Deep Switching Koopman Networks: Discovery of Switching Dynamic Regimes in Industrial Systems

Abstract

Reliable modeling of non-stationary multivariate time series, particularly those arising in industrial monitoring, requires capturing the dynamics that govern sequential observations. Existing CNN- and Transformer-based classifiers often rely on stationary discriminative patterns and therefore do not explicitly represent transitions among operating regimes. To address this limitation, we introduce the Deep Switching Koopman Network (DSKN), which integrates Koopman operator theory with a Mixture of Experts (MoE) architecture to represent switching nonlinear dynamics. DSKN lifts observations into a latent space and combines two core designs: a spectrumaware router that identifies frequency-domain regime signatures, and a Koopman Expert Bank that approximates local linear evolution. A composite objective regularizes the latent trajectories through classification, reconstruction, and dynamical consistency losses. Empirical evaluations on representative UEA multivariate benchmarks show that DSKN achieves strong classification performance while providing operator-theoretic interpretability through learned Koopman spectra and transparent transition logic. The source code will be released on GitHub.