4 papers
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…
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…
Improved high-index saddle dynamics for finding saddle points and solution landscape
Hua Su, Haoran Wang, Lei Zhang +2
We present an improved high-index saddle dynamics (iHiSD) for finding saddle points and constructing solution landscapes, which is a crossover dynamics from gradient flow to tradit…
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…