Physics Machine Learning for Spatio-Temporal Systems: ANN Generalization using Adaptive Grids, Domain Decomposition and Parallelization

We focus on learning the physics underlying experimental data for unknown spatio-temporal systems (Machine Physics Learning, MPL). MPL runtime demands are currently close to inhibitive for real-world systems, making parallelization via domain decomposition and other HPC techniques indispensable and leading to load-balancing problems that remain unsolved in HPC. In particular, we generalize the Finite Volume Neural Network (FINN) by incorporating numerical techniques, including unstructured grids and adaptivity. Based on FINN, we create an adaptive, flexible learning of differential operators using, e.g., dedicated flux and state kernels in neural networks to represent arbitrary numerical discretization stencils. Additionally, we will develop a concept to estimate the combined (numerical forward and learning inverse) error of MPL and extend FINN towards multilevel PDE representation. By combining FINN, modern numerics, and HPC, we make learning of computationally demanding physical problems tractable.