Graph-Informed Neural Networks

Graph-Informed Neural Networks (GINNs) present a strategy for incorporating domain knowledge into scientific machine learning for complex physical systems. The construction utilizes probabilistic graphical models (PGMs) to incorporate expert knowledge, available data, constraints, etc. with physics-based models such as systems of ordinary and partial differential equations (ODEs and PDEs). Computationally intensive nodes in this hybrid model are replaced by the hidden nodes of a neural network (i.e., learned features). Once trained, the resulting GINN surrogate can cheaply generate physically-relevant predictions at scale thereby enabling robust sensitivity analysis and uncertainty quantification (UQ). As proof of concept, we build a GINN for a multiscale model of electrical double-layer capacitor dynamics embedded into a Bayesian network (BN) PDE hybrid model.