A0537
Title: SIGMA: Stochastic differential equations informed Gaussian process model for parameter inference
Authors: Zhaohui Li - Academy of Mathematics and Systems Science,Chinese Academy of Sciences (China) [presenting]
Abstract: Stochastic differential equations (SDEs) have been extensively applied in diverse fields such as systems biology, pandemic, financial engineering, physics, etc. However, due to their inherent stochasticity and the complexity of the underlying dynamic systems, parameter estimation and uncertainty quantification for SDEs pose significant challenges. A novel method called the SDE-informed Gaussian process model for parameter inference (SIGMA), is proposed to address these challenges. The new method employs a nonstationary Gaussian process (GP) model to approximate the solutions of SDEs. The approach incorporates a nonparametric mean function and a parametric variance function, providing flexibility in the approximation process. The Matern 1/2 kernel is employed for the GP prior, as it yields non-differentiable sample paths that resemble those of SDEs. A Kullback-Leibler (KL) divergence is designed as a metric to quantify the discrepancy between the GP and the SDE. SIGMA adopts a Bayesian paradigm to incorporate the KL divergence into the posterior density, which enables thorough uncertainty quantification for both the parameters and the unobserved SDE solutions.
