Hybrid evolutionary meta-optimization assisted by recurrent neural networks for interpretable parametric symbolic models

Abstract

The modeling of complex nonlinear systems poses persistent challenges for evolutionary optimization due to high-dimensional search spaces, fragile convergence behavior, and the difficulty of balancing exploration and exploitation under computational constraints. To address these limitations, this study investigated a hybrid evolutionary meta-optimization strategy assisted by recurrent neural networks, designed to guide and stabilize the search process during the identification of analytical models. The proposed framework integrates symbolic structure discovery with continuous parametric refinement, enabling the simultaneous optimization of coefficients and real-valued exponents within an evolutionary setting. A recurrent neural network was embedded in the meta-optimization loop to adaptively influence the evolutionary dynamics, improving convergence stability and search efficiency while preserving structural diversity. Comprehensive search trajectories were recorded and subsequently analyzed using Shapley Additive Explanations, allowing the association of optimized parameters with dominant physical mechanisms. The method was evaluated on synthetic benchmarks, electromechanical systems, thermodynamic maps, and physicochemical surfaces, consistently preserving global morphological features and structural coherence. In all cases, stable generalization behavior was observed, with normalized relative errors typically of the order of and structural similarity indices exceeding 0.85, along with a statistically consistent separation from reference methods. The results demonstrate that neural-assisted evolutionary meta-optimization constitutes a viable strategy for improving convergence robustness and analytical model discovery in complex system identification problems.