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

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.

References in corpus (11)

• Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
• DGM: A deep learning algorithm for solving partial differential equations
• Time Series Forecasting With Deep Learning: A Survey
• Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations
• Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting
• Deep Transformer Models for Time Series Forecasting: The Influenza Prevalence Case
• A Multi-Horizon Quantile Recurrent Forecaster
• An introduction to domain adaptation and transfer learning
• Incorporating Symmetry into Deep Dynamics Models for Improved Generalization
• Learning Dynamical Systems from Partial Observations
• Solving Nonlinear and High-Dimensional Partial Differential Equations via Deep Learning

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