3 papers
quant-ph2026
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…
math.NA2026
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…
cs.LG2025
-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…