4 papers
PI-DOSnet: A Physics-Informed Deep Operator-Splitting Network for Evolution Partial Differential Equations
Jizu Huang, Yue Qian, Tao Zhou
Evolution partial differential equations (PDEs) describe time-dependent physical systems governed by differential laws and arise widely across science and engineering. In recent ye…
Frequency-adaptive tensor neural networks for high-dimensional multi-scale problems
Jizu Huang, Yue Qiu, Rukang You
Tensor neural networks (TNNs) have demonstrated their superiority in solving high-dimensional problems. However, similar to conventional neural networks, TNNs are also influenced b…
Deep learning for the semi-classical limit of the Schrödinger equation
Jizu Huang, Rukang You, Tao Zhou
In this paper, we integrate neural networks and Gaussian wave packets to numerically solve the Schrödinger equation with a smooth potential near the semi-classical limit. Our focu…
Frequency-adaptive Multi-scale Deep Neural Networks
Jizu Huang, Rukang You, Tao Zhou
Multi-scale deep neural networks (MscaleDNNs) with downing-scaling mapping have demonstrated superiority over traditional DNNs in approximating target functions characterized by hi…