Bootstrap-Driven Adaptive Resampling for Enhanced Solutions of Second-Order Differential Equations in RLC Circuits Using PINNs

Physics-informed neural networks (PINNs) offer a flexible framework for solving differential equations using physical constraints and data. This study focuses on second-order Resistor–Inductor–Capacitor (RLC) circuit equations under underdamped conditions, where accurate modeling of small-amplitude oscillations is challenging. We introduce a bootstrap-driven adaptive resampling mechanism to enhance the effectiveness of the residual-based adaptive refinement (B-RAR) strategy. By integrating bootstrap perturbations and transfer initialization, our method improves convergence and robustness across both forward and inverse problems. Experiments show that the proposed method achieves precise voltage prediction and accurate parameter identification under noisy and limited data. Comparative evaluations across five sampling strategies—Grid, Latin hypercube, Halton, Residual-based adaptive distribution (RAD), and Residual-based adaptive refinement (RAR), highlight the critical role of bootstrap-enhanced resampling in improving the performance of PINN training for second-order differential equations.