CONFIDE: CONtextual FInite DifferencE modelling of PDEs

Ori Linial, Orly Avner, Dotan Di Castro

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

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Keywords: partial differential equations, hybrid modelling, physics informed models, time series modeling

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Abstract:

We introduce a method for inferring an explicit PDE from a data sample generated by previously unseen dynamics, based on a learned context.
The training phase integrates knowledge of the form of the equation with a differential scheme, while the inference phase yields a PDE that fits the data sample and enables both signal prediction and data explanation.
We include results of extensive experimentation, comparing our method to SOTA approaches, together with ablation studies that examine different flavors of our solution in terms of prediction error and explainability.

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Submission Number: 3505