2024年04月20日 星期六 登录 EN

学术活动
learning stochastic differential equations from data
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报告人:
Aiqing Zhu, Doctor, Department of Mathematics, National University of Singapore
邀请人:
Benzhuo Lu, Professor
题目:
learning stochastic differential equations from data
时间地点:
15:30-16:30 April 3 (Wednesday) , N702
摘要:

Learning unknown stochastic differential equations (SDEs) from observed data is a significant and challenging task with applications in various fields. Current approaches often use neural networks to represent drift and diffusion functions, and construct likelihood-based loss by approximating the transition density to train these networks. However, these methods often rely on one-step stochastic numerical schemes, necessitating data with sufficiently high time resolution. In this talk, we will introduce novel approximations to the transition density of the parameterized SDE: a Gaussian density approximation inspired by the random perturbation theory of dynamical systems, and its extension, the dynamical Gaussian mixture approximation (DynGMA). Benefiting from the robust density approximation, our method exhibits superior accuracy compared to baseline methods in learning the fully unknown drift and diffusion functions and computing the invariant distribution from trajectory data. And it is capable of handling trajectory data with low time resolution and variable, even uncontrollable, time step sizes, such as data generated from Gillespie's stochastic simulations. We then show several experiment results across various scenarios to verify the advantages and robustness of the proposed method.