Speaker: Yiwei Wang, University of California, Riverside

Title: Energetic Variational Neural Network Discretizations for Variational Models

Abstract: Many problems in physics, materials science, biology, and machine learning can be formulated as variational models, where multiscale coupling and competition are encoded through an energy–dissipation law. Preserving structures of variational models at the discrete level is crucial for accuracy and robustness, especially in long-time simulations. In this talk, I will present an energetic-variational, structure-preserving discretization framework for variational models. The key idea is to design algorithms based on the energy–dissipation law, rather than on strong- or weak-form PDE discretizations. Within this framework, we develop a memory-efficient, mesh-free neural-network discretization for gradient flows using a temporal-then-spatial discretization approach. As a representative example, we discuss a neural-network-based Lagrangian method for generalized diffusions (Wasserstein-type gradient flows), which yields an efficient Lagrangian implementation of the celebrated Jordan–Kinderlehrer–Otto (JKO) scheme.

A short bio: Prof. Yiwei Wang is an Assistant Professor in the Department of Mathematics at the University of California, Riverside. Prior to joining UCR, he was a postdoctoral researcher at the Illinois Institute of Technology, where he worked with Prof. Chun Liu. He received his Ph.D. from Peking University and earned his B.S. from Zhejiang University. His research lies at the intersection of variational modeling, scientific computing, and machine learning, with applications spanning physics, materials science, biology, and data science. He focuses on the development of multiscale, thermodynamically consistent variational models and structure-preserving numerical methods for complex dissipative systems, including liquid crystals, polymeric fluids, reaction-diffusion processes, and biological systems. More recently, his work explores the integration of machine learning with variational modeling and computation, including learning unknown dynamics, constructing coarse-grained closures, improving numerical methods, solving high-dimensional PDEs, and investigating variational perspectives on machine learning through energy-dissipation principles and structure-preserving algorithm design.