ODEFormer: Symbolic Regression of Dynamical Systems with Transformers
This addresses the challenge of symbolic regression for dynamical systems, which is incremental as it builds on transformer architectures for a specific domain.
The paper tackles the problem of inferring symbolic ordinary differential equation systems from single solution trajectories, introducing ODEFormer, a transformer model that outperforms existing methods with improved robustness to noise and irregular sampling, and faster inference.
We introduce ODEFormer, the first transformer able to infer multidimensional ordinary differential equation (ODE) systems in symbolic form from the observation of a single solution trajectory. We perform extensive evaluations on two datasets: (i) the existing "Strogatz" dataset featuring two-dimensional systems; (ii) ODEBench, a collection of one- to four-dimensional systems that we carefully curated from the literature to provide a more holistic benchmark. ODEFormer consistently outperforms existing methods while displaying substantially improved robustness to noisy and irregularly sampled observations, as well as faster inference. We release our code, model and benchmark dataset publicly.