5 papers
A Score Filter Enhanced Data Assimilation Framework for Data-Driven Dynamical Systems
Jingqiao Tang, Ryan Bausback, Feng Bao +2
We introduce a score-filter-enhanced data assimilation framework designed to reduce predictive uncertainty in machine learning (ML) models for data-driven dynamical system forecast…
Maximum Principles for Partially Observed Controls of Forward SPDEs and Backward SDEs with Jumps
Hongjiang Qian, George Yin, Yanzhao Cao +1
This work establishes two versions of the Pontryagin-type maximum principles for partially observed optimal control of coupled forward stochastic partial differential equations (FS…
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…
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…
An End-to-End Deep Learning Method for Solving Nonlocal Allen-Cahn and Cahn-Hilliard Phase-Field Models
Yuwei Geng, Olena Burkovska, Lili Ju +2
We propose an efficient end-to-end deep learning method for solving nonlocal Allen-Cahn (AC) and Cahn-Hilliard (CH) phase-field models. One motivation for this effort emanates from…