mlsanityData to 7 Oct 2026

Learning Equations for Extrapolation and Control

arXiv 1806.07259 ↗First posted 19 Jun 2018cs.LG stat.MLcited by 151

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Abstract (arXiv)

We present an approach to identify concise equations from data using a shallow neural network approach. In contrast to ordinary black-box regression, this approach allows understanding functional relations and generalizing them from observed data to unseen parts of the parameter space. We show how to extend the class of learnable equations for a recently proposed equation learning network to include divisions, and we improve the learning and model selection strategy to be useful for challenging real-world data. For systems governed by analytical expressions, our method can in many cases identify the true underlying equation and extrapolate to unseen domains. We demonstrate its effectiveness by experiments on a cart-pendulum system, where only 2 random rollouts are required to learn the forward dynamics and successfully achieve the swing-up task.

Key facts. Cited by 151 papers in the map (data through 7 Oct 2026). First posted on arXiv 19 Jun 2018.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 16; 2022: 25; 2023: 27; 2024: 26; 2025: 34; 2026: 23.

151 papers.

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  1. 2022End-to-end symbolic regression with transformerscited by 195
  2. 2021Neural Symbolic Regression that Scalescited by 185
  3. 2022Interpretable Scientific Discovery with Symbolic Regression: A Reviewcited by 105
  4. 2021SymbolicGPT: A Generative Transformer Model for Symbolic Regressioncited by 101
  5. 2021Symbolic Regression via Neural-Guided Genetic Programming Population Seedingcited by 97
  6. 2022Rediscovering orbital mechanics with machine learningcited by 71
  7. 2022Symbolic Physics Learner: Discovering governing equations via Monte Carlo tree searchcited by 61
  8. 2022SymFormer: End-to-end symbolic regression using transformer-based architecturecited by 56
  9. 2022Deep Symbolic Regression for Recurrent Sequencescited by 53
  10. 2021Physics-Guided Deep Learning for Dynamical Systems: A Surveycited by 43
  11. 2024Pruner-Zero: Evolving Symbolic Pruning Metric from scratch for Large Language Modelscited by 40
  12. 2023Generating Synergistic Formulaic Alpha Collections via Reinforcement Learningcited by 37
38 more
  1. 2023Interpretable Machine Learning for Science with PySR and SymbolicRegression.jlcited by 36
  2. 2023Discovering Causal Relations and Equations from Datacited by 33
  3. 2022gLaSDI: Parametric Physics-informed Greedy Latent Space Dynamics Identificationcited by 30
  4. 2021Shape-constrained Symbolic Regression -- Improving Extrapolation with Prior Knowledgecited by 27
  5. 2021Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modelingcited by 27
  6. 2023Predicting Ordinary Differential Equations with Transformerscited by 26
  7. 2024AlphaForge: A Framework to Mine and Dynamically Combine Formulaic Alpha Factorscited by 25
  8. 2022Discovering Nonlinear PDEs from Scarce Data with Physics-encoded Learningcited by 24
  9. 2022Deep Learning and Symbolic Regression for Discovering Parametric Equationscited by 22
  10. 2025DrSR: LLM based Scientific Equation Discovery with Dual Reasoning from Data and Experiencecited by 20
  11. 2021Physics-informed Spline Learning for Nonlinear Dynamics Discoverycited by 18
  12. 2022Taylor Genetic Programming for Symbolic Regressioncited by 18
  13. 2023Automated Scientific Discovery: From Equation Discovery to Autonomous Discovery Systemscited by 18
  14. 2025A Comprehensive Survey on Self-Interpretable Neural Networkscited by 18
  15. 2024End-to-End Neuro-Symbolic Reinforcement Learning with Textual Explanationscited by 17
  16. 2025Call for Action: towards the next generation of symbolic regression benchmarkcited by 16
  17. 2023Toward Physically Plausible Data-Driven Models: A Novel Neural Network Approach to Symbolic Regressioncited by 14
  18. 2023A Neural-Guided Dynamic Symbolic Network for Exploring Mathematical Expressions from Datacited by 14
  19. 2022Integration of knowledge and data in machine learningcited by 13
  20. 2022From Perception to Programs: Regularize, Overparameterize, and Amortizecited by 13
  21. 2024LLM4ED: Large Language Models for Automatic Equation Discoverycited by 13
  22. 2026Think like a Scientist: Physics-guided LLM Agent for Equation Discoverycited by 13
  23. 2023Theory and implementation of inelastic Constitutive Artificial Neural Networkscited by 12
  24. 2022GSR: A Generalized Symbolic Regression Approachcited by 11
  25. 2023Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrologycited by 11
  26. 2021Informed Equation Learningcited by 10
  27. 2023Efficient Symbolic Policy Learning with Differentiable Symbolic Expressioncited by 9
  28. 2025Hadamard product in deep learning: Introduction, Advances and Challengescited by 9
  29. 2021Identifying Physical Law of Hamiltonian Systems via Meta-Learningcited by 8
  30. 2022Symbolic Recovery of Differential Equations: The Identifiability Problemcited by 8
  31. 2023Simultaneous identification of models and parameters of scientific simulatorscited by 8
  32. 2023Physics-constrained robust learning of open-form partial differential equations from limited and noisy datacited by 8
  33. 2023ParFam -- (Neural Guided) Symbolic Regression Based on Continuous Global Optimizationcited by 8
  34. 2021Inferring the Structure of Ordinary Differential Equationscited by 7
  35. 2022Symbolic Expression Transformer: A Computer Vision Approach for Symbolic Regressioncited by 7
  36. 2022CoNSoLe: Convex Neural Symbolic Learningcited by 7
  37. 2022Extrapolation and Spectral Bias of Neural Nets with Hadamard Product: a Polynomial Net Studycited by 7
  38. 2023RSRM: Reinforcement Symbolic Regression Machinecited by 7

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