Symbolic Regression Techniques in Evolutionary Computation

Symbolic regression is an evolutionary computation technique that automatically discovers analytical expressions to describe complex datasets. Candidate expressions are typically encoded as tree structures and evolved through genetic operators such as crossover, mutation and selection, guided by composite fitness measures that balance accuracy and model simplicity. Traditional implementations rely on genetic programming, while recent innovations integrate neural networks, reinforcement learning and domain-specific constraints to steer the search. Dimensional analysis, logical axioms or expert knowledge may be incorporated to reduce the search space and improve interpretability. Hybrid frameworks extend symbolic regression to hierarchical and multi-instance tasks, enabling the extraction of underlying laws across related datasets. Applications span the automated derivation of physical laws, engineering-scale process modelling and data-driven discovery in biology, demonstrating global significance and cross-disciplinary impact.

Research from Nature Portfolio

Recent studies have combined logical reasoning with symbolic regression to embed general axioms directly into the search process, enabling the derivation of classical laws such as Kepler’s third law and relativistic time-dilation from minimal observations. By pruning candidate expressions that violate prior constraints, the search converges faster and yields more physically consistent formulae. In parallel, a scientist-in-the-loop computational framework couples genetic-algorithm-based wrapper selection with layered symbolic regressors, integrating discipline-specific wisdom within an automated pipeline. This approach demonstrates robust recovery of meaningful relationships under high noise levels and can flag potential missing features in experimental data, outperforming standard symbolic regression packages on benchmark problems.

Symbolic Regression Techniques in Evolutionary Computation publication trend

The graph below shows the total number of articles in symbolic regression techniques in evolutionary computation across all publications each year (not limited to Nature Index journals).

Technical terms

Symbolic regression: An optimisation technique that searches for mathematical expressions to fit data without assuming a predefined model structure.

Genetic programming: An evolutionary algorithm that encodes candidate solutions as tree structures and applies variation operators to evolve optimal programs or expressions.

Reinforcement learning: A machine learning paradigm where agents learn to make decisions by maximising reward signals through trial and error.

Axiomatic knowledge: A set of logical or mathematical constraints derived from prior scientific principles used to guide model discovery.

References

1. Interpretable scientific discovery with symbolic regression: a review. Artificial Intelligence Review (2024).
2. Combining data and theory for derivable scientific discovery with AI-Descartes. Nature Communications (2023).
3. A computational framework for physics-informed symbolic regression with straightforward integration of domain knowledge. Scientific Reports (2023).
4. Class Symbolic Regression: Gotta Fit ’Em All. The Astrophysical Journal Letters (2024).
5. Deep Symbolic Regression for Physics Guided by Units Constraints: Toward the Automated Discovery of Physical Laws. The Astrophysical Journal (2023).
6. Integration of Neural Network-Based Symbolic Regression in Deep Learning for Scientific Discovery. IEEE Transactions on Neural Networks and Learning Systems (2021).
7. Symbolic regression based hybrid semiparametric modelling of processes: An example case of a bending process. Applications in Engineering Science (2021).