USACM Technical Thrust Areas

Committee: Mathematical Methods in Computational Engineering & Sciences

Description: The Mathematical Methods in Computational Engineering & Sciences TTA advances mathematical techniques for the modeling, simulation, and analysis of complex systems in engineering and science. Researchers in this TTA focus on developing and applying theoretical concepts, numerical methods, and computational strategies to enhance the reliability, accuracy, efficiency, and scalability of computational frameworks. Topics of interest include numerical analysis, scientific computing, multiscale and multiphysics modeling, uncertainty quantification, optimization, and scientific machine learning, with broad applications in computational mechanics. By integrating innovative mathematics with practical engineering, this TTA also fosters interdisciplinary collaborations that drive the advancement of mathematical analysis as well as computational tools and methodologies.

Chair: Pablo Seleson, Oak Ridge National Laboratory
Vice-Chair: Yue Yu, Lehigh University
Members-at-Large: Guglielmo Scovazzi, Duke University
Aditya Kumar, George Institute of Technology

Math Methods Asia-USA Seminar Series

TBA

Past Math Methods Asia-USA Seminar Series

Main organizer: Gianmarco Mengaldo, National University of Singapore

December 2nd at 8:00 PM EST (New York time) / December 3rd at 9:00 AM CST (Beijing time)

Speaker: Dr. Qianxiao Li, National University of Singapore

Title: Constructing Macroscopic Dynamics Using Deep Learning

Abstract: We discuss some recent work on constructing stable and interpretable macroscopic dynamics from trajectory data using deep learning. We adopt a modelling approach: instead of generic neural networks as functional approximators, we use a model-based ansatz for the dynamics following a suitable generalisation of the classical Onsager principle for non-equilibrium systems. This allows the construction of macroscopic dynamics that are physically motivated and can be readily used for subsequent analysis and control. We discuss applications in the analysis of polymer stretching in elongational flow. Moreover, we will also discuss some algorithmic challenges associated with learning (macroscopic) dynamics for scientific applications.

Bio: Qianxiao Li is an assistant professor in the Department of Mathematics, and a principal investigator in the Institute for Functional Intelligent Materials, National University of Singapore. He graduated with a BA in mathematics from the University of Cambridge and a PhD in applied mathematics from Princeton University. His research interests include the interplay of machine learning and dynamical systems, control theory, stochastic optimisation algorithms and data-driven methods for science and engineering.

Speaker: Dr. Oliver Schmidt, University of California San Diego

Title: Data-Driven Forecasting of High-Dimensional Transient and Stationary Processes via Space-Time Projection

Abstract: In this talk, I present Space-Time Projection (STP), a data-driven forecasting method tailored for high-dimensional, transient datasets. STP builds on space-time Proper Orthogonal Decomposition (POD) to derive orthogonal modes capturing both past (hindcast) and future (forecast) dynamics. Forecasting involves projecting new observations onto these modes, exploiting their inherent spatiotemporal correlations. The method combines dimensionality reduction and time-delay embedding, requiring only the truncation rank as a tunable parameter. Hindcast performance reliably predicts short-term forecasting accuracy, setting a practical lower bound on expected errors. I illustrate STP’s effectiveness using two cases: simulations of anisotropic turbulence from supernova explosions and experimental velocity measurements of a turbulent, high-subsonic flow. In comparisons with standard Long Short-Term Memory (LSTM) neural networks and classical Dynamic Mode Decomposition (DMD), STP consistently delivers better or comparable forecasting accuracy.

Bio: Oliver Schmidt is an Associate Professor in the Department of Mechanical and Aerospace Engineering at the University of California San Diego. He earned his Ph.D. in Aeronautical Engineering from the University of Stuttgart in 2014 and subsequently held a postdoctoral position in Mechanical and Civil Engineering at the California Institute of Technology before joining UC San Diego. Schmidt’s research focuses on the simulation and data-driven modeling of complex turbulent flows. His group develops advanced tools for reduced-complexity modeling, including modal decomposition techniques, mesh-free numerical methods, and stochastic modeling approaches. These methods are applied across a range of engineering and natural systems, including aeroacoustics, aero-optics, noise control, thermal management, and design optimization. He is a recipient of the NSF CAREER award and was recently named one of ASME’s Rising Stars of Mechanical Engineering.

November 4, 2025

VIDEO

Speaker: Dr. Lin Fu, Hong Kong University of Science and Technology

Title: Physics and modeling of hypersonic wall-bounded turbulent flows

Abstract: In this work, we will report our progress in understanding and modeling of hypersonic wall-bounded turbulence. Particular attention will be given to the scalings of mean velocity, temperature and skin friction coefficient, as well as the advanced wall-modeled large-eddy simulation (WMLES) framework. We will show how the new wall models substantially improve the prediction accuracy of classical ones when coupled with the novel high-order numerical methods (e.g., the high-order TENO schemes).

Bio: Prof. Fu is an Assistant professor in the Department of Mechanical and Aerospace Engineering and the Department of Mathematics at the Hong Kong University of Science and Technology (HKUST). Before he joined HKUST, he was a postdoctoral fellow working with Prof. Parviz Moin at Center for Turbulence Research (CTR), Stanford University, for more than 3 years and he also did postdoctoral research with Prof. Nikolaus A. Adams in Technical University of Munich (TUM), where he obtained his Ph.D. degree with a grade of Summa Cum Laude (passed with the highest distinction). He was recognized with the Early Career Award by the Research Grants Council (RGC) of Hong Kong in 2022 and the National Natural Science Fund for Excellent Young Scientists by NSFC in 2024 (国家优秀青年科学基金). He was elected to receive the 19th Youth Science and Technology Award of The Chinese Society of Theoretical and Applied Mechanics (CSTAM) in 2025. He is the Editorial Board Member (Early Career member) of Physical Review Fluids (PRF) and the Associate Editor of Advances in Applied Mathematics and Mechanics (AAMM). He has published around 100 papers in prestigious international journals, including PNAS, JFM, PRF, JCP, CMAME, etc.

Speaker: Dr. Romit Maulik, Pennsylvania State University

Title: Differentiable Physics: A physics-constrained and data-driven paradigm for scientific machine learning

Abstract: Machine learning stands poised to revolutionize the process of scientific discovery across various disciplines. In this talk, we will introduce a state-of-the-art scientific machine learning paradigm - differentiable physics (DiffPhys). DiffPhys can be considered a system identification paradigm that can be applied to determine neural network approximations of governing laws given data. It can also be used to improve first-principles-based simulations of physical phenomena by learning corrections to governing laws (for instance for closure modeling in multiscale applications). Notably, optimizing these neural networks necessitates a differentiable programming paradigm where gradients of a loss function can be propagated through a numerical solver. In this talk, we will introduce DiffPhys algorithms that (1) can learn models for dynamical systems from sparse data, (2) efficiently compute sensitivities for systems exhibiting deterministic chaos, and (3) provide physically meaningful interpretations for neural network behavior thereby engendering scientific discovery. We will demonstrate the capabilities of DiffPhys on canonical and realistic scientific computing problems and close with a discussion of the future possibilities of this approach.

Bio: Romit Maulik is an Assistant Professor in the College of Information Sciences and Technology at Pennsylvania State University (Penn State). He is also a co-hire in the Institute for Computational and Data Sciences at Penn State and a Joint Appointment Faculty at Argonne National Laboratory. He obtained his PhD in Mechanical and Aerospace Engineering at Oklahoma State University (in 2019) and was the Margaret Butler Postdoctoral Fellow (from 2019-2021) before becoming an Assistant Computational Scientist at Argonne National Laboratory (from 2021-2023). His group studies high-performance multifidelity scientific machine learning algorithm development with applications to various multiphysical nonlinear dynamical systems such as those that arise in fluid dynamics, geophysical modeling, nuclear fusion, and beyond. He is an Early Career Awardee of the Army Research Office.