PhysNODE: Fusion of data and expert knowledge for modeling dynamical systems

Abstract Building a representative model of a complex system remains a highly challenging problem. While by now there is basic understanding of most physical domains, model design is often hindered by lack of detail, for example concerning model dimensions or its relevant constraints. Here we present a novel model-building approach – physNODE – augmenting basic system descriptions, based on expert knowledge in the form of ordinary differential equations, with continuous adjoint sensitivity analysis related to artificial neural network principles, based on observable data. With this we have created a general tool, that can be applied to any physical system described by ordinary differential equations. PhysNODE allows validating or extending the initial description, for example with different variables and constraints. This way one arrives at a better-optimised, representative lowdimensional model, which can fit existing data and predict novel experimental outcomes.