4 papers
Diffusion-Based Stochastic Operator Networks for Uncertainty Quantification in Stochastic Partial Differential Equations
Phuoc-Toan Huynh, Richard Archibald, Feng Bao
We introduce a novel framework for uncertainty quantification of solution operators associated with stochastic partial differential equations (SPDEs). Although SPDEs play a central…
Finite Expression Method with TranNet-based Function Learning for High-Dimensional Partial Differential Equations
Phuoc-Toan Huynh, Feng Bao, Haizhao Yang +1
In this paper, we study a machine-learning-based solver for high-dimensional partial differential equations (PDEs). Computing accurate solutions efficiently for such problems remai…
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…
Parameter Estimation for the Reduced Fracture Model via a Direct Filter Method
Phuoc Toan Huynh, Feng Bao, Thi-Thao-Phuong Hoang
In this work, we present a numerical method that provides accurate real-time detection for the widths of the fractures in a fractured porous medium based on observational data on p…