# Explainable quantum-compressed machine learning for complex fluid flows

arXiv: https://arxiv.org/abs/2607.21688 · HTML: https://mlsanity.com/paper/2607.21688/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 71 references that are in the map.
- First posted on arXiv 23 Jul 2026.

## Builds on (most cited first, 21 of 21)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Restormer: Efficient Transformer for High-Resolution Image Restoration](https://mlsanity.com/paper/2111.09881/) (2021)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [Quantum-enhanced machine learning](https://mlsanity.com/paper/1610.08251/) (2016)
- [On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operator](https://mlsanity.com/paper/1703.04680/) (2017)
- [Towards Stability of Autoregressive Neural Operators](https://mlsanity.com/paper/2306.10619/) (2023)
- [Universal Approximation Property of Quantum Machine Learning Models in Quantum-Enhanced Feature Spaces](https://mlsanity.com/paper/2009.00298/) (2020)
- [Learning Dissipative Dynamics in Chaotic Systems](https://mlsanity.com/paper/2106.06898/) (2021)
- [Kilometer-Scale Convection Allowing Model Emulation using Generative Diffusion Modeling](https://mlsanity.com/paper/2408.10958/) (2024)
- [Plasma Surrogate Modelling using Fourier Neural Operators](https://mlsanity.com/paper/2311.05967/) (2023)
- [Quantum-Informed Machine Learning for Predicting Spatiotemporal Chaos with Practical Quantum Advantage](https://mlsanity.com/paper/2507.19861/) (2025)
- [Uni-Flow: a unified autoregressive-diffusion model for complex multiscale flows](https://mlsanity.com/paper/2602.15592/) (2026)
- [Development and performance of a HemeLB GPU code for human-scale blood flow simulation](https://mlsanity.com/paper/2202.11770/) (2022)
- [A Parameter-Efficient Quantum Anomaly Detection Method on a Superconducting Quantum Processor](https://mlsanity.com/paper/2412.16867/) (2024)
- [On the Reliability of AI Methods in Drug Discovery: Evaluation of Boltz-2 for Structure and Binding Affinity Prediction](https://mlsanity.com/paper/2603.05532/) (2026)

## Abstract (arXiv)

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.