Time/Space Separation-Based Physics-Informed Machine Learning for Spatiotemporal Modeling of Distributed Parameter Systems

This article introduces a novel time/space separation-based physics-informed machine learning (T/S-PIML) modeling method by making full use of the complementary strengths of the physics-informed neural network (PINN) and the time/space separation methodology. T/S-PIML is the first attempt to seamlessly integrate structural (including spatial and temporal) physical information with data for effective spatiotemporal modeling of distributed parameter systems (DPSs). With the help of the spectral method, spatial basis functions are first extracted to capture spatial physical information. Subsequently, a reduced-order system is derived to characterize the corresponding temporal physical information. Upon the structural physical information, PINN is developed for temporal modeling. Following the time/space synthesis, a small amount of sensing data is utilized to calibrate system errors. Experiments on a benchmark DPS and the thermal process of a lithium-ion battery demonstrate the effectiveness of T/S-PIML.