Predicting Ordinary Differential Equations with Transformers

• URL: http://arxiv.org/abs/2307.12617v1
• Date: Mon, 24 Jul 2023 08:46:12 GMT
• Title: Predicting Ordinary Differential Equations with Transformers
• Authors: S\"oren Becker, Michal Klein, Alexander Neitz, Giambattista Parascandolo, Niki Kilbertus
• Abstract summary: We develop a transformer-based sequence-to-sequence model that recovers scalar ordinary differential equations (ODEs) in symbolic form from irregularly sampled and noisy observations of a single solution trajectory. Our method is efficiently scalable: after one-time pretraining on a large set of ODEs, we can infer the governing law of a new observed solution in a few forward passes of the model.
• Score: 65.07437364102931
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop a transformer-based sequence-to-sequence model that recovers scalar ordinary differential equations (ODEs) in symbolic form from irregularly sampled and noisy observations of a single solution trajectory. We demonstrate in extensive empirical evaluations that our model performs better or on par with existing methods in terms of accurate recovery across various settings. Moreover, our method is efficiently scalable: after one-time pretraining on a large set of ODEs, we can infer the governing law of a new observed solution in a few forward passes of the model.

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