3 papers
stat.CO2025
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…
cs.LG2025
Stochastic Operator Network: A Stochastic Maximum Principle Based Approach to Operator Learning
Ryan Bausback, Jingqiao Tang, Lu Lu +2
We develop a novel framework for uncertainty quantification in operator learning, the Stochastic Operator Network (SON). SON combines the stochastic optimal control concepts of the…
math.NA2025
Joint State-Parameter Estimation for the Reduced Fracture Model via the United Filter
Toan Huynh, Thi-Thao-Phuong Hoang, Guannan Zhang +1
In this paper, we introduce an effective United Filter method for jointly estimating the solution state and physical parameters in flow and transport problems within fractured poro…