Optimization of Neural Network Architectures for Dynamic System Prediction Using LSTM-Based NODE and Water Wave Optimization

Abstract

Scientific computing faces challenges in accurately predicting complex dynamic systems due to initial conditions and non-stationary behavior, with rational neural networks often requiring human tuning. To overcome these limitations, this research proposes a Long Short-Term Neural Ordinary Differential Water Wave Optimization (LST-NODE-WWO) for dynamic system prediction. The goal is to automatically discover the optimal network architecture that adapts to the dynamics of each system. The proposed methodology includes five steps: collection of time-series data (e.g., position and velocity), preprocessing with z-score normalization for temporal consistency, and multi-resolution feature extraction using the discrete wavelet transform (DWT). The hybrid model integrates LSTM for capturing temporal dependencies, NODE as a variational differential equation (VDE) for continuous-time modeling, and WWO as a metaheuristic strategy for structure and hyperparameter optimization. This fusion enables the system to learn both physical consistency and long-range temporal patterns. Experimental results on a coupled damped harmonic oscillator dataset show that the LST-NODE-WWO outperforms baseline models. Experimental evaluations using a coupled damped harmonic oscillator dataset exhibit that the suggested model outperforms baseline approaches. The LST-NODE-WWO achieves a test MAE of 0.0914 and RMSE of 0.1298 for Oscillator 1, and a test MAE of 0.0213 and RMSE of 0.0301 for Oscillator 2, significantly improving prediction accuracy. Hence, LST-NODE-WWO offers a robust solution for modeling nonlinear, time-varying dynamic systems with minimal manual intervention.