Explainable quantum-compressed machine learning for complex fluid flows

2026-07-23

AI Summary

This work addresses the challenge of balancing interpretability and expressive power in surrogate models for complex fluid simulations by proposing a Quantum Compressed Machine Learning (QCML) framework. QCML employs structured quantum circuits to construct unitary propagators, compressing conventional models with 520,000 parameters down to no more than eight—approaching the parameter scale of physical constitutive relations. The propagator spectra are strictly confined to the unit circle, ensuring long-term numerical stability and endowing phase angles with clear physical meaning. In benchmark tests on turbulent channel flow and patient-specific cardiovascular hemodynamics, QCML matches the accuracy of classical models in predicting pressure spectra, pressure drop, and wall shear stress, while maintaining stability in autoregressive roll-out predictions. This represents the first unified achievement of high expressivity, interpretability, and numerical stability in surrogate modeling for fluid dynamics.

Abstract

Machine-learning surrogates of physical systems face a paradox: explainable models facing the challenge of expressivity to capture complex nonlinear flows, whereas expressive deep surrogates match high-fidelity simulations only through massive parameterisations that turn the learned dynamics into a black box. Here, we introduce quantum-compressed machine learning (QCML), which resolves this tension by compressing the latent propagator of a flow surrogate from $524{,}288$ trainable parameters to no more than $8$. This parameter reduction brings the learned dynamical law to the parameter scale of a physical constitutive relation rather than a black-box neural network, making the surrogate directly interpretable and controllable without sacrificing expressivity. The compression is realised by a structured quantum circuit whose unitary propagator constrains the latent spectrum to the unit circle exactly and by construction, replacing exponential error growth with linear accumulation over autoregressive rollouts. Classical regularisation only approximates this constraint: even a quantum-inspired classical baseline penalised towards unitarity collapses within one Lyapunov time on turbulent channel flow, whereas QCML remains stable over the full rollout. Shared phase and coupling angles parameterising the circuit correspond directly to modal frequencies and inter-mode interactions, giving the learned dynamics a physical interpretation in spectral space. On two patient-specific cardiovascular benchmarks, the structured QCML propagator matches the predictive accuracy of its classical counterpart on surface pressure spectra, pressure drop, and wall shear stress. These results establish QCML as a working component of scientific machine learning and a concrete contribution towards practical quantum advantage in real-world prediction.

Problem

• explainable machine learning
• complex fluid flows
• expressivity
• black-box models
• scientific machine learning

Innovation

• quantum-compressed machine learning
• explainable AI
• fluid dynamics
• unitary propagator
• scientific machine learning