2 papers
math.NA2024
A Priori Error Estimation of Physics-Informed Neural Networks Solving Allen--Cahn and Cahn--Hilliard Equations
Guangtao Zhang, Jiani Lin, Qijia Zhai +4
Physics-Informed Neural Networks (PINNs) encounter accuracy limitations when solving the Allen--Cahn (AC) and Cahn--Hilliard (CH) partial differential equations (PDEs). To overcome…
cs.LG2023
Parameter Identification for Partial Differential Equations with Spatiotemporal Varying Coefficients
Guangtao Zhang, Yiting Duan, Guanyu Pan +3
To comprehend complex systems with multiple states, it is imperative to reveal the identity of these states by system outputs. Nevertheless, the mathematical models describing thes…