22 papers
Dimension-Free Convergence of Discrete Diffusion Models: Adjoint Equations Induce the Right Space
Kelvin Kan, Xingjian Li, Benjamin J. Zhang +3
Discrete diffusion has become a leading framework for generative modeling in various applications including language, vision, and biology. Existing convergence theory, however, exh…
A Natural Primal-Dual Hybrid Gradient Method for Adversarial Neural Network Training on Solving Partial Differential Equations
Shu Liu, Stanley Osher, Wuchen Li
We propose a scalable preconditioned primal-dual hybrid gradient algorithm for solving partial differential equations (PDEs). We multiply the PDE with a dual test function to obtai…
Preconditioned Regularized Wasserstein Proximal Sampling
Hong Ye Tan, Stanley Osher, Wuchen Li
We consider sampling from a Gibbs distribution by evolving finitely many particles. We propose a preconditioned version of a recently proposed noise-free sampling method, governed…
Zero-Shot Transferable Solution Method for Parametric Optimal Control Problems
Xingjian Li, Kelvin Kan, Deepanshu Verma +3
This paper presents a transferable solution method for optimal control problems with varying objectives using function encoder (FE) policies. Traditional optimization-based approac…
Scalable Fixed-Point Framework for High-Dimensional Hamilton-Jacobi Equations
Yesom Park, Stanley Osher
We propose a novel, mesh-free, and gradient-free fixed-point approach for computing viscosity solutions of high-dimensional Hamilton-Jacobi (HJ) equations. By leveraging the Hopf-L…
SymPlex: A Structure-Aware Transformer for Symbolic PDE Solving
Yesom Park, Annie C. Lu, Shao-Ching Huang +3
We propose SymPlex, a reinforcement learning framework for discovering analytical symbolic solutions to partial differential equations (PDEs) without access to ground-truth express…