mlsanityData to 7 Oct 2026

ODEFormer: Symbolic Regression of Dynamical Systems with Transformers

arXiv 2310.05573 ↗First posted 9 Oct 2023cs.LGcited by 58

Not on the map. Why?

Abstract (arXiv)

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.

Key facts. Cited by 58 papers in the map (data through 7 Oct 2026). Builds on 29 of its 69 references that are in the map. First posted on arXiv 9 Oct 2023.

Builds on

29 of 69 references.

References · 29

  1. 2017Attention Is All You Needcited by 59,932
  2. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  3. 2018Neural Ordinary Differential Equationscited by 3,733
  4. 2019Mastering Atari, Go, Chess and Shogi by Planning with a Learned Modelcited by 1,327
  5. 2017Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learningcited by 935
  6. 2019AI Feynman: a Physics-Inspired Method for Symbolic Regressioncited by 536
  7. 2019A Survey on Explainable Artificial Intelligence (XAI): Towards Medical XAIcited by 403
  8. 2020Generative Language Modeling for Automated Theorem Provingcited by 379
  9. 2019Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradientscited by 294
  10. 2019Deep Learning for Symbolic Mathematicscited by 266
  11. 2021Contemporary Symbolic Regression Methods and their Relative Performancecited by 209
  12. 2022End-to-end symbolic regression with transformerscited by 195
17 more
  1. 2022Interpretable Scientific Discovery with Symbolic Regression: A Reviewcited by 105
  2. 2021SymbolicGPT: A Generative Transformer Model for Symbolic Regressioncited by 101
  3. 2021Chaos as an interpretable benchmark for forecasting and data-driven modellingcited by 87
  4. 2021Linear algebra with transformerscited by 62
  5. 2020A Bayesian machine scientist to aid in the solution of challenging scientific problemscited by 61
  6. 2022SymFormer: End-to-end symbolic regression using transformer-based architecturecited by 56
  7. 2020Teaching Temporal Logics to Neural Networkscited by 51
  8. 2018Learning concise representations for regression by evolving networks of treescited by 33
  9. 2019Epsilon-Lexicase Selection for Regressioncited by 31
  10. 2023Predicting Ordinary Differential Equations with Transformerscited by 26
  11. 2020Symbolic Pregression: Discovering Physical Laws from Distorted Videocited by 21
  12. 2019Data-driven discovery of free-form governing differential equationscited by 16
  13. 2022GSR: A Generalized Symbolic Regression Approachcited by 11
  14. 2021Identifiability Analysis of Linear Ordinary Differential Equation Systems with a Single Trajectorycited by 10
  15. 2021Accelerating Understanding of Scientific Experiments with End to End Symbolic Regressioncited by 8
  16. 2021Inferring the Structure of Ordinary Differential Equationscited by 7
  17. 2023MMViT: Multiscale Multiview Vision Transformerscited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 11; 2025: 24; 2026: 22.

58 papers.

Sort:

By area:

  1. 2024Out-of-Domain Generalization in Dynamical Systems Reconstructioncited by 33
  2. 2024Marrying Causal Representation Learning with Dynamical Systems for Sciencecited by 22
  3. 2024Zero-shot Imputation with Foundation Inference Models for Dynamical Systemscited by 13
  4. 2024LLM4ED: Large Language Models for Automatic Equation Discoverycited by 13
  5. 2025Panda: A pretrained forecast model for chaotic dynamicscited by 12
  6. 2024Data-driven model discovery with Kolmogorov-Arnold networkscited by 9
  7. 2024Self-supervised contrastive learning performs non-linear system identificationcited by 9
  8. 2025In-Context Learning of Stochastic Differential Equations with Foundation Inference Modelscited by 7
  9. 2025Identifiability Challenges in Sparse Linear Ordinary Differential Equationscited by 7
  10. 2025MDBench: Benchmarking Data-Driven Methods for Model Discoverycited by 7
  11. 2025In-Context Learning of Temporal Point Processes with Foundation Inference Modelscited by 7
  12. 2026LLM-AutoSciLab: Closed-Loop Scientific Discovery via Active Experimentation with LLMscited by 7
38 more
  1. 2024Vertical Symbolic Regression via Deep Policy Gradientcited by 6
  2. 2025Can Large Language Models Adequately Perform Symbolic Reasoning Over Time Series?cited by 6
  3. 2024A Comparison of Recent Algorithms for Symbolic Regression to Genetic Programmingcited by 5
  4. 2024Scalable Mechanistic Neural Networks for Differential Equations and Machine Learningcited by 5
  5. 2025Adaptive parameters identification for nonlinear dynamics using deep permutation invariant networkscited by 5
  6. 2025Discovering Physics Laws of Dynamical Systems via Invariant Function Learningcited by 5
  7. 2025Towards Foundational Models for Dynamical System Reconstruction: Hierarchical Meta-Learning via Mixture of Expertscited by 5
  8. 2025Grammar-based Ordinary Differential Equation Discoverycited by 5
  9. 2025Al-Khwarizmi: Discovering Physical Laws with Foundation Modelscited by 4
  10. 2025Mechanistic PDE Networks for Discovery of Governing Equationscited by 4
  11. 2025Position: Biology is the Challenge Physics-Informed ML Needs to Evolvecited by 4
  12. 2024Active Symbolic Discovery of Ordinary Differential Equations via Phase Portrait Sketchingcited by 3
  13. 2025Neuronal Attention Circuit (NAC) for Representation Learningcited by 3
  14. 2026Foundation Inference Models for Ordinary Differential Equationscited by 3
  15. 2026LLM-ODE: Data-driven Discovery of Dynamical Systems with Large Language Modelscited by 3
  16. 2026Data-driven discovery of governing differential equations across physical systemscited by 3
  17. 2024Neural Symbolic Regression of Complex Network Dynamicscited by 2
  18. 2025Data-driven Discovery of Digital Twins in Biomedical Researchcited by 2
  19. 2025KAN-SR: A Kolmogorov-Arnold Network Guided Symbolic Regression Frameworkcited by 2
  20. 2025Predicting symbolic ODEs from multiple trajectoriescited by 2
  21. 2025Automated Discovery of Conservation Laws via Hybrid Neural ODE-Transformerscited by 2
  22. 2026Neuro-Symbolic ODE Discovery with Latent Grammar Flowcited by 2
  23. 2025Bridging Logic and Learning: Decoding Temporal Logic Embeddings via Transformerscited by 1
  24. 2025Tree-Based Deep Learning for Ranking Symbolic Integration Algorithmscited by 1
  25. 2025Learning Explicit Single-Cell Dynamics Using ODE Representationscited by 1
  26. 2025Towards Fast Coarse-graining and Equation Discovery with Foundation Inference Modelscited by 1
  27. 2026FLUID: Continuous-Time Hyperconnected Sparse Transformer for Sink-Free Learningcited by 1
  28. 2026Symbolic Density Estimation for Discrete Distributionscited by 1
  29. 2026Extracting Governing Equations from Latent Dynamics via Multi-View Contrastive Learningcited by 1
  30. 2026The Dynamics of Discoverability: How Trajectories and Priors Shape Equation Recoverycited by 1
  31. 2023A projected nonlinear state-space model for forecasting time series signalscited by 0
  32. 2025DDOT: A Derivative-directed Dual-decoder Ordinary Differential Equation Transformer for Dynamic System Modelingcited by 0
  33. 2025Towards Foundation Inference Models that Learn ODEs In-Contextcited by 0
  34. 2026Knowledge-Informed Kernel State Reconstruction from Heterogeneous Partial Observationscited by 0
  35. 2026Breaking the Simplification Bottleneck in Amortized Neural Symbolic Regressioncited by 0
  36. 2026A machine learning framework for uncovering stochastic nonlinear dynamics from noisy datacited by 0
  37. 2026Discovering Ordinary Differential Equations with LLM-Based Qualitative and Quantitative Evaluationcited by 0
  38. 2026Data Enrichment for Symbolic Regression Using Diffusion Modelscited by 0

50 most cited of 58 All 58 (JSON)