Extended Kalman Filter Informed Neural Network for discrete-time system identification and state reconstruction

This paper presents a discrete-time framework for parameter identification and state reconstruction of stochastic nonlinear systems with additive noise. Specifically, we build on the Physics-Informed Neural Network (PINN) framework and integrate a discrete-time Extended Kalman Filter (EKF) to manage stochastic noise. The EKF serves as the information model for the neural network, complemented by the likelihood function of the output innovation sequence to enhance accuracy. Numerical simulations on the Chialvo oscillator demonstrate the effectiveness of the proposed approach in handling noisy and nonlinear system dynamics.