This talk presents two effective mathematical frameworks integrating explainable nonlinear stochastic models with machine learning algorithms to achieve these goals.

The first framework is a causality-based sparse learning algorithm that leverages information theory and DA to discover the underlying nonlinear dynamics with an appropriate UQ using only partial observations. The second framework aims to develop systematic stochastic nonlinear neural differential equations that characterize underlying physics and implement efficient DA and UQ.

海报.pdf