GeneExpressionProgramming.jl Documentation

GeneExpressionProgramming.jl is a Julia package for symbolic regression by Gene Expression Programming (GEP): it evolves explicit equations that fit data.

Features

• Gene Expression Programming: a model is a chromosome of Int8 tokens – genes, each a head and a tail, joined by connectors. Its karva string is scored by a batched evaluator that applies every operator to whole data columns, in buffers allocated once per thread.
• Multi-objective optimisation: a custom loss can score several objectives (accuracy, size, ...); parents are then selected by NSGA-II.
• Physical dimensions: given the SI dimensions of the features and of the target, semantic backpropagation (SBP) repairs candidates towards the target dimension, and only homogeneous candidates are scored.
• Tensor regression: scalar, vector and tensor features (Tensors.jl) side by side, through the same batched evaluator.
• Constant optimisation and linear scaling (fit! on data): Nelder-Mead tuning of the constants of the best model, or one least-squares coefficient per gene.
• Surrogate screening of expensive losses: Gaussian processes over the behaviour of the candidates decide which few individuals per epoch the loss scores, and predict the loss of the others (SurrogateScreening), for one or several objectives and for chromosomes that carry several expressions.
• Constants against an expensive loss: Nelder-Mead whose loss calls a Gaussian process over the constants places where it expects the minimum (ScreenedNelderMead), after a screened particle swarm in a box for a loss with several minima (swarm_box), for the constants of the best model inside a search (constant_optimizer of fit!) or on their own (optimize_constants!, simplex_search), e.g. with a CFD simulation as the cost function.
• Threads: fitness evaluation, genetic operators and repair run on the threads Julia is started with (julia --threads=auto).

Quick Start

using Pkg
Pkg.add(url="https://github.com/maxreiss123/GeneExpressionProgramming.jl.git")

using GeneExpressionProgramming
using Random

# Generate sample data
Random.seed!(42)
x_data = randn(100, 2)
y_data = @. x_data[:,1]^2 + x_data[:,2]

# Create and train regressor
regressor = GepRegressor(2)
fit!(regressor, 1000, 1000, x_data', y_data; loss_fun="mse")

# View the discovered expression
println(regressor.best_models_[1])
# e.g. ((x1 * x1) + x2) -- the exact form varies from run to run

Documentation Structure

• Installation: install the package and start Julia with threads
• Getting Started: a first symbolic regression, step by step
• Core Concepts: chromosomes, genetic operators, selection, dimensions and the evaluator
• API Reference: functions, types and keyword arguments
• Examples:
  • Basic Regression: the complete workflow on a known function
  • Multi-Objective Optimization: accuracy against expression size
  • Physical Dimensionality: a search held to physical units
  • Tensor Regression: a vector-valued target from scalar and vector features
  • Surrogate Screening: expensive losses (a solver in the loop), with one objective and with several expressions and objectives
  • Coefficient Tuning: the constants of a model against an expensive loss, inside a search and on their own, and a closure model searched with a fictive CFD solver in the loop

Research Foundation

The package implements the constraint of genetic symbolic regression by semantic backpropagation described in:

Reissmann, M., Fang, Y., Ooi, A. S. H., & Sandberg, R. D. (2025). Constraining genetic symbolic regression via semantic backpropagation. Genetic Programming and Evolvable Machines, 26(1), 12.

It builds on concepts explored and developed in:

Ferreira, C. (2001). Gene Expression Programming: a New Adaptive Algorithm for Solving Problems. Complex Systems, 13.

K. Deb, A. Pratap, S. Agarwal and T. Meyarivan, (2002) "A fast and elitist multiobjective genetic algorithm: NSGA-II," in IEEE Transactions on Evolutionary Computation, vol. 6, no. 2, pp. 182-197

Weatheritt, J., Sandberg, R. D. (2016) A novel evolutionary algorithm applied to algebraic modifications of the RANS stress–strain relationship. Journal of Computational Physics, vol. 325, pp. 22-37

Waschkowski, F., Zhao, Y., Sandberg R. D., Klewicki J., (2022), Multi-objective CFD-driven development of coupled turbulence closure models. Journal of Computational Physics, vol. 452,

Fang, Y., Waschkowski, F., Reissmann, M., Sandberg, R. D., Oda, T., & Tanimoto, K. (2025). A surrogate-augmented symbolic CFD-driven training framework for accelerating multi-objective physical model development. arXiv. https://arxiv.org/abs/2512.19031

Community and Support

Report bugs, request features and ask questions on the GitHub repository. Contributions – fixes, features, documentation and examples – are welcome.

Citation

If you use GeneExpressionProgramming.jl in your research, please cite:

@article{Reissmann2025,
  author   = {Maximilian Reissmann and Yuan Fang and Andrew S. H. Ooi and Richard D. Sandberg},
  title    = {Constraining Genetic Symbolic Regression via Semantic Backpropagation},
  journal  = {Genetic Programming and Evolvable Machines},
  year     = {2025},
  volume   = {26},
  number   = {1},
  pages    = {12},
  doi      = {10.1007/s10710-025-09510-z},
  url      = {https://doi.org/10.1007/s10710-025-09510-z}
}

Version Information

These pages describe the current code in the GitHub repository, which may be ahead of the latest registered release.

Acknowledgement

• Tensor-valued features and operations build on Tensors.jl.
• Earlier versions evaluated expressions with DynamicExpressions.jl; the current evaluator is a batched stack machine written for this package.