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Discovering ordinary differential equations that govern time-series
Sören Becker · Michal Klein · Alexander Neitz · Giambattista Parascandolo · Niki Kilbertus
Event URL: https://openreview.net/forum?id=vhrtZYgxLzV »

Natural laws are often described through differential equations yet finding a differential equation that describes the governing law underlying observed data is a challenging and still mostly manual task. In this paper we make a step towards the automation of this process: we propose a transformer-based sequence-to-sequence model that recovers scalar autonomous ordinary differential equations (ODEs) in symbolic form from time-series data of a single observed solution 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. 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.

Author Information

Sören Becker (Helmholtz Center Munich)
Michal Klein (Technical University of Munich)
Alexander Neitz (DeepMind)
Giambattista Parascandolo (OpenAI)
Niki Kilbertus (TUM & Helmholtz AI)

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