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

2025-09-19

AI Summary

Modeling multi-mechanism coupled engineering systems—such as steel fiber-reinforced concrete beams—poses significant challenges for symbolic regression. To address this, we propose a domain-knowledge-guided Genetic Superposition Programming (GSP) framework. GSP ensures physical consistency through physics-driven input-space decomposition and symbolic superposition. It further incorporates an Adaptive Hierarchical Symbolic Abstraction Mechanism (AHSAM), ANOVA-based feature screening, and validation-guided pruning to enable multi-population coevolution and statistically significant symbolic compression and fusion. In 30 independent experiments, GSP significantly outperforms multi-gene genetic programming baselines: it achieves lower training and test RMSE (p < 0.01), tighter error distribution, and superior generalization. The framework thus enhances interpretability, convergence reliability, and modeling accuracy of symbolic regression for complex engineering systems.

Technology Category

• Cognitive Modeling & Cognitive Systems: Symbolic Representations
• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Neuro-Symbolic Learning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

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.

Problem

• Develops symbolic regression for engineering systems with separable mechanisms
• Partitions input space to model material-specific effects independently
• Enables symbolic superposition through adaptive hierarchical abstraction

Innovation

• Domain-informed genetic programming partitions input space
• Adaptive symbolic abstraction compresses significant individuals
• Hierarchical superposition mechanism enables interpretable modeling