Modelling Physics-based Dynamic System using Machine Learning

Abstract

Partial differential equations (PDEs) have been widely used to describe a wide range of phenomena such as fluid dynamics and quantum mechanics and classical numerical methods express their limitation dealing with PDEs. Due to the recent advances in machine learning(ML), we could utilize the ML methods as a powerful tool towards our problem. Therefore, it is necessary to combine physical based approaches with ML that can be used to simulate and verify PDE driven systems. In order to verify PDE dynamic system, we present a new type of hybrid automaton with partial differential equation dynamic. Meanwhile, to simulate these systems, we present a physics-guided machine learning approach that incorporates PDEs in a graph neural network model to improve the prediction of water temperature in river networks and another physics-guided neural network for reconstructing frequent high resolution image from sparse low resolution data. Finally, we propose a transfer learning based method to handle inaccurate physical rules.