Learning Dynamical Systems with Helmholtz-Hodge Decomposition and Gaussian Processes
Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)
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Keywords: Gaussian process, dynamical system, Helmholtz-Hodge decomposition
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Abstract: Machine learning models provide alternatives for efficiently recognizing complex patterns from data, but two main concerns in applying them to modeling physical systems stem from their physics-agnostic design and lack of interpretability. This paper mitigates these concerns by encoding the Helmholtz-Hodge decomposition into a Gaussian process model, leading to a versatile framework that simultaneously learns the curl-free and divergence-free components of a dynamical system. Learning a predictive model in this form facilitates the exploitation of symmetry priors. In addition to improving predictive power, these priors link the identified features to comprehensible scientific properties of the system, thus complex responses can be modeled while retaining interpretability. We show that compared to baseline models, our model achieves better predictive performance on several benchmark dynamical systems while allowing accurate estimation of the energy evolution of the systems from noisy and sparse data.
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Submission Number: 8944
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