摘要：

In this talk, I will introduce our recent progress on developing an adaptive spectral method for efficiently solving spatiotemporal problems in unbounded domains with applications in biophysics and quantum mechanics. Specifically, I will discuss how our approaches could be applied to solve both forward-type problems of accurately solving spatiotemporal integrodifferential equations and inverse-type problems of inferring the underlying integrodifferential equations from spatiotemporal data, when equipped with machine learning techniques.