Reduced-order modeling of nonlinear multiscale industrial systems via sparse regression in latent representations

Data-driven modeling of nonlinear industrial processes is often complicated by heterogeneous temporal dynamics, measurement noise, and fixed-rate data acquisition. Under such conditions, direct regression on raw time-series data may become sensitive to sampling imbalance and fast transient behavior, leading to degraded predictive performance. This work proposes a structured reduced-order modeling framework for constructing compact and numerically stable predictive surrogates. The approach integrates adaptive resampling to redistribute temporal information, spline-based smoothing for stable derivative estimation, delay embedding to incorporate short-term temporal structure, kernel-based dimensionality reduction to extract dominant patterns, and sparse regression in a latent coordinate space to obtain parsimonious dynamical models. Within this framework, sparsity is used primarily to control model complexity in the reduced representation rather than to recover explicit governing equations. The method is evaluated on two benchmark reactor systems and a real grinding-classification process using chronological train/test splits and multi-step rollout prediction. The results indicate that the proposed approach can improve predictive robustness and numerical stability compared with direct sparse regression and its partial variants, particularly in the presence of multiscale temporal behavior and moderate measurement noise. The framework provides a practical strategy for predictive reduced-order modeling under realistic industrial data constraints. Its design emphasizes stability and compactness of the learned dynamics, while acknowledging that the resulting models are defined in a latent representation and are not intended as exact reconstructions of physical governing equations.