Data-driven and physics-guided neural approaches for LCR circuit modeling: a comparative analysis

This study compares a data-driven recurrent (RNN–LSTM) predictor with physics-guided neural networks for the forced charge response of a series LCR circuit whose resistive term carries a Caputo fractional memory of order 0.6. The reference trajectory is generated by an explicit Sumudu transform–Adomian decomposition recursion. In an independent recomputation, the magnitude of component 50 on the 1001-point grid is \(3.43018× 10⁻²⁰\) , and the maximum residual under extended-precision evaluation is approximately \(1.69974× 10⁻⁹\) . A product-trapezoidal solver exhibits second-order convergence. With a chronological split before sequence windowing, the reported experiments evaluate one-step and autonomous LSTM prediction, a data-only network, networks penalized by an integer-order residual, and a fractional physics-informed network (fPINN). Across five seeds, teacher-forced LSTM prediction gives a test charge RMSE of \(0.01537± 0.00369\) , whereas autonomous rollout gives \(0.16095± 0.04806\) . The fPINN with the residual enforced over the whole interval gives \(2.15109× 10⁻⁴± 2.03608× 10⁻⁴\) , compared with \(0.05414± 1.84137× 10⁻⁴\) for the integer-order residual. The mean test RMSEs of the three feedforward variants without a residual on the test interval range from 0.39211 to 0.92453. These differences reflect the information and prior knowledge supplied to each model rather than an intrinsic ranking of architectures. The data are synthetic and noise-free, and only one parameter set and a short extrapolation interval are studied.