Second order extended ensemble Kalman filter with stochastically perturbed innovation for initializing artificial neural network weights

Artificial neural networks are widely applied in solving non-linear state-space dynamic models, yet the challenge of inaccurate initial weights remains a critical bottleneck. Weight initialization methods significantly influence convergence speed and model efficiency. While conventional approaches such as random initialization and filtering techniques are commonly used, the Bayesian method—though highly accurate—suffers from the computational burden of inverting highdimensional matrices. This study has developed a novel solution: the Second Order Extended Ensemble Filter with Perturbed Innovation (SoEEFPI). Developed from a second-order Taylor expansion of the stochastically perturbed KushnerStratonovich equation, SoEEFPI provides a tractable numerical solution to the inverse covariance matrix problem. Validation is conducted using the Lorenz63 system, comparing SoEEFPI’s performance to that of the Kalman-Bucy Filter (SoEKBF) and the First Order Extended Ensemble Filter (FoEEF) in MATLAB. Furthermore, SoEEFPI is employed to initialize neural network weights, yielding a new model whose convergence time, RMSE, and epoch count are evaluated. Results demonstrate improved convergence efficiency and accuracy, positioning SoEEFPI as a robust alternative for neural network initialization.