mlsanityData to 14 Oct 2026

Extrapolation and learning equations

arXiv 1610.02995 ↗First posted 10 Oct 2016cs.LG cs.AIcited by 110

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Abstract (arXiv)

In classical machine learning, regression is treated as a black box process of identifying a suitable function from a hypothesis set without attempting to gain insight into the mechanism connecting inputs and outputs. In the natural sciences, however, finding an interpretable function for a phenomenon is the prime goal as it allows to understand and generalize results. This paper proposes a novel type of function learning network, called equation learner (EQL), that can learn analytical expressions and is able to extrapolate to unseen domains. It is implemented as an end-to-end differentiable feed-forward network and allows for efficient gradient based training. Due to sparsity regularization concise interpretable expressions can be obtained. Often the true underlying source expression is identified.

Key facts. Cited by 110 papers in the map (data through 14 Oct 2026). First posted on arXiv 10 Oct 2016.

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Citing papers per year: 2021: 8; 2022: 16; 2023: 21; 2024: 23; 2025: 23; 2026: 19.

110 papers.

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  1. 2024KAN: Kolmogorov-Arnold Networkscited by 649
  2. 2022End-to-end symbolic regression with transformerscited by 203
  3. 2021Neural Symbolic Regression that Scalescited by 192
  4. 2024KAN 2.0: Kolmogorov-Arnold Networks Meet Sciencecited by 118
  5. 2021SymbolicGPT: A Generative Transformer Model for Symbolic Regressioncited by 105
  6. 2022Interpretable Scientific Discovery with Symbolic Regression: A Reviewcited by 105
  7. 2022Symbolic Physics Learner: Discovering governing equations via Monte Carlo tree searchcited by 66
  8. 2022SymFormer: End-to-end symbolic regression using transformer-based architecturecited by 59
  9. 2023Deep symbolic regression for physics guided by units constraints: toward the automated discovery of physical lawscited by 55
  10. 2021Physics-Guided Deep Learning for Dynamical Systems: A Surveycited by 44
  11. 2024Pruner-Zero: Evolving Symbolic Pruning Metric from scratch for Large Language Modelscited by 40
  12. 2022Deep Learning and Symbolic Regression for Discovering Parametric Equationscited by 23
38 more
  1. 2025DrSR: LLM based Scientific Equation Discovery with Dual Reasoning from Data and Experiencecited by 22
  2. 2022Scientific Inference With Interpretable Machine Learning: Analyzing Models to Learn About Real-World Phenomenacited by 21
  3. 2022Taylor Genetic Programming for Symbolic Regressioncited by 19
  4. 2021Physics-informed Spline Learning for Nonlinear Dynamics Discoverycited by 18
  5. 2024End-to-End Neuro-Symbolic Reinforcement Learning with Textual Explanationscited by 17
  6. 2023A Neural-Guided Dynamic Symbolic Network for Exploring Mathematical Expressions from Datacited by 16
  7. 2026Think like a Scientist: Physics-guided LLM Agent for Equation Discoverycited by 16
  8. 2023Toward Physically Plausible Data-Driven Models: A Novel Neural Network Approach to Symbolic Regressioncited by 14
  9. 2024LLM4ED: Large Language Models for Automatic Equation Discoverycited by 14
  10. 2025Interpretable Machine Learning in Physics: A Reviewcited by 14
  11. 2023Efficient Generator of Mathematical Expressions for Symbolic Regressioncited by 13
  12. 2024A predictive machine learning force field framework for liquid electrolyte developmentcited by 13
  13. 2023Theory and implementation of inelastic Constitutive Artificial Neural Networkscited by 12
  14. 2022GSR: A Generalized Symbolic Regression Approachcited by 11
  15. 2021Informed Equation Learningcited by 10
  16. 2023ParFam -- (Neural Guided) Symbolic Regression Based on Continuous Global Optimizationcited by 10
  17. 2023Efficient Symbolic Policy Learning with Differentiable Symbolic Expressioncited by 10
  18. 2024Discovering Mathematical Formulas from Data via GPT-guided Monte Carlo Tree Searchcited by 10
  19. 2021AI Descartes: Combining Data and Theory for Derivable Scientific Discoverycited by 8
  20. 2022Symbolic Recovery of Differential Equations: The Identifiability Problemcited by 8
  21. 2023RSRM: Reinforcement Symbolic Regression Machinecited by 8
  22. 2023Simultaneous identification of models and parameters of scientific simulatorscited by 8
  23. 2021Inferring the Structure of Ordinary Differential Equationscited by 7
  24. 2022CoNSoLe: Convex Neural Symbolic Learningcited by 7
  25. 2022Extrapolation and Spectral Bias of Neural Nets with Hadamard Product: a Polynomial Net Studycited by 7
  26. 2023GINN-LP: A Growing Interpretable Neural Network for Discovering Multivariate Laurent Polynomial Equationscited by 7
  27. 2024SymbolNet: Neural Symbolic Regression with Adaptive Dynamic Pruning for Compressioncited by 7
  28. 2024OccamLLM: Fast and Exact Language Model Arithmetic in a Single Stepcited by 7
  29. 2025Knowledge Integration for Physics-informed Symbolic Regression Using Pre-trained Large Language Modelscited by 7
  30. 2025MDBench: Benchmarking Data-Driven Methods for Model Discoverycited by 7
  31. 2022Quant 4.0: Engineering Quantitative Investment with Automated, Explainable and Knowledge-driven Artificial Intelligencecited by 6
  32. 2023MetaPhysiCa: OOD Robustness in Physics-informed Machine Learningcited by 6
  33. 2023Class Symbolic Regression: Gotta Fit 'Em Allcited by 6
  34. 2025Discovering Symbolic Differential Equations with Symmetry Invariantscited by 6
  35. 2025When is a System Discoverable from Data? Discovery Requires Chaoscited by 6
  36. 2025Adaptive parameters identification for nonlinear dynamics using deep permutation invariant networkscited by 5
  37. 2023Symbolic expression generation via Variational Auto-Encodercited by 4
  38. 2023Differentiable Genetic Programming for High-dimensional Symbolic Regressioncited by 4

50 most cited of 110 All 110 (JSON)