3 papers
math.NA2026
Two-scale neural networks for optimal control of linear convection-dominated equations
Sijing Liu, Marcus Sarkis, Yi Zhang +1
We propose a two-scale neural network method for optimal control problems governed by convection-dominated convection-diffusion-reaction equations. Building on two-scale architectu…
stat.CO2025
Solving Fokker-Planck-Kolmogorov Equation by Distribution Self-adaptation Normalized Physics-informed Neural Networks
Yi Zhang, Yiting Duan, Xiangjun Wang +1
Stochastic dynamical systems provide essential mathematical frameworks for modeling complex real-world phenomena. The Fokker-Planck-Kolmogorov (FPK) equation governs the evolution…
stat.ML2024
Parameters Inference for Nonlinear Wave Equations with Markovian Switching
Yi Zhang, Zhikun Zhang, Xiangjun Wang
Traditional partial differential equations with constant coefficients often struggle to capture abrupt changes in real-world phenomena, leading to the development of variable coeff…