MetaPhysiCa: Causality-aware Robustness to OOD Initial Conditions in Physics-informed Machine Learning

A fundamental challenge in physics-informed machine learning (PIML) is the design of robust PIML methods for out-of-distribution (OOD) forecasting tasks, where the tasks require learning-to-learn from observations of the same (ODE) dynamical system with different unknown parameters, and demand accurate forecasts even under initial conditions outside the training support. In this work we propose a solution for such tasks, which we define as a meta-learning procedure for causal structural discovery (including invariant risk minimization). Using three different OOD tasks, we empirically observe that the proposed approach significantly outperforms existing state-of-the-art PIML and deep learning methods.