报告题目：Stochastic Symplectic Methods for Stochastic Hamiltonian Systems
报告人：陈楚楚副研究员(中国科学院数学与系统科学研究院)
报告时间：2024年7月14日14:00-15:00
报告地点：数学科学学院B327
内容简介：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.
报告人简介：陈楚楚，中国科学院数学与系统科学研究院副研究员，国家级称号人才。2015年在数学与系统科学研究院获博士学位，2015-2017年先后在普渡大学和密歇根州立大学从事博士后研究工作。主要研究方向为随机偏微分方程保结构算法及其理论分析，研究成果发表在SIAM J. Numer. Anal.、SIAM/ASA J. Uncertain. Quantif.、Multiscale Model. Simul.、J. Comput. Phys.、IMA J. Numer. Anal.等学术刊物上，在Springer出版社著名系列丛书Lecture Notes in Mathematic中合作出版专著《LNM 2341》。
（撰稿：张倩影 审核：张国）
数学科学学院
2024年7月11日
