5 papers
Computing Saddle Points in Stiff Problems via a Preconditioned High-index Saddle Dynamics Method
Bingzhang Huang, Hua Su, Lei Zhang +1
High-index saddle dynamics (HiSD) is an effective approach for computing saddle points of a prescribed Morse index and constructing solution landscapes for complex nonlinear system…
SaddleScape V1.0: A Python Package for Constructing Solution Landscapes via High-index Saddle Dynamics
Yuyang Liu, Hua Su, Zixiang Xiao +2
We present SaddleScape V1.0, a Python software package designed for the exploration and construction of solution landscapes in complex systems. The package implements the High-inde…
pETNNs: Partial Evolutionary Tensor Neural Networks for Solving Time-dependent Partial Differential Equations
Tunan Kao, He Zhang, Lei Zhang +1
We present the partial evolutionary tensor neural networks (pETNNs), a novel framework for solving time-dependent partial differential equations with high accuracy and capable of h…
SPIKE: Stable Physics-Informed Kernel Evolution Method for Solving Hyperbolic Conservation Laws
Hua Su, Lei Zhang, Jin Zhao
We introduce the Stable Physics-Informed Kernel Evolution (SPIKE) method for numerical computation of inviscid hyperbolic conservation laws. SPIKE resolves a fundamental paradox: h…
Neural Network-based High-index Saddle Dynamics Method for Searching Saddle Points and Solution Landscape
Yuankai Liu, Lei Zhang, Jin Zhao
The high-index saddle dynamics (HiSD) method is a powerful approach for computing saddle points and solution landscape. However, its practical applicability is constrained by the n…