Published: Apr 10, 2026 by Daning Huang
This year, we will be organizing a 3-part minisymposia on “Modern Scientific Computational Methods for Learning Dynamical Systems” in the upcoming SIAM Annual Meeting. The event is co-organized with Dr. Maxwell Kreider and Dr. John Harlim from Penn State Math.
Abstract: Modeling dynamical systems is central to a wide range of scientific and engineering applications. Recent advances in scientific computing have shown that machine learning provides powerful new tools for uncovering the underlying dynamics from time-series data. This minisymposium focuses on recent progress in this area, with an emphasis on numerical methods and surrogate models that (1) remain stable for long-term prediction, (2) scale effectively to high-dimensional dynamical systems, and (3) exhibit robustness to noise. Topics will include, but are not limited to, reduced-order modeling, symmetry discovery, and geometry-aware approaches.
Part I, MS56, 4:00 PM - 6:00 PM, Room 7
- 4:00-4:25 Computational Advances in Weak Form Scientific Machine Learning; David M. Bortz, April Tran, Daniel Messenger, Nora Heitzman-Breen, Rainey Lyons, and Vanja Dukic, University of Colorado Boulder.
- 4:30-4:55 Generalized Moving Least-Squares Methods for Solving Vector-Valued PDEs on Unknown Manifolds; Rongji Li, ShanghaiTech University; Qile Yan, University of Minnesota.; Shixiao Jiang, ShanghaiTech University.
- 5:00-5:25 Generative Artificial Intelligence Methods for Particle-Based Kinetic Computations in Bounded Domains; Minglei Yang, Oak Ridge National Laboratory; Yanfang Liu, Middle Tennessee State University; Guannan Zhang, Oak Ridge National Laboratory; Diego del Castillo Negrete, University of Texas at Austin; Yanzhao Cao, Auburn University.
- 5:30-5:55 Resolvent compactification methods for spectral approximation of Koopman operators; Trevor Camper and Dimitrios Giannakis, Dartmouth College.
Part II, MS71, 8:00 AM - 10:00 AM, Room 7
- 8:00-8:25 From Single to Multiple Kernels: Learning Interacting Particle Systems on Networks; Quanjun Lang, Duke University.; Xiong Wang, Fei Lu, and Mauro Maggioni, Johns Hopkins University.
- 8:30-8:55 TBD.
- 9:00-9:25 A Model-Free Method for Discovering Symmetry in Differential Equations; Max Kreider, John Harlim, and Daning Huang, Pennsylvania State University.
- 9:30-9:55 Learning Solution Operator of Dynamical Systems with Diffusion Maps Kernel Ridge Regression; Jiwoo Song, Daning Huang, and John Harlim, Pennsylvania State University.
Part III, MS87, 4:00 PM - 6:00 PM, Room 7
- 4:00-4:25 Data-Driven Modeling of Transition Dynamics for 2D Wall-Bounded Turbulence; Xuping Xie, Old Dominion University.
- 4:30-4:55 Blending Data and Physics for Reduced-Order Modeling of Systems with Complex Dynamics; Mike Graham, University of Wisconsin-Madison.; Alex Guo, Los Alamos National Laboratory.
- 5:00-5:25 Adaptive Reduced-Order Models with Online Learning for Subspace and Operator Updates; Amirpasha Kamalhedayat and Karthik Duraisamy, University of Michigan.
- 5:30-5:55 Zero-Shot Size Transfer of Graph Neural Differential Equations for Learning Graph Diffusion Dynamics; Charle Kulick, Sui Tang, and Mingsong Yan, University of California, Santa Barbara.