5 papers
Learning Optimal Robust-Pathwise Control of Elliptic Equations with Random Coefficients
Qi Sun, Yanhan Cui, Ling Guo +1
Conventional control approaches to optimization problems under uncertainty entail a practical compromise: deterministic controls offer robustness at the expense of pathwise accurac…
Parallel-in-Time Solution of Allen-Cahn Equations by Integrating Operator Learning into the Parareal Method
Yuwei Geng, Junqi Yin, Eric C. Cyr +2
While recent advances in deep learning have shown promising efficiency gains in solving time-dependent partial differential equations (PDEs), matching the accuracy of conventional…
Learning Singularity-Encoded Green's Functions with Application to Iterative Methods
Qi Sun, Shengyan Li, Bowen Zheng +2
Green's function provides an inherent connection between theoretical analysis and numerical methods for elliptic partial differential equations, and general absence of its closed-f…
A Score-based Diffusion Model Approach for Adaptive Learning of Stochastic Partial Differential Equation Solutions
Toan Huynh, Ruth Lopez Fajardo, Guannan Zhang +2
We propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a re…
Optimal error estimates of the diffuse domain method for parabolic equations
Wenrui Hao, Lili Ju, Yuejin Xu
In this paper, we study the convergence behavior of the diffuse domain method (DDM) for solving a class of second-order parabolic partial differential equations with Neumann bounda…