Joint State Prediction and Parameter Estimation in a Nonlinear Oscillator using Physics Inf armed LSTM

Abstract

Modeling nonlinear dynamical systems from data remains a challenging problem, especially when measurements are noisy or limited. Purely data-driven models fail to follow the underlying physical laws of the system and result in poor gen­eralization along with large data requirements. We use a hybrid approach, the Physics Informed LSTM (PI-LSTM) network, for parameter estimation of a partially known physics-based system in addition to state prediction. A nonlinear oscillator with an unknown damping factor is used for modeling through PI-LSTM network. The results show that PI-LSTM achieves accurate state prediction in addition to reliable parameter estimation for different levels of nonlinearity in the system based on damping factor, compared to standard DNN and LSTM models. We also make a baseline comparison with Extended Kalman Filter (EKF) with different initial damping factor guesses for each system, and PI-LSTM shows consistent estimation as compared to EKF even as system nonlinearity increases. This framework establishes a physics-informed digital twin of the nonlinear oscillator, enabling simultaneous state prediction and adaptive parameter estimation under time-varying dynamics.