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

We look at learning the physics behind 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 still unsolved in HPC. In particular, we generalize the Finite Volume Neural Network (FINN) developed previously in the project PN 5-6, by including numerical techniques such as unstructured grids and adaptivity. Based on FINN, we develop an adaptive and flexible learning of differential operators using, e.g., dedicated flux and state kernels in neural networks to represent arbitrary forms of 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.