# Domain-Informed Genetic Superposition Programming: A Case Study on SFRC Beams

arXiv: https://arxiv.org/abs/2509.21355 · HTML: https://mlsanity.com/paper/2509.21355/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 29 references that are in the map.
- First posted on arXiv 20 Sep 2025.

## Builds on (most cited first, 8 of 8)

- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Numerical analysis of physics-informed neural networks and related models in physics-informed machine learning](https://mlsanity.com/paper/2402.10926/) (2024)
- [Genetic Programming Based Symbolic Regression for Analytical Solutions to Differential Equations](https://mlsanity.com/paper/2302.03175/) (2023)
- [Benchmarking symbolic regression constant optimization schemes](https://mlsanity.com/paper/2412.02126/) (2024)
- [Embedding Domain-Specific Knowledge from LLMs into the Feature Engineering Pipeline](https://mlsanity.com/paper/2503.21155/) (2025)
- [A Novel Ontology-guided Attribute Partitioning Ensemble Learning Model for Early Prediction of Cognitive Deficits using Quantitative Structural MRI in Very Preterm Infants](https://mlsanity.com/paper/2202.04134/) (2022)
- [Semantic-Preserving Feature Partitioning for Multi-View Ensemble Learning](https://mlsanity.com/paper/2401.06251/) (2024)
- [From Embeddings to Equations: Genetic-Programming Surrogates for Interpretable Transformer Classification](https://mlsanity.com/paper/2509.21341/) (2025)

## Abstract (arXiv)

This study presents domain-informed genetic superposition programming (DIGSP), a symbolic regression framework tailored for engineering systems governed by separable physical mechanisms. DIGSP partitions the input space into domain-specific feature subsets and evolves independent genetic programming (GP) populations to model material-specific effects. Early evolution occurs in isolation, while ensemble fitness promotes inter-population cooperation. To enable symbolic superposition, an adaptive hierarchical symbolic abstraction mechanism (AHSAM) is triggered after stagnation across all populations. AHSAM performs analysis of variance- (ANOVA) based filtering to identify statistically significant individuals, compresses them into symbolic constructs, and injects them into all populations through a validation-guided pruning cycle. The DIGSP is benchmarked against a baseline multi-gene genetic programming (BGP) model using a dataset of steel fiber-reinforced concrete (SFRC) beams. Across 30 independent trials with 65% training, 10% validation, and 25% testing splits, DIGSP consistently outperformed BGP in training and test root mean squared error (RMSE). The Wilcoxon rank-sum test confirmed statistical significance (p < 0.01), and DIGSP showed tighter error distributions and fewer outliers. No significant difference was observed in validation RMSE due to limited sample size. These results demonstrate that domain-informed structural decomposition and symbolic abstraction improve convergence and generalization. DIGSP offers a principled and interpretable modeling strategy for systems where symbolic superposition aligns with the underlying physical structure.