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ODEFormer: Symbolic Regression of Dynamical Systems with Transformers

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arxiv 2310.05573 v1 pith:NISLFO67 submitted 2023-10-09 cs.LG

Stéphane d'Ascoli , Sören Becker , Alexander Mathis , Philippe Schwaller , Niki Kilbertus This is my paper · ORCID
classification cs.LG
keywords systemsodeformerbenchmarkdatasetexistingsymbolicablecarefully
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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.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Neuro-Symbolic ODE Discovery with Latent Grammar Flow

    cs.LG 2026-04 unverdicted novelty 7.0 of 10

    Latent Grammar Flow embeds grammar-based ODE representations into a discrete latent space with a behavioural loss and samples candidate equations via discrete flow to fit observed data.

  2. Neural operator discovery from heterogeneous trajectories

    cs.LG 2026-07 conditional novelty 6.0 of 10

    Trajectory grouping plus a low-dimensional latent bottleneck lets a neural operator discover each system's hidden governing factors and extrapolate to unseen systems.

  3. Modelling Chemical Reaction Networks using Neural Ordinary Differential Equations

    q-bio.MN 2025-02 conditional novelty 5.0 of 10

    A neural ODE correction to mass-action kinetics improved predicted oscillation periods when transferred to new settings, but did not improve classifying sustained versus damped oscillations.

  4. Drag modelling for flows through assemblies of spherical particles with machine learning: A comparison of approaches

    physics.comp-ph 2025-07 conditional novelty 4.0 of 10

    Applying genetic programming to outputs of a graph neural network yields compact symbolic drag-variation formulas at Reynolds numbers up to 280, though with lower accuracy than the network.

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