Multi-objective structural risk minimization in multi-gene genetic programming for mathematical modeling of battery digital twin

Battery digital twins (BDT) require models that are both accurate and interpretable to ensure reliable monitoring and control in practical applications. Genetic programming (GP) provides human-interpretable models. However, fitness principles (FPs) often suffer from overfitting and weak generalization under the nonlinear behavior and dynamic operating conditions of lithium-ion (Li-ion) batteries. Structural Risk Minimization (SRM) partially addresses these issues, but it remains limited by its single-objective nature. To address this limitation, a novel FP, Multi-Objective Structural Risk Minimization (MOSRM) has been proposed. The proposed FP introduces an adaptive trade-off between predictive error and model complexity, which guides algorithm to select robust and interpretable symbolic equations. The framework is validated on dynamic stress test (DST) profiles for state-of-charge (SoC), state-of-energy (SoE), state-of-power (SoP) estimation as well as a theoretical battery degradation model. Results show that MOSRM improves predictive accuracy by more than 60% on unscaled data, reduces estimation error by approximately 30%, and decreases model complexity by over 75% compared to existing FPs. These findings establish MOSRM as a significant advancement in symbolic modeling for BDTs, with potential extension to diverse chemistries, real-time degradation, and varied operating conditions.