報告題目：Stochastic Symplectic Methods for Stochastic Hamiltonian Systems

報告人：陳楚楚副研究員(中國科學院數學與系統科學研究院)

報告時間：2024年7月14日14:00-15:00

報告地點：數學科學學院B327

內容簡介：The stochastic Hamiltonian system is a key model across various fields such as physics, chemistry, and engineering. A defining characteristic of this system is the preservation of the stochastic symplectic structure by its phase flow. When it comes to numerically approximating the stochastic Hamiltonian system, there is an expectation that the numerical methods should preserve the symplecticity, which has driven the development of stochastic symplectic methods. These methods have demonstrated superior performance over non-symplectic counterparts in plenty of numerical experiments, especially excelling in capturing the asymptotic behaviors of the underlying solution process. In this talk, we delve into the theoretical explanations for the superiority of stochastic symplectic methods from the perspectives of the large deviation principle and the law of iterated logarithm, respectively. We prove that stochastic symplectic methods can preserve the asymptotic behaviors of the original systems over long time horizons, while non-symplectic ones do not.

報告人簡介：陳楚楚，中國科學院數學與系統科學研究院副研究員，國家級稱號人才。2015年在數學與系統科學研究院獲博士學位，2015-2017年先后在普渡大學和密歇根州立大學從事博士后研究工作。主要研究方向為隨機偏微分方程保結構算法及其理論分析，研究成果發表在SIAM J. Numer. Anal.、SIAM/ASA J. Uncertain. Quantif.、Multiscale Model. Simul.、J. Comput. Phys.、IMA J. Numer. Anal.等學術刊物上，在Springer出版社著名系列叢書Lecture Notes in Mathematic中合作出版專著《LNM 2341》。

（撰稿：張倩影  審核：張國）

數學科學學院

2024年7月11日