Hierarchical Cross-State Mamba With Hyperbolic Fusion for Mach Number Forecasting of Intermittent Wind Tunnels

Abstract

Accurate multi-step forecasting of the test-section Mach number is important for real-time process monitoring and may provide predictive information for future control and diagnostic applications in intermittent wind tunnels. However, forecasting complex aerodynamic responses from heterogeneous historical actuator commands and operating-state variables remains challenging because of long mechanical inertia, rapid transient fluctuations, and error accumulation over extended prediction horizons. Although state space models, such as Mamba, provide linear-time sequence modeling, their effectiveness on wind tunnel are still challenging. To this end, this paper proposes the $H$ ierarchical $C$ ross- $S$ tate Mamba with hyperbolic fusion (HCS-Mamba). First, a dynamic multi-scale frequency decoupling module decomposes the multivariate representation into slowly varying trends, intermediate-frequency variations, and high-frequency residuals, thereby reducing cross-frequency interference and facilitating scale-specific feature extraction. Second, a hierarchical cascaded modulation based cross-state modulation mechanism is designed to introduce directed cross-scale conditioning, allowing low-frequency representations to adaptively modulate the extraction of intermediate- and high-frequency features. Finally, a hyperbolic gating fusion module maps multi-scale representations into a Poincaré ball and performs gating-weighted fusion in its ambient coordinates, providing a geometry-aware alternative to direct Euclidean fusion and encouraging the representation of hierarchical relations. Extensive experiments on real-world datasets from a 2.4-meter intermittent transonic wind tunnel demonstrate that HCS-Mamba outperforms ten state-of-the-art baselines. The experiments are conducted in an open-loop forecasting setting, where only historical observations and control commands are available to the model. Note to Practitioners—This study focuses on accurate and computationally efficient open-loop multi-step forecasting of the test-section Mach number in an intermittent transonic wind tunnel. The proposed HCS-Mamba model uses historical Mach number measurements together with historical actuator and operating-state variables to predict future Mach number trajectories. The current formulation does not use future planned actuator commands. The experimental results demonstrate the model’s forecasting accuracy, long-horizon stability, and low computational overhead under offline open-loop evaluation. These properties make the model potentially useful as a predictive component for real-time process monitoring and future control-oriented systems. Incorporating planned command trajectories into the system and integrating the predictor into the closed-loop controller is considered a future research direction.