Discovering ordinary differential equations that govern time-series

TL;DR

This paper introduces a transformer-based model that automates the discovery of scalar autonomous ordinary differential equations from time-series data, improving accuracy and scalability over existing methods.

Contribution

The authors develop a scalable, pretrained transformer model capable of recovering symbolic ODEs from single solution time-series data, advancing automation in law discovery.

Findings

Model outperforms existing methods in accuracy for complex ODEs

Efficient inference after one-time pretraining

Effective in recovering symbolic forms of ODEs

Abstract

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.