Methods

SR methods are grouped into different categories to be most useful. A minimal number of categories is chosen in order to be as simple and useful as possible. SR methods are listed for each category.

Regression-based SR

Linear approaches

Linear approach

• Discovering governing equations from data by sparse identification of nonlinear dynamical systems[DOI] (SINDY)
• Sparse identification of nonlinear dynamics for rapid model recovery [DOI]
• Data-driven discovery of coordinates and governing equations [DOI] code (SINDY_AE)

Non-linear approaches

Non-linear approach

• AI Feynman: a Physics-Inspired Method for Symbolic Regression [DOI] code (AIFeynman)
• Integration of Neural Network-Based Symbolic Regression in Deep Learning for Scientific Discovery
• Symbolic regression for scientific discovery: an application to wind speed forecasting
• Relational inductive biases, deep learning, and graph networks
• Extrapolation and learning equations (EQL)
• Learning Equations for Extrapolation and Control(EQL\(_\div\))

Expression tree-based SR

Genetic programming (GP-based SR)

Genetic programming

• Eurequa
• PySR: High-Performance Symbolic Regression in Python and Julia
• Genetic programming as a means for programming computers by natural selection [DOI]
• Order of Nonlinearity as a Complexity Measure for Models Generated by Symbolic Regression via Pareto Genetic Programming [DOI]
• Improving Symbolic Regression with Interval Arithmetic and Linear Scaling [DOI]
• Accuracy in Symbolic Regression [DOI]
• Semantically-based crossover in genetic programming: application to real-valued symbolic regression [DOI]
• Rethinking Symbolic Regression: Morphology and adaptability for evolutionary algorithms [DOI]

Reinforcement learning (RL-based SR)

Reinforcement learning

• Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients [DOI] code(DSR)
• Symbolic Regression via Neural-Guided Genetic Programming Population Seeding [DOI]code (DSR)
• Physical Symbolic Optimization code (\(\phi\)-SO)

Transformer neural network (TNN-based SR)

Transformer neural network

• End-to-end symbolic regression with transformers code (E2ET)
• Neural Symbolic Regression that Scales code (NeSymReS)
• A Generative Transformer Model for Symbolic Regression code (SymbolicGPT)
• SYMBA: Symbolic Computation of squared amplitudes in high energy physics with machine learning code (SYMBA)
• Deep Generative Symbolic Regression with Monte-Carlo-Tree-Search (DGSR-MCTS)
• Controllable Neural Symbolic Regression (NSRwH)
• A Transformer Model for symbolic regression towards scientific discovery [DOI] code
• ODEFormer: Symbolic regression of dynamical systems with transformer [DOI]code (ODEFormer)
• A Transformer Model for Symbolic Regression towards Scientific Discovery [DOI] codecode] (transformer4sr)
• Transformer-based Planning for Symbolic Regression [DOI] codecode] (TPSR)

Other SR approaches

Physics-inspired

Physics-inspired

• AI Feynman: a Physics-Inspired Method for Symbolic Regression [DOI] code
• Physical Symbolic Optimization code (\(\phi\)-SO)

Mathematics-inspired

Mathematics-inspired

• Demystifying Black-box Models with Symbolic Metamodels [DOI] code

Computational approach

Computational approach

• Distilling Free-Form Natural Laws from Experimental Data

• GFN-SR: Symbolic Regression with Generative Flow Networks [DOI] codecode]