Searching the solution landscape by generalized high-index saddle dynamics  

作　　者：Jianyuan Yin Bing Yu Lei Zhang 

机构地区：[1]School of Mathematical Sciences,Peking University,Beijing 100871,China [2]Beijing International Center for Mathematical Research,Center for Quantitative Biology,Peking University,Beijing 100871,China

出　　处：《Science China Mathematics》2021年第8期1801-1816,共16页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11861130351);the support from the Elite Program of Computational and Applied Mathematics for Ph D Candidates of Peking University。

摘　　要：We introduce a generalized numerical algorithm to construct the solution landscape,which is a pathway map consisting of all the stationary points and their connections.Based on the high-index optimizationbased shrinking dimer(Hi OSD)method for gradient systems,a generalized high-index saddle dynamics(GHi SD)is proposed to compute any-index saddles of dynamical systems.Linear stability of the index-k saddle point can be proved for the GHi SD system.A combination of the downward search algorithm and the upward search algorithm is applied to systematically construct the solution landscape,which not only provides a powerful and efficient way to compute multiple solutions without tuning initial guesses,but also reveals the relationships between different solutions.Numerical examples,including a three-dimensional example and the phase field model,demonstrate the novel concept of the solution landscape by showing the connected pathway maps.

关 键 词：saddle point energy landscape solution landscape pathway map dynamical system phase field 

分 类 号：O19[理学—数学]