Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bridging Physics-based and Data-driven modeling 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.

22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg