Bridging Physics-based and Data-driven modeling for Learning Dynamical Systems

TL;DR

This paper introduces AutoODE, a method that combines physics-based models with automatic differentiation for better learning and forecasting of dynamical systems, especially under distribution shifts, outperforming deep learning approaches.

Contribution

The paper formalizes AutoODE for learning physics-based models, demonstrating its superior performance over deep learning in COVID-19 forecasting and highlighting issues of distribution shift in dynamical system learning.

Findings

AutoODE reduces mean absolute errors by 57.4% in COVID-19 forecasting.

Physics-based models outperform deep learning under distribution shift.

Deep learning models struggle with changes in data and parameter domains.

Abstract

How can we learn a dynamical system to make forecasts, when some variables are unobserved? For instance, in COVID-19, we want to forecast the number of infected and death cases but we do not know the count of susceptible and exposed people. While mechanics compartment models are widely used in epidemic modeling, data-driven models are emerging for disease forecasting. We first formalize the learning of physics-based models as AutoODE, which leverages automatic differentiation to estimate the model parameters. Through a benchmark study on COVID-19 forecasting, we notice that physics-based mechanistic models significantly outperform deep learning. Our method obtains a 57.4% reduction in mean absolute errors for 7-day ahead COVID-19 forecasting compared with the best deep learning competitor. Such performance differences highlight the generalization problem in dynamical system learning due to distribution shift. We identify two scenarios where distribution shift can occur: changes in data domain and changes in parameter domain (system dynamics). Through systematic experiments on several dynamical systems, we found that deep learning models fail to forecast well under both scenarios. While much research on distribution shift has focused on changes in the data domain, our work calls attention to rethink generalization for learning dynamical systems.