MetaPhysiCa: Improving OOD Robustness in Physics-informed Machine Learning

This repository is the official implementation of MetaPhysiCa: Improving OOD Robustness in Physics-informed Machine Learning

Abstract: 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 to improve the OOD robustness of PIML via a meta-learning procedure for causal structure discovery. Using three different OOD tasks, we empirically observe that the proposed approach significantly outperforms existing state-of-the-art PIML and deep learning methods (with 2 to 28 times lower OOD errors).

Requirements

To install requirements:

pip install -r requirements.txt

Experiments

Run MetaPhysiCa:

python metaphysica.py --data=damped_pendulum --datatype=2

Arguments:

--data                             Dataset ("damped_pendulum", "lotka_volterra" or "sir")
--datatype                         Type of OOD task. 2 for OOD initial condition X0, 3 for OOD initial condition X0 and OOD parameters W*.
--polynomial_power=p               Max power of polynomial basis [default: 3]
--lr=lr                            Learning rate [default: 1e-2]
--lambda_phi=r1                    L1 regularization strength [default: 1e-2]
--lambda_vrex=r2                   V-REx penalty strength [default: 0]