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math.NA2025
Integral regularization PINNs for evolution equations
Xiaodong Feng, Haojiong Shangguan, Tao Tang +1
Evolution equations, including both ordinary differential equations (ODEs) and partial differential equations (PDEs), play a pivotal role in modeling dynamic systems. However, achi…
math.NA2024
A hybrid FEM-PINN method for time-dependent partial differential equations
Xiaodong Feng, Haojiong Shangguan, Tao Tang +2
In this work, we present a hybrid numerical method for solving evolution partial differential equations (PDEs) by merging the time finite element method with deep neural networks.…