Constrained physical-statistics models for dynamical system identification and prediction

International audienceModeling dynamical systems combining prior physical knowledge and machinelearning (ML) is promising in scientific problems when the underlying processesare not fully understood, e.g. when the dynamics is partially known. A commonpractice to identify the respective parameters of the physical and ML componentsis to formulate the problem as supervised learning on observed trajectories.However, this formulation leads to an infinite number of possible decompositions.To solve this ill-posedness, we reformulate the learning problem by introducingan upper bound on the prediction error of a physical-statistical model. This allowsus to control the contribution of both the physical and statistical componentsto the overall prediction. This framework generalizes several existing hybridschemes proposed in the literature. We provide theoretical guarantees on the wellposednessof our formulation along with a proof of convergence in a simple affinesetting. For more complex dynamics, we validate our framework experimentall