4 papers
TensorSpectra: Bridging the Spectral and Tensor Worlds for High-Dimensional PDEs
Bingcheng Hu, Tianchi Yu, Zhaoxiang Li +1
High-dimensional partial differential equations (PDEs) remain challenging for spectral methods due to the exponential growth of multidimensional coefficient spaces. We propose Tens…
CARE-SAV: A Conditioning-Aware Random-Feature Framework for Energy-Stable Simulation of Gradient Flows
Bingcheng Hu, Zhaoxiang Li
Gradient-flow models are characterized by an intrinsic energy-dissipation structure, and faithfully preserving this structure at the discrete level is important for stable and reli…
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 eq…
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 w…