3 papers
math.NA2026
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…
math.NA2025
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…
cs.LG2024
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…