Quantum machine learning for efficient reduced order modelling of turbulent flows

TL;DR

This paper introduces a hybrid quantum-classical framework combining quantum proper orthogonal decomposition and quantum-enhanced deep kernel learning to enable faster and more accurate turbulence prediction, demonstrating significant improvements over classical methods.

Contribution

The paper presents a novel hybrid quantum-classical approach for turbulence modeling that integrates quantum eigenvalue decomposition with quantum-enhanced kernel learning, advancing quantum fluid dynamics modeling.

Findings

Achieved faster-than-real-time turbulence prediction.

Improved predictive accuracy at reduced model ranks.

Reduced parameter counts and increased training speed.

Abstract

Accurately predicting turbulent flows remains a central challenge in fluid dynamics due to their high dimensionality and intrinsic nonlinearity. Recent developments in quantum algorithms and machine learning offer new opportunities for overcoming the computational barriers inherent in turbulence modeling. Here we present a new hybrid quantum-classical framework that enables faster-than-real-time turbulence prediction by integrating machine learning, quantum computation, and fluid dynamics modeling, in particular, the reduced-order modeling. The novel framework combines quantum proper orthogonal decomposition (QPOD) with a quantum-enhanced deep kernel learning (QDKL) approach. QPOD employs quantum circuits to perform efficient eigenvalue decomposition for low-rank flow reconstruction, while QDKL exploits quantum entanglement and nonlinear mappings to enhance kernel expressivity and dynamic prediction accuracy. The new method is demonstrated on three benchmark turbulent flows, our architecture achieves significantly improved predictive accuracy at reduced model ranks, with training speeds up to 10 times faster and parameter counts reduced by a factor of 1/N compared to classical counterparts, where N is the input dimensionality. Although constrained by current noisy intermediate-scale quantum (NISQ) hardware, our results demonstrate the potential of quantum machine learning to transform turbulence simulation and lay a solid foundation for scalable, real-time quantum fluid modeling in future quantum computers.