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…