Congratulations to the following seven members of the SIAM community who will receive awards at the virtual SIAM Conference on Computational Science and Engineering (CSE21). Additional information about each recipient, including Q&As, can be found below.
George Em Karniadakis
George Em Karniadakis is the 2021 recipient of the SIAM/ACM Prize in Computational Science and Engineering. He will present a virtual lecture at the SIAM Conference on Computational Science and Engineering titled “DeepOnet: Learning Linear, Nonlinear and Multiscale Operators Using Deep Neural Networks Based on the Universal Approximation Theorem of Operators” on Friday, March 5, 2021 at 12:45 p.m. CST.
The prize is awarded to Karniadakis for advancing spectral elements, reduced-order modeling, uncertainty quantification, dissipative particle dynamics, fractional PDEs, and scientific machine learning, while pushing applications to extreme computational scales and mentoring many leaders. SIAM and the Association for Computing Machinery (ACM) jointly awards the SIAM/ACM Prize in Computational Science and Engineering every two years at the SIAM Conference on Computational Science and Engineering for outstanding contributions to the development and use of mathematical and computational tools and methods for the solution of science and engineering problems.
Native to Crete, Dr. Karniadakis is both a SIAM Fellow and The Charles Pitts Robinson and John Palmer Barstow Professor of Applied Mathematics and Engineering at Brown University. He received his SM and PhD from Massachusetts Institute of Technology (1984/87) where he was appointed Lecturer in the Department of Mechanical Engineering and subsequently joined the Center for Turbulence Research at Stanford / Nasa Ames. He joined Princeton University as Assistant Professor in the Department of Mechanical and Aerospace Engineering and as Associate Faculty in the Program of Applied and Computational Mathematics. He was a Visiting Professor at Caltech in 1993 in the Aeronautics Department and joined Brown University as Associate Professor of Applied Mathematics in the Center for Fluid Mechanics in 1994. His h-index is 105 and he has been cited over 53,500 times.
Q: Why are you excited to receive the SIAM/ACM CSE Prize?
A: For the last 30 years, I have been developing methods for real-life applications because I am interested to see how engineers and physicists can use them to solve hard multiscale and multiphysics and not what we call “academic” problems. This award is very meaningful to me because it confirms that the work I have been doing with my many students and postdocs has had some impact on the CSE community. It complements the Ralph Kleinman prize that I received by SIAM in 2015 for my work on bridging the gap between mathematics and applications.
Q: Could you tell us a bit about the research that won you the prize?
A: The selection committee stated that they wish to recognize my work “on advancing spectral elements, reduced-order modeling, uncertainty quantification, dissipative particle dynamics, fractional PDEs, and scientific machine learning, while pushing applications to extreme computational scales and mentoring many leaders.” These areas represent different stages in my career almost chronologically in the aforementioned list and target different types of applications across different disciplines. For example, my work on uncertainty quantification targeted nonlinear problems with non-Gaussian distributions using generalized polynomial chaos and variants, and it was followed up by many research groups, including many DOE labs that established new institutes on this topic. Of course, I should mention that after my former student Professor Dongbin Xiu organized many sessions on this topic in the annual SIAM conference, SIAM realized the need for a separate conference so now we have a SIAM Uncertainty Quantification Conference every two years. Similarly, for modeling materials in the mesoscopic regime, we developed several dissipative dynamics algorithms and introduced the Mori-Zwanzig rigorous formulation to analyze such methods. Currently, the physics-informed learning paradigm that my group has introduced is changing the way the CSE community, including big companies like Nvidia and Ansys, are doing simulations, and this is very exciting.
Q: What does your work mean to the public?
A: I believe that the work of my group has had broader impact in educating a new cadre of simulation scientists with new tools such as uncertainty quantification and physics-informed neural networks. My work on computational biomedicine on modeling blood diseases, especially sickle-cell anemia (which was featured by Siam News twice) has had considerable impact among clinicians, and a couple of years ago I was invited to present my work at NIH in a conference for medical doctors and patient groups supporting new research on this disease – this was very rewarding!
Q: What does being a SIAM member mean to you?
A: I am a SIAM Fellow (Class of 2010), and I am currently associate editor in three SIAM Journals, including the SIREV Education section. It is great to be part of this community that has grown so much around the world, and I travelled to other countries to promote the SIAM mission, e.g., I was in Korea for the 22 KSIAM in 2019 and it was a great experience. I support the educational initiatives of SIAM and I am looking forward to contributing in the next few years towards diversity and inclusion and supporting applied math research at HBCUs and MSIs. I have started working closely with UTEP and this is a very rewarding experience, so I encourage all my former students and other colleagues to get more involved with this great cause in the next few years to make sure that the field is leveled.
Stefan Güttel
Stefan Güttel, University of Manchester, is the 2021 recipient of the James H. Wilkinson Prize for Numerical Analysis and Scientific Computing. He will present a virtual lecture at the SIAM Conference on Computational Science and Engineering titled “Rational Krylov: A Toolkit for Scientific Computing” on Thursday, March 4, 2021 at 11:30 a.m. CST.
The prize is awarded to Güttel for his contributions to the analysis, implementation, and application of rational and block Krylov methods.
The James H. Wilkinson Prize for Numerical Analysis and Scientific Computing is awarded every four years to one individual for research in, or other contributions to, numerical analysis and scientific computing during the six years preceding the award year. The purpose of the prize is to stimulate early career contributors and to help them in their careers. Candidates must have no more than 12 years (full time equivalent) of involvement in mathematics since receiving their PhD at the award date, allowing for breaks in continuity.
Güttel is currently a Reader in Numerical Analysis at the University of Manchester (UK). He obtained his PhD in Applied Mathematics in 2010 at TU Bergakademie Freiberg (Germany). His main research interests are in the field of computational mathematics, in the numerical analysis of algorithms for high-dimensional linear algebra problems, and in approximation theory.
Q: Why are you excited to receive the SIAM James H. Wilkinson Prize?
A: I am proud to be awarded the 2021 SIAM James H. Wilkinson Prize in Numerical Analysis and Scientific Computing and honoured to join such a distinguished and accomplished group of recipients.
Q: Could you tell us a bit about the research that won you the prize?
A: Rational Krylov methods are applicable to many computational kernels in numerical analysis and scientific computing such as (nonlinear) eigenvalue problems, exponential integrators, and model order reduction. I am interested in the fundamentals that make these methods work and in developing them further. I have also been interested in new applications of these methods and their implementation in numerical software.
Q: What does your work mean to the public?
A: Numerical analysis is concerned with the study of algorithms that use numerical approximation to solve problems in mathematical analysis. As such, the work of the numerical analysis community naturally finds applications in engineering and physical sciences. Although our work is often hidden in numerical libraries, it is fundamental to the most relevant numerical computations affecting our lives, ranging from climate modelling to simulating the spread of viruses.
Q: What does being a SIAM member mean to you?
A: I have been a SIAM member for many years now and I am particularly grateful that SIAM has sponsored several travel awards for PhD students in our department, including four awards to my own students in the last five years. SIAM's conferences and journals are certainly among the most professional and relevant in my field. I also appreciate the many opportunities for members to get involved in SIAM though committees, local sections, and the many student chapters.
Paris Perdikaris
Paris Perdikaris, University of Pennsylvania, is the 2021 recipient of the SIAM Activity Group on Computational Science and Engineering Early Career Prize. He will present a virtual lecture at SIAM Conference on Computational Science and Engineering titled “Bridging Physical Models and Observational Data with Physics-Informed Deep Learning” on Friday, March 5, 2021 at 12:15 p.m. CST.
The prize is awarded to Perdikaris for his work on machine learning using Gaussian processes and neural networks, which has set the foundation for a new paradigm in data-driven and physics-informed scientific computing.
The SIAM Activity Group on Computational Science and Engineering (SIAG/CSE) awards the SIAG/CSE Early Career Prize every two years to a post-PhD early career researcher in the field of computational science and engineering for outstanding, influential, and potentially long-lasting contributions to the field within seven years of receiving the PhD or equivalent degree as of January 1 of the award year.
Perdikaris is an Assistant Professor in the Department of Mechanical Engineering and Applied Mechanics at the University of Pennsylvania. He received his PhD in Applied Mathematics at Brown University in 2015, and, prior to joining Penn in 2018, he was a postdoctoral researcher at the department of Mechanical Engineering at the Massachusetts Institute of Technology working on physics-informed machine learning and design optimization under uncertainty. His work spans a wide range of areas in computational science and engineering, with a focus on the analysis and design of complex physical and biological systems using machine learning, stochastic modeling, computational mechanics, and high-performance computing. Current research thrusts include physics-informed machine learning, uncertainty quantification in deep learning, engineering design optimization, and data-driven non-invasive medical diagnostics. His work and service has received several distinctions including the DOE Early Career Award (2018), the AFOSR Young Investigator Award (2019), and the Ford Motor Company Award for Faculty Advising (2020).
The prize is awarded to Perdikaris for his work on machine learning using Gaussian processes and neural networks, which has set the foundation for a new paradigm in data-driven and physics-informed scientific computing.
Q: Why are you excited to receive the SIAG/CSE Early Career Prize?
A: I am truly humbled and thrilled to be selected for the SIAG/CSE Early Career Prize! I have been extremely lucky to work with brilliant mentors, students and collaborators, and I am very happy to see that our work is being recognized by the SIAM community.
Q: Could you tell us a bit about the research that won you the prize?
A: Our work aspires to create computational methods that can seamlessly integrate observational data and mathematical physics models, even in partially understood, uncertain and high-dimensional contexts. The leading motivation here is that such prior knowledge/constraints can yield more interpretable machine learning methods that remain robust in the presence of imperfect data (e.g., missing or noisy values, outliers, etc.), and can provide accurate and physically consistent predictions, even for extrapolation tasks. Ultimately, we are pushing towards creating robust and interpretable data-driven methods that can serve as a bridge for connecting computational and experimental science, opening new paths to tackling the challenging multi-disciplinary problems we face in practice.
Q: What does your work mean to the public?
A: Thanks to the rapid development of sensor networks we are now able to exploit wealth of variable fidelity observations using data-driven methods. However, our growing ability to collect and create observational data far outpaces our ability to sensibly assimilate it, let alone understand it. To this end, our work aims to leverage fundamental physical laws and domain knowledge to "teach" machine learning models about governing physical rules, with the goal of enhancing our ability to interpret and expediently predict the behavior of complex systems across diverse disciplines and applications, from climate modeling and geophysics, to materials characterization, fluid dynamics and biophysics.
Q: What does being a SIAM member mean to you?
A: SIAM provides a unique ecosystem for promoting collaborative and interdisciplinary research that has been pivotal in helping me grow as a scientist. I have been attending SIAM conferences since my early years in grad school, and the SIAM Journals have been a key enabling resource in my work. I've always been fascinated by how mathematical modeling and computing can bridge scientific disciplines to help us solve important problems in science and engineering, and SIAM has been the backbone for creating a vibrant community for us to interact and share our work.
Ventakaramanan Balakrishnan, Stephen Cauley, James Vogel, and Jianlin Xia
Ventakaramanan Balakrishnan, Purdue University, Stephen Cauley, Massachusetts General Hospital, James Vogel, Purdue University, and Jianlin Xia, Purdue University, are the recipients of the 2021 SIAM Activity Group on Computational Science and Engineering Best Paper Prize. A virtual lecture will be given at the SIAM Conference on Computational Science and Engineering titled “Superfast Divide-and-Conquer Hermitian Eigenvalue Solutions” on Wednesday March 3, 2021 at 11:30 a.m. CST.
The prize is awarded to Balakrishnan, Cauley, Vogel, and Xia for their impressive work which reduces the computational complexity of a whole eigendecomposition of Hermitian matrices from cubic to loglinear by utilizing the hierarchical semi-separable structure.
Established in 2018, the SIAM Activity Group on Computational Science and Engineering Best Paper Prize is awarded every two years to the authors of the best paper, as determined by the selection committee, on the development and use of mathematical and computational tools and methods for solving problems that may arise in broad areas of science, engineering, technology, and society. The prize recognizes a paper that makes an outstanding and potentially long-lasting contribution to the field.
Balakrishnan is the Charles H. Phipps Dean of the Case School of Engineering at Case Western Reserve University, where he is also a professor in the Department of Electrical, Computer & Systems Engineering. Prior to joining the Case School of Engineering, he was the Michael and Katherine Birck Head of the School of Electrical and Computer Engineering at Purdue University. Balakrishnan received his PhD degree in electrical engineering from Stanford University in 1992. His research interests are primarily in the areas of control, and the application of convex optimization to problems from systems, control, robotics, communication and signal processing. He is a Fellow of IEEE and serves as an elected member of the IEEE Control Systems Society Board of Governors for 2019-21.
Cauley is an Assistant Professor in Radiology at Harvard Medical School and Assistant in Biomedical Engineering at Massachusetts General Hospital. He received his PhD at Purdue University. His research interests lie in the development of high-performance computing techniques for MRI applications. His current work focuses on the optimization of data acquisition and image reconstruction methodologies for high patient throughput imaging.
Vogel is a Senior Scientist at Systems & Technology Research in Boston. He received an undergraduate degree in mathematics and physics from the University of Michigan and a PhD in applied mathematics from Purdue University. His research interests include numerical linear algebra, optimization, and computational physics. He enjoys finding new areas of computational science and engineering where structured matrices and other tools from linear algebra can be applied to speed up and stabilize difficult problems.
Xia is a professor in the Department of Mathematics at Purdue University, with a courtesy appointment in the Department of Computer Science. He received his PhD in Applied Mathematics at UC Berkeley. His research interests lie in numerical linear algebra and numerical analysis. The current focus of his work is on structured matrices, fast solvers, randomized methods, and their connections to broader numerical problems. He was named a University Faculty Scholar in 2018 and received an NSF CAREER Award in 2013. He currently serves on the editorial boards of multiple numerical analysis journals.
Q: Why are you excited to receive the SIAG/CSE Best Paper Prize?
A: We are greatly honored that our work has been chosen for the SIAG/CSE Best Paper Prize. It means a lot to the fields of structured matrices and fast solvers, where decades of exciting research is what our work in this paper has been built on.
Q: Could you tell us a bit about the research that won you the prize?
A: For a large class of dense Hermitian matrices that have small off-diagonal (numerical) ranks and are represented by hierarchically semiseparable forms, the paper develops an eigensolver that reduces the complexity of full eigenvalue decompositions from cubic to nearly linear in the matrix size. The eigensolver uses a divide-and-conquer approach and further avoids the need of tridiagonal reductions. Some of the key ideas include a structure-preserving strategy to hierarchically break the eigendecomposition into smaller structured eigendecompositions plus low-rank updates, assembling data and structuring computations in sequences of nested eigendecomposition updates, and maintaining structures with nearly linear overall data amount throughout all the steps despite the output being a full matrix eigendecomposition. The resulting eigenvectors form a structured matrix that can be quickly applied to vectors. The work provides an efficient and reliable way to find full eigendecompositions of problems such as Hermitian banded matrices, Hermitian Toeplitz matrices, various kernel matrices, and many discretized problems.
Q: What does your work mean to the public?
A: Hermitian matrices with small off-diagonal ranks or numerical ranks appear frequently in mathematical computations and engineering simulations. Their eigenvalue decompositions provide a powerful tool for numerical tasks such as PDE solutions, polynomial computations, imaging, signal processing, physics modeling, statistics, and data analysis. However, the full eigendecompositions have typically been considered impractical due to the quadratic data amount and cubic computational complexity. Our work effectively reduces both the data storage and the complexity to around linear in the problem size, making full eigendecompositions very viable. The work also provides an intuitive model for researchers to rethink large matrix computations by discovering underlying structures.
Q: What does being a SIAM member mean to you?
A: Being a SIAM member means getting involved in an organization that cares deeply about the future of applied mathematics and the applications of computations and also means staying connected to the world's leading applied mathematicians and computational scientists. SIAM not only helps promote its members' research excellence but also especially provides valuable opportunities to its early-career members to grow professionally and deepen their love of mathematics. Vogel, a recent graduate, recalls some of his favorite memories of graduate school at Purdue University being in serving as vice president of Purdue's SIAM student chapter where he got to plan local student research workshops, travel to SIAM conferences, and make lots of friends in the community whom he might otherwise have never met if not for being connected through SIAM.