ODEFormer: Symbolic Regression of Dynamical Systems with Transformers

• URL: http://arxiv.org/abs/2310.05573v1
• Date: Mon, 9 Oct 2023 09:54:12 GMT
• Title: ODEFormer: Symbolic Regression of Dynamical Systems with Transformers
• Authors: St\'ephane d'Ascoli, S\"oren Becker, Alexander Mathis, Philippe Schwaller, Niki Kilbertus
• Abstract summary: We introduce ODEFormer, the first transformer able to infer multidimensional ordinary differential equation (ODE) systems in symbolic form. We perform extensive evaluations on two datasets: (i) the existing "Strogatz" dataset featuring two-dimensional systems; (ii) ODEBench, a collection of one- to four-dimensional systems.
• Score: 47.75031734856786
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce ODEFormer, the first transformer able to infer multidimensional ordinary differential equation (ODE) systems in symbolic form from the observation of a single solution trajectory. We perform extensive evaluations on two datasets: (i) the existing "Strogatz" dataset featuring two-dimensional systems; (ii) ODEBench, a collection of one- to four-dimensional systems that we carefully curated from the literature to provide a more holistic benchmark. ODEFormer consistently outperforms existing methods while displaying substantially improved robustness to noisy and irregularly sampled observations, as well as faster inference. We release our code, model and benchmark dataset publicly.

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