Data-driven PDE discovery with evolutionary approach

03/19/2019

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by   Michail Maslyaev, et al.

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The data-driven models allow one to dene the model struc-ture in cases when a priori information is not sucient to build othertypes of models. The possible way to obtain physical interpretation is the data-driven differential equation discovery techniques. The existingmethods of PDE (partial derivative equations) discovery are bound with the sparse regression. However, sparse regression is restricting the result-ing model form, since the terms for PDE are defined before regression. The evolutionary approach described in the article has a symbolic regression as the background instead and thus has fewer restrictions onthe PDE form. The evolutionary method of PDE discovery (EPDE) is described and tested on several canonical PDEs. The question of robust-ness is examined on a noised data example.