2 papers
math.NA2026
C-PINN: A neural network framework based on the Cordès condition for solving linear and fully nonlinear equations in non-divergence form and its applications
Bingcheng Hu, Lixiang Jin, Zhaoxiang Li
In this paper, we propose a novel Physics-Informed Neural Network (PINN) framework based on the Cordès condition for solving both linear and fully nonlinear partial differential e…
math.NA2025
Solving the fully nonlinear Monge-Ampère equation using the Legendre-Kolmogorov-Arnold Network method
Bingcheng Hu, Lixiang Jin, Zhaoxiang Li
In this paper, we propose a novel neural network framework, the Legendre-Kolmogorov-Arnold Network (Legendre-KAN) method, designed to solve fully nonlinear Monge-Ampère equations…