# Neuro-Evolutionary Approach to Physics-Aware Symbolic Regression

arXiv: https://arxiv.org/abs/2504.16503 · HTML: https://mlsanity.com/paper/2504.16503/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 45 references that are in the map.
- First posted on arXiv 23 Apr 2025.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Informed Machine Learning -- A Taxonomy and Survey of Integrating Knowledge into Learning Systems](https://mlsanity.com/paper/1903.12394/) (2019)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [Learning Equations for Extrapolation and Control](https://mlsanity.com/paper/1806.07259/) (2018)
- [Extrapolation and learning equations](https://mlsanity.com/paper/1610.02995/) (2016)
- [SymbolicGPT: A Generative Transformer Model for Symbolic Regression](https://mlsanity.com/paper/2106.14131/) (2021)
- [Integration of Neural Network-Based Symbolic Regression in Deep Learning for Scientific Discovery](https://mlsanity.com/paper/1912.04825/) (2019)
- [SymFormer: End-to-end symbolic regression using transformer-based architecture](https://mlsanity.com/paper/2205.15764/) (2022)
- [Deep Symbolic Regression for Recurrent Sequences](https://mlsanity.com/paper/2201.04600/) (2022)
- [Shape-constrained Symbolic Regression -- Improving Extrapolation with Prior Knowledge](https://mlsanity.com/paper/2103.15624/) (2021)
- [Toward Physically Plausible Data-Driven Models: A Novel Neural Network Approach to Symbolic Regression](https://mlsanity.com/paper/2302.00773/) (2023)
- [Symbolic Regression Driven by Training Data and Prior Knowledge](https://mlsanity.com/paper/2004.11947/) (2020)
- [Symbolic regression outperforms other models for small data sets](https://mlsanity.com/paper/2103.15147/) (2021)
- [Constructing Parsimonious Analytic Models for Dynamic Systems via Symbolic Regression](https://mlsanity.com/paper/1903.11483/) (2019)
- [Logic Guided Genetic Algorithms](https://mlsanity.com/paper/2010.11328/) (2020)
- [PruneSymNet: A Symbolic Neural Network and Pruning Algorithm for Symbolic Regression](https://mlsanity.com/paper/2401.15103/) (2024)
- [[RETRACTED]Evolving Form and Function: Dual-Objective Optimization in Neural Symbolic Regression Networks](https://mlsanity.com/paper/2502.17393/) (2025)
- [Shape Constraints in Symbolic Regression using Penalized Least Squares](https://mlsanity.com/paper/2405.20800/) (2024)

## Built on by (most cited first, 1 of 1)

- [Shared Symbolic Backbones for Physically Consistent Multi-Output Symbolic Regression](https://mlsanity.com/paper/2607.26528/) (2026)

## Abstract (arXiv)

Symbolic regression is a technique that can automatically derive analytic models from data. Traditionally, symbolic regression has been implemented primarily through genetic programming that evolves populations of candidate solutions sampled by genetic operators, crossover and mutation. More recently, neural networks have been employed to learn the entire analytical model, i.e., its structure and coefficients, using regularized gradient-based optimization. Although this approach tunes the model's coefficients better, it is prone to premature convergence to suboptimal model structures. Here, we propose a neuro-evolutionary symbolic regression method that combines the strengths of evolutionary-based search for optimal neural network (NN) topologies with gradient-based tuning of the network's parameters. Due to the inherent high computational demand of evolutionary algorithms, it is not feasible to learn the parameters of every candidate NN topology to full convergence. Thus, our method employs a memory-based strategy and population perturbations to enhance exploitation and reduce the risk of being trapped in suboptimal NNs. In this way, each NN topology can be trained using only a short sequence of backpropagation iterations. The proposed method was experimentally evaluated on three real-world test problems and has been shown to outperform other NN-based approaches regarding the quality of the models obtained.