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. 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 for 7-day ahead COVID-19 forecasting 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 domain or the parameter domain. This calls attention to rethink generalization especially for learning dynamical systems.
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.
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widely-used
widely used
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As a case study, we compare these two types of models for
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
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and
, we
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mechanistic
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models. We present a hybrid approach, AutoODE-COVID, which combines a novel compartmental model with automatic differentiation.
.
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To understand the inferior performance of deep learning, we investigate
Such performance differences highlight
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forecasting.
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).
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on several dynamical systems
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under shifted distributions either
well under both scenarios. While much research on distribution shift has focused on changes
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or the parameter domain. This
, our work
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especially