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

Rui Wang, Danielle Maddix, Christos Faloutsos, Yuyang Wang, Rose Yu
Proceedings of the 3rd Conference on Learning for Dynamics and Control, PMLR 144:385-398, 2021.

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 patients and death cases but we do not know the count of susceptible and exposed people. How to proceed? While mechanics compartment models are widely-used in epidemic modeling, data-driven models are emerging for disease forecasting. As a case study, we compare these two types of models for COVID-19 forecasting and notice that physics-based models significantly outperform deep learning models. We present a hybrid approach, AutoODE-COVID, which combines a novel compartmental model with automatic differentiation. Our method obtains a 57.4% reduction in mean absolute errors of the 7-day ahead COVID-19 trajectories prediction compared with the best deep learning competitor. To understand the inferior performance of deep learning, we investigate the generalization problem in forecasting. Through systematic experiments, we found that deep learning models fail to forecast under shifted distributions either in the data and parameter domains of dynamical systems. This calls attention to rethink generalization especially for learning dynamical systems.

Cite this Paper

BibTeX
@InProceedings{pmlr-v144-wang21a, title = {Bridging Physics-based and Data-driven modeling for Learning Dynamical Systems}, author = {Wang, Rui and Maddix, Danielle and Faloutsos, Christos and Wang, Yuyang and Yu, Rose}, booktitle = {Proceedings of the 3rd Conference on Learning for Dynamics and Control}, pages = {385--398}, year = {2021}, editor = {Jadbabaie, Ali and Lygeros, John and Pappas, George J. and A. Parrilo, Pablo and Recht, Benjamin and Tomlin, Claire J. and Zeilinger, Melanie N.}, volume = {144}, series = {Proceedings of Machine Learning Research}, month = {07 -- 08 June}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v144/wang21a/wang21a.pdf}, url = {https://proceedings.mlr.press/v144/wang21a.html}, 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 patients and death cases but we do not know the count of susceptible and exposed people. How to proceed? While mechanics compartment models are widely-used in epidemic modeling, data-driven models are emerging for disease forecasting. As a case study, we compare these two types of models for COVID-19 forecasting and notice that physics-based models significantly outperform deep learning models. We present a hybrid approach, AutoODE-COVID, which combines a novel compartmental model with automatic differentiation. Our method obtains a 57.4% reduction in mean absolute errors of the 7-day ahead COVID-19 trajectories prediction compared with the best deep learning competitor. To understand the inferior performance of deep learning, we investigate the generalization problem in forecasting. Through systematic experiments, we found that deep learning models fail to forecast under shifted distributions either in the data and parameter domains of dynamical systems. This calls attention to rethink generalization especially for learning dynamical systems.} }
Endnote
%0 Conference Paper %T Bridging Physics-based and Data-driven modeling for Learning Dynamical Systems %A Rui Wang %A Danielle Maddix %A Christos Faloutsos %A Yuyang Wang %A Rose Yu %B Proceedings of the 3rd Conference on Learning for Dynamics and Control %C Proceedings of Machine Learning Research %D 2021 %E Ali Jadbabaie %E John Lygeros %E George J. Pappas %E Pablo A. Parrilo %E Benjamin Recht %E Claire J. Tomlin %E Melanie N. Zeilinger %F pmlr-v144-wang21a %I PMLR %P 385--398 %U https://proceedings.mlr.press/v144/wang21a.html %V 144 %X 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 patients and death cases but we do not know the count of susceptible and exposed people. How to proceed? While mechanics compartment models are widely-used in epidemic modeling, data-driven models are emerging for disease forecasting. As a case study, we compare these two types of models for COVID-19 forecasting and notice that physics-based models significantly outperform deep learning models. We present a hybrid approach, AutoODE-COVID, which combines a novel compartmental model with automatic differentiation. Our method obtains a 57.4% reduction in mean absolute errors of the 7-day ahead COVID-19 trajectories prediction compared with the best deep learning competitor. To understand the inferior performance of deep learning, we investigate the generalization problem in forecasting. Through systematic experiments, we found that deep learning models fail to forecast under shifted distributions either in the data and parameter domains of dynamical systems. This calls attention to rethink generalization especially for learning dynamical systems.
APA
Wang, R., Maddix, D., Faloutsos, C., Wang, Y. & Yu, R.. (2021). Bridging Physics-based and Data-driven modeling for Learning Dynamical Systems. Proceedings of the 3rd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 144:385-398 Available from https://proceedings.mlr.press/v144/wang21a.html.

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