Discovering ordinary differential equations that govern time-series
This addresses the challenge of automating the discovery of governing laws from observed data, which is currently mostly manual, but it is incremental as it builds on existing methods for ODE recovery.
The authors tackled the problem of automatically discovering ordinary differential equations (ODEs) from time-series data by proposing a transformer-based sequence-to-sequence model that recovers scalar autonomous ODEs in symbolic form, showing it performs better or on par with existing methods in terms of accurate symbolic recovery, especially for complex expressions.
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.