energy will depend on the weather condition. Machine learning and real-time predictive modeling are thus critical to many important practical problems such as power system stability analysis and social cyber-network prediction, etc. For large-scale power systems, deterministic simulations can be very time-consuming, and conducting predictive simulations further increases the simulation cost and can be prohibitively expensive. One of the biggest challenges in machine learning and real-time predictive modeling is how to develop hierarchical reduced-order models and how to fuse information from such hierarchical reduced-order models. This project aims to address these critical challenges. A novel set of deep-learning based multi-fidelity algorithms (deep Gaussian processes) will be developed for real-time prediction of power systems. The approach under development in this research project is based on scalable algorithms for building deep-learning based reduced-order models for efficient power system dimension reduction. The new algorithms will be based on building multi-fidelity models via deep learning for power systems, and they will significantly advance the current state of the art of deep learning and real-time predictive modeling. The project will also integrate educational opportunities and will expand the population of modelers who use machine learning and predictive modeling tools to solve network problems. The project will expose a diverse group of undergraduates and minority students to machine learning and predictive modeling.

Project Summary The spleen plays a key role in the human immune system but also clears senescent red blood cells (RBC) from the circulation and those altered by acquired or inherited diseases. In patients with sickle cell disease (SCD), the spleen is one of the first targets of pathogenic processes and a potential protector against major complications. Under hypoxic conditions, mutated sickle hemoglobin (HbS) polymerizes to fibers which increase both the stiffness and adhesion of RBC. Splenic filtration of altered RBC prone to sickling (a process that cannot be directly observed in human subjects) contributes to anemia and likely triggers acute splenic sequestration crises (ASSC). On the other hand, it potentially prevents complications associated with intravascular sickling. Self- amplified blockade of vessels with sickled RBCs is indeed a hallmark of vaso-occlusive crises, acute chest syndrome, and acute hepatic crises, that severely impact the life quality and expectancy of patients with SCD. We propose to formulate and validate a new predictive modeling framework for how the spleen filters altered RBC in SCD by synergistically integrating in silico, in vitro, ex vivo and in vivo data using multifidelity-based neural networks (NN). This will deliver predictive models that can continuously learn when new data become available, a paradigm shift in biomedical modeling. We will develop multiscale/multifidelity computational models (and corresponding NN implementations) that link sub-cellular, cellular, and vessel level phenomena spanning across four orders of magnitude in spatio-temporal scales. This scale coupling will be accomplished using a molecular dynamics/dissipative particle dynamics (MD/DPD) framework. We will validate these predictive computational models by data from in vitro and ex vivo experiments, and RBC quantitative features collected in SCD patients. Specifically, we will use three new spleen-on-a-chip microfluidic devices with oxygen control and the unique human spleen perfusion setup of our foreign partner, with the following aims: Aim 1: Develop and validate a splenic inter-endothelial slit filtration model; Aim 2: Develop new models of RBC macrophage adhesion and of phagocytosis in the spleen; Aim 3: Perform Spleen-on-a-Chip experiments and validation; Aim 4: Validate the predictive framework based on RBC samples from patients. Realization of our four Specific Aims will significantly increase our understanding of the complex pathogenic and protective roles of the spleen in SCD. Feeding our new multifidelity neural networks with morphological and functional measures of RBC circulating in SCD patients will lead to models for residual spleen function in SCD, which should help predict the risk of acute splenic sequestration crises, and guide optimal timing for Stem Cell Transplantation or Gene Therapy. The new paradigm in using deep learning tools to integrate data from different sources will be applicable to modeling many other blood diseases.