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.

Retrieval-Augmented Generation (RAG) has become a foundational component of modern AI systems, yet it introduces significant privacy risks by exposing user queries to service providers. To address this, we introduce PIR-RAG, a practical system for privacy-preserving RAG. PIR-RAG employs a novel architecture that uses coarse-grained semantic clustering to prune the search space, combined with a fast, lattice-based Private Information Retrieval (PIR) protocol. This design allows for the efficient retrieval of entire document clusters, uniquely optimizing for the end-to-end RAG workflow where full document content is required. Our comprehensive evaluation against strong baseline architectures, including graph-based PIR and Tiptoe-style private scoring, demonstrates PIR-RAG's scalability and its superior performance in terms of "RAG-Ready Latency"-the true end-to-end time required to securely fetch content for an LLM. Our work establishes PIR-RAG as a viable and highly efficient solution for privacy in large-scale AI systems.