RAL-MoE-ROM: Hierarchical Mixture-of-Experts for Regime-Adaptive Reduced-Order Model

Reduced-order models (ROMs) approximate high-dimensional dynamical systems using a small number of state variables. However, their predictive accuracy can deteriorate when parameter changes lead to different dynamical regimes. Different regimes may require different reduced representations and dynamics, making it difficult for a single model to remain accurate across the full parameter range. We introduce RAL-MoE-ROM, a hierarchical mixture-of-experts framework with two levels: regime-local specialists and cross-regime routing with fusion. At the first level, each local model, called a specialist, uses a structured sparse mixture of experts to improve its reduced dynamics and is trained through multi-step autonomous rollouts. At the second level, a parameter-only outer router provides preferences within prescribed adjacent specialist pairs, supporting Top-1 selection or history-conditioned specialists fusion. When two specialists are selected, a learned gate uses the initial physical history to combine their reconstructed fields. Across three flow benchmarks spanning steady, Hopf-onset, and periodic regimes, the local specialists provide accurate autonomous predictions, while cross-regime routing further improves prediction in the evaluated regime overlaps.