7 citations · 11 across the 5 of their papers we have counts for
5 papers
A General First- and Second-Order Numerical Solver for Non-Markovian Quantum State Diffusion
Zhenning Cai, Quanhui Zhu
The numerical simulation of non-Markovian open quantum systems based on the non-Markovian quantum state diffusion (NMQSD) equation is complicated by functional derivatives with res…
Energy Dissipation Preserving Feature-based DNN Galerkin Methods for Gradient Flows
Tao Tang, Jiang Yang, Yuxiang Zhao +1
In recent years, deep learning methods, exemplified by Physics-Informed Neural Networks (PINNs), have been widely applied to the numerical solution of differential equations. Howev…
-rank and the Staircase Phenomenon: New Insights into Neural Network Training Dynamics
Jiang Yang, Yuxiang Zhao, Quanhui Zhu
Understanding the training dynamics of deep neural networks (DNNs), particularly how they evolve low-dimensional features from high-dimensional data, remains a central challenge in…
Priori Error Estimate of Deep Mixed Residual Method for Elliptic PDEs
Lingfeng Li, Xue-cheng Tai, Jiang Yang +1
In this work, we derive a priori error estimate of the mixed residual method when solving some elliptic PDEs. Our work is the first theoretical study of this method. We prove that…
A Local Deep Learning Method for Solving High Order Partial Differential Equations
Quanhui Zhu, Jiang Yang
At present, deep learning based methods are being employed to resolve the computational challenges of high-dimensional partial differential equations (PDEs). But the computation of…