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, Georgia Institute of Technology

 

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Math Methods Asia-USA Seminar Series

TBA

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Past Math Methods Asia-USA Seminar Series

Main organizer: Gianmarco Mengaldo, National University of Singapore

Spring 2026

April 6, 2026

VIDEO

Speaker: Dr. WaiChing Sun, Columbia University

Title: Geometry-Informed Neural Atlas for Boundary Value Problems of 3D Geometries

Abstract: When three-dimensional bodies contain thin features, non-trivial topology, or scan-derived surfaces, volumetric meshing can become the dominant bottleneck in simulation workflows. We replace this step with a learned geometric representation: overlapping volumetric coordinate charts, each equipped with a neural decoder and Jacobian, trained from point-cloud or level-set data to form a differentiable atlas. Governing equations are pulled back to chart-local reference coordinates via the Piola identity, and local solutions are coupled through multiplicative Schwarz iterations on the overlap graph. Because the atlas is constructed independently of the downstream discretization, one frozen geometric substrate can support fundamentally different solvers (for example, a meshfree physics-informed neural network and a conventional finite-element method) without re-meshing or re-parametrization. Benchmark and verification studies show that the learned atlas preserves expected finite-element convergence behavior and enables both forward and inverse analyses on geometries that would otherwise require solver-specific volumetric meshing.

Bio: Dr. Steve Sun is currently an associate professor of civil engineering and engineering mechanics at Columbia University. He received his PhD from Northwestern in 2011. From 2011 to 2013, He worked as a research engineer at Sandia National Laboratories. Sun’s research focuses on computational mechanics and scientific machine learning for material modeling. He received several awards, including the Walter Huber Prize and the da Vinci Award from ASCE, the John Argyris Award from IACM, and the CAREER award from NSF, the Army, and the Air Force. Since April 1st, 2025, he has become an editor of the International Journal for Numerical Methods in Engineering.

Speaker: Dr. Wentao Yan, National University of Singapore 

Title: High-Fidelity Multi-Physics Modeling of Additive Manufacturing: Process, Microstructure, and Property

Abstract: The wide applications of additive manufacturing are hindered by the lack of comprehensive understanding of process-structure-property relationships. To this end, we have developed and seamlessly integrated a series of high-fidelity multi-physics models. Specifically, multiphase flow models using the coupled computational fluid dynamics and discrete element method simulate the powder spreading procedure and powder spattering and denudation phenomena in the powder melting procedure. The powder melting model is powerful to reproduce the molten pool flow and relevant defects (e.g., lack-of-fusion and keyhole pores) by incorporating the major physical factors, e.g., the composition-dependent evaporation and physically-informed heat source models. The microstructure evolutions at both the grain- and dendrite- scales are modelled using the phase field and cellular automaton methods. The mechanical properties and thermal stresses are simulated using the crystal plasticity finite element model, which incorporates the realistic geometry (rough surfaces and voids), temperature profiles and microstructures. These models have proven powerful in revealing the physical mechanisms and optimizing the manufacturing processes, which have been well validated against various experiments, particularly in-situ observations.

Bio: Dr. Wentao Yan is an associate professor in the Department of Mechanical Engineering, National University of Singapore (NUS). Before joining NUS in 2018, Dr. Yan was a postdoctoral fellow at Northwestern University in the USA. He received his Ph.D. degree jointly at Tsinghua University, Beijing and Northwestern University, USA, in 2017. He got his Bachelor degree from the Department of Mechanical Engineering, Tsinghua University, Beijing in 2012. Supported by multi-million grants, his research group focuses on multi-scale multi-physics modeling, experimental investigation and data analysis of additive manufacturing. ~30 of his former postdocs and PhD students have got faculty positions. He has published >150 papers on flagship journals, such as Nature Communications, Acta Materialia, JMPS and CMAME, which have received ~10,000 citations. His team was the biggest winner in the 2022 NIST AM-Bench Simulation Challenges by winning 9 awards in the total 25 tests (totally 40 awards were presented). He has won multiple best paper awards in various journals. He currently serves as the Senior Editor for Additive Manufacturing Journal and an editorial board member for IJMTM and Materials & Design.

March 2, 2026

VIDEO

Speaker: Dr. George Em Karniadakis, Brown University

Title: Agentic Scientific Machine Learning

Abstract: Scientific Machine Learning (SciML) integrates data-driven inference with physical modeling to solve complex problems in science and engineering. However, the design of SciML architectures, loss formulations, and training strategies remains an expert-driven research process, requiring extensive experimentation and problem-specific insights. We introduce AgenticSciML, a collaborative multi-agent system in which over 10 specialized AI agents collaborate to propose, critique, and refine SciML solutions through structured reasoning and iterative evolution. The framework integrates structured debate, retrieval-augmented method memory, and ensemble-guided evolutionary search, enabling the agents to generate and assess new hypotheses about architectures and optimization procedures. Across physics-informed learning and operator learning tasks, the framework discovers solution methods that outperform single-agent and human-designed baselines by up to four orders of magnitude in error reduction. The agents produce novel strategies -- including adaptive mixture-of-expert architectures, decomposition-based PINNs, and physics-informed operator learning models -- that do not appear explicitly in the curated knowledge base. These results show that collaborative reasoning among AI agents can yield emergent methodological innovation, suggesting a path toward scalable, transparent, and autonomous discovery in scientific computing.

Bio: George Karniadakis is from Crete. He is an elected member of the National Academy of Engineering, National Academy of Arts and Sciences, and a Vannevar Bush Faculty Fellow. He received his S.M. and Ph.D. from Massachusetts Institute of Technology (1984/87). He was appointed Lecturer in the Department of Mechanical Engineering at MIT and subsequently he 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. After becoming a full professor in 1996, he continued to be a Visiting Professor and Senior Lecturer of Ocean/Mechanical Engineering at MIT. He is an AAAS Fellow (2018-), Fellow of the Society for Industrial and Applied Mathematics (SIAM, 2010-), Fellow of the American Physical Society (APS, 2004-), Fellow of the American Society of Mechanical Engineers (ASME, 2003-) and Associate Fellow of the American Institute of Aeronautics and Astronautics (AIAA, 2006-). He received the William Benter Prize (2026), SES G.I. Taylor medal (2014), the SIAM/ACM Prize on Computational Science & Engineering (2021), the Alexander von Humboldt award in 2017, the SIAM Ralf E Kleinman award (2015), the J. Tinsley Oden Medal (2013), and the CFD award (2007) by the US Association in Computational Mechanics. His h-index is 160 (highest in Applied Mathematics) and he has been cited over 157,000 times.

Speaker: Dr. Dixia Fan, Westlake University

Title: Dive into the Deep Blue: My Humble Vision for Future Intelligent Bio-inspired Underwater Robots

Abstract: Biomimetics leverages insights from biological systems to create innovative engineering solutions, a paradigm especially compelling in ocean science where life itself originated. Marine organisms have evolved extraordinary efficiency and agility in environments that challenge human-made vehicles, which typically suffer from high drag and limited maneuverability. This talk explores how inspiration from sea turtles, rainbow trout, and other species can inform next-generation underwater robotics. I will present recent advances using deep reinforcement learning to achieve efficient flapping propulsion and agile surface-skimming maneuvers, and highlight the successful 2000 m sea trials of the Sea Guru biomimetic submersible. Together, these results illustrate the progress of bio-inspired technologies in ocean engineering and point toward a future of more capable and adaptive marine robots.

Bio: Dixia Fan is an Assistant Professor at Westlake University’s School of Engineering, and an awardee of the National Youth Talent Program. He earned his B.Eng. from Shanghai Jiao Tong University (2013) and his M.S. and Ph.D. from MIT (2016, 2019). He later worked at the Woods Hole Oceanographic Institution, where he established the Intelligent Hydrodynamics Laboratory and developed the world’s first intelligent towing tank, and served as Assistant Professor at Queen’s University, Canada. At Westlake, he leads the Fluid Intelligence & Informatics Laboratory, focusing on AI in fluid mechanics, amphibious bio-inspired robotics, and metamaterials for large-deformation systems. His work appears in Science Robotics, PNAS, and Journal of Fluid Mechanics.

February 2, 2026

VIDEO

Speaker: Dr. Liu Yang, National University of Singapore

Title: Towards Large Scientific Learning Models with In-Context Operator Networks (ICON)

Abstract: Can we build a single large model for a wide range of scientific problems? We proposed a new framework for scientific machine learning, namely “In-Context Operator Learning” and the corresponding model “In-Context Operator Networks” (ICON). A distinguishing feature of ICON is its ability to learn operators from numerical prompts during the inference phase, without weight adjustments. A single ICON model can tackle a wide range of tasks involving different operators, since it is trained as a generalist operator learner, rather than being tuned to approximate a specific operator. This is similar to how a single Large Language Model can solve a variety of natural language processing tasks specified by the language prompt. We will show how a single ICON model (without fine-tuning) manages multiple distinct problem types, encompassing forward and inverse ODE, PDE, and mean-field control problems. Through a case study on 1D conservation laws, we will show ICON’s strong generalization capability to new PDEs, as well as its advantage compared with classic operator learning methods, e.g., Fourier neural operator (FNO). We will also show the application of ICON in 2D fluid problems, where a single model can make predictions for incompressible or compressible fluids, with different viscosity.

Bio: Dr. Yang is currently an Assistant Professor in the Department of Mathematics at National University of Singapore (NUS), awarded the NUS Presidential Young Professorship and National Science Foundation Fellowship. Before joining NUS, he was an Assistant Adjunct Professor in the Department of Mathematics at UCLA. He obtained his Ph.D. in Applied Mathematics from Brown University in 2021, and B.E. in Engineering Mechanics from Tsinghua University in 2016. He is interested in building foundation AI models for scientific challenges, including multi-physics prediction, control design, inverse problems, etc. See more details on the website: https://scaling-group.github.io/

Speaker: Dr. Baskar Ganapathysubramanian, Iowa State University

Title: INR–SBM: Direct Multiphysics Simulation on Neural Signed-Distance Geometries

Abstract: Implicit Neural Representations (INRs), particularly neural signed distance fields (Neural SDFs), offer a compact, differentiable, and resolution-independent way to encode complex geometry. However, most simulation workflows still convert these representations into explicit surfaces or volume meshes, which introduces additional approximation error and slows iteration. This talk describes a more natural algorithmic pairing: the Shifted Boundary Method (SBM) enforces boundary conditions on a grid-aligned surrogate boundary and primarily needs distance-to-boundary information, which a Neural SDF provides directly. We eliminate intermediate mesh extraction by querying the INR during analysis for inside/outside classification and distance vectors used to construct the surrogate boundary and apply SBM’s corrected boundary conditions. We also enable adaptive octree discretizations that refine near geometric features or sharp solution gradients. I will demonstrate this INR–SBM pipeline across three physics settings: elliptic PDEs (Poisson-type problems), linear elasticity on complex CAD- and data-derived geometries, and incompressible flow across complex geometries. These examples show accuracy comparable to conventional mesh-based baselines while substantially simplifying geometry handling and enabling fast design iteration. Finally, I will discuss emerging theory that links INR/SDF approximation error and regularity to PDE solution accuracy, giving principled guidance on when a learned geometry is analysis suitable. This is collaborative work with Krishnamurthy (Iowa State) and Scovazzi (Duke).

Bio: Baskar Ganapathysubramanian is the Anderlik Professor of Engineering at Iowa State University. He received his B.Tech. from IIT Madras (2003) and Ph.D. from Cornell University. He leads a curiosity-driven group working at the intersection of scientific computing, computational mechanics, and machine learning, with applications in sustainable food systems, energy, water and health. He also directs the NSF/USDA AI Institute for Resilient Agriculture (AIIRA), a multi-institutional effort advancing use-inspired AI for agricultural resilience (https://aiira.iastate.edu). He is also the founding associate director for the translational AI research center at Iowa State University (https://trac-ai.iastate.edu/).

 

Fall 2025

December 2, 2025

VIDEO

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.