Efficient Discovery of Dynamical Laws in Symbolic Form

Sören Becker, Michal Klein, Alexander Neitz, Giambattista Parascandolo, Niki Kilbertus

Keywords: Symbolic, ODE, Transformer

TL;DR: Given a time series that is governed by an ordinary differential equation (ODE), our model infers the mathematical expression of the ODE.

Abstract: We propose a transformer-based sequence-to-sequence model that recovers scalar ordinary differential equations (ODEs) in symbolic form from time-series data of a single observed solution trajectory of the ODE. Our method is efficiently scalable: after one-time pretraining on a large set of ODEs, we can infer the governing laws of a new observed solution in a few forward passes of the model. First, we generate and make available a large dataset of more than 3M ODEs together with more than 63M numerical solutions for different initial conditions that may serve as a useful benchmark for future work on machine learning for dynamical systems. Then we show that our model performs better or on par with existing methods in various test cases in terms of accurate symbolic recovery of the ODE, especially for more complex expressions. Reliably recovering the symbolic form of dynamical laws is important as it allows for further dissemination of the inferred dynamics as well as meaningful modifications for predictions under interventions.

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