Yeonhyang Kim (kim4y AT cmich DOT edu)
Leela Rakesh (leela.rakesh AT cmich DOT edu)
Xiaoming Zheng (zheng1x AT cmich DOT edu)
If you would like to give a talk, please email any one of us. Fridays without prior reservations are open for talks throughout the CMU academic year.
Fridays, 2:00pm – 3:00pm, on Webex or Perce Hall 223
|
Date |
Speaker |
Title |
| 10/9/2026, 1-2pm |
Zhiliang Xu (University of Notre Dame) | ENERGETIC VARIATIONAL NEURAL NETWORK DISCRETIZATIONS OF GRADIENT FLOWS |
| TBA |
TBA | TBA |
Speaker: Zhiliang Xu
Title: ENERGETIC VARIATIONAL NEURAL NETWORK DISCRETIZATIONS OF GRADIENT FLOWS
Abstract: In this talk, I will describe structure-preserving neural-network-based numerical schemes to solve both L2-gradient flows and generalized diffusions. By leveraging neural networks as tools for spatial discretization, we introduce a structure-preserving Eulerian algorithm to solve L2-gradient flows and a structure-preserving Lagrangian algorithm to solve generalized diffusions. The Lagrangian algorithm for a generalized diffusion evolves the “flow map" which determines the dynamics of the system. This avoids the non-trivial task of computing the Wasserstein distance between two probability functions. Unlike most existing methods that construct numerical discretizations based on the strong or weak form of the underlying PDE, our schemes are constructed using variational formulations of these PDEs for preserving their variational structures. Instead of directly solving the obtained nonlinear systems after temporal and spatial discretization, the minimizing movement scheme is utilized to evolve the solutions. This guarantees the monotonic decay of the energy of the system, and is crucial for the long-term stability of numerical computation. I will describe a few numerical experiments to demonstrate the accuracy and energy stability of the numerical schemes and some recent developments.
Speaker: TBA
Title:
Abstract: