A fundamental challenge in physics-informed machine learning (PIML) is the design of robust PIML methods for out-of-distribution (OOD) forecasting tasks. These OOD tasks require learning-to-learn from observations of the same (ODE) dynamical system with different unknown ODE parameters, and demand accurate forecasts even under out-of-support initial conditions and out-of-support ODE parameters. In this work we propose a solution for such tasks, which we define as a meta-learning procedure for causal structure 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.
@article{arxiv.2303.03181,
title = {MetaPhysiCa: OOD Robustness in Physics-informed Machine Learning},
author = {S Chandra Mouli and Muhammad Ashraful Alam and Bruno Ribeiro},
journal= {arXiv preprint arXiv:2303.03181},
year = {2023}
}