Construction of Solution Landscape on the Energy Landscape by Saddle Dynamics
发布时间：2021年10月26日
浏览次数：4739
发布者: He Liu
主讲人： Bing Yu (PKU)
活动时间： 从 2021-11-03 15:15 到 17:00
场地： 北京国际数学研究中心，全斋全29教室
The energy landscape, which is a mapping of all possible configurations of the system to their energy, exhibits a number of local minima separated by barriers. An intriguing mathematical-physics problem is to efficiently search all stationary points of a multivariable energy function, including both minima and saddle points. Most existing methods focus on the computing of the minima and transition states (index-1 saddle point), and depend on a mass of initial guesses.
In this talk, we introduce a novel and more informative concept of the solution landscape based on the energy landscape, which is a pathway map consisting of all stationary points and their connections. In particular, a high-index saddle dynamics method is proposed to compute any-index saddles of the energy landscape. A combination of the downward search algorithm and the upward search algorithm is applied to systematically construct the solution landscape. The solution landscape not only provides a powerful and efficient way to compute multiple solutions without tuning initial guesses, but also reveals the relationships between different solutions. Furthermore, we generalize the saddle dynamics method to non-gradient systems and obtain similar results, indicating the concept of solution landscape could be applied in dynamical systems. Numerical examples, including the phase field model and its modified non-gradient models, are presented to show the wide applications of the solution landscape. Joint work with Jianyuan Yin, Lei Zhang, Xiangcheng Zheng.
