Learn to Adapt Parametric Solvers Under Incomplete Physics

Abstract

Modelling physical systems when only partial knowledge of the physics is available is a recurrent problem in science. Within this context, we consider hybrid models that complement PDE solvers, providing incomplete physics information, with NN components for modelling dynamical systems. A critical challenge with this approach lies in generalising to unseen environments that share similar dynamics but have different physical contexts. To tackle this, we introduce a meta-learning strategy that captures context-specific variations inherent in each system, enhancing the model's adaptability to generalise to new PDE parameters and initial conditions. We emphasise the advantages of adaptation strategies compared to a pure empirical risk minimisation approach, the superiority of the solver-neural network combination over soft physics constraints, and the enhanced generalisation ability compared to alternative approaches