# Quantum-Informed Machine Learning for Predicting Spatiotemporal Chaos with Practical Quantum Advantage

arXiv: https://arxiv.org/abs/2507.19861 · HTML: https://mlsanity.com/paper/2507.19861/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 134 references that are in the map.
- First posted on arXiv 26 Jul 2025.

## Builds on (most cited first, 30 of 34)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Learning to Prompt for Vision-Language Models](https://mlsanity.com/paper/2109.01134/) (2021)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [A Survey on Evaluation of Large Language Models](https://mlsanity.com/paper/2307.03109/) (2023)
- [Vision-Language Models for Vision Tasks: A Survey](https://mlsanity.com/paper/2304.00685/) (2023)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [PDE-Net: Learning PDEs from Data](https://mlsanity.com/paper/1710.09668/) (2017)
- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers](https://mlsanity.com/paper/2308.05732/) (2023)
- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [Quantum advantage in learning from experiments](https://mlsanity.com/paper/2112.00778/) (2021)
- [Quantum generative adversarial networks](https://mlsanity.com/paper/1804.08641/) (2018)
- [Quantum Natural Gradient](https://mlsanity.com/paper/1909.02108/) (2019)
- [Differentiable Learning of Quantum Circuit Born Machine](https://mlsanity.com/paper/1804.04168/) (2018)
- [Towards Stability of Autoregressive Neural Operators](https://mlsanity.com/paper/2306.10619/) (2023)
- [Scientific multi-agent reinforcement learning for wall-models of turbulent flows](https://mlsanity.com/paper/2106.11144/) (2021)
- [Out-of-distribution generalization for learning quantum dynamics](https://mlsanity.com/paper/2204.10268/) (2022)
- [Learning Dissipative Dynamics in Chaotic Systems](https://mlsanity.com/paper/2106.06898/) (2021)
- [Enhancing Generative Models via Quantum Correlations](https://mlsanity.com/paper/2101.08354/) (2021)
- [Shadows of quantum machine learning](https://mlsanity.com/paper/2306.00061/) (2023)
- [DySLIM: Dynamics Stable Learning by Invariant Measure for Chaotic Systems](https://mlsanity.com/paper/2402.04467/) (2024)
- [Learning and Inference on Generative Adversarial Quantum Circuits](https://mlsanity.com/paper/1808.03425/) (2018)
- [Enabling Multi-programming Mechanism for Quantum Computing in the NISQ Era](https://mlsanity.com/paper/2102.05321/) (2021)
- [Quantum autoencoders via quantum adders with genetic algorithms](https://mlsanity.com/paper/1709.07409/) (2017)
- [Towards a theory of machine learning](https://mlsanity.com/paper/2004.09280/) (2020)
- [Experimental Implementation of a Quantum Autoencoder via Quantum Adders](https://mlsanity.com/paper/1807.10643/) (2018)
- [Machine learning for modelling unstructured grid data in computational physics: a review](https://mlsanity.com/paper/2502.09346/) (2025)

## Built on by (most cited first, 7 of 7)

- [Uni-Flow: a unified autoregressive-diffusion model for complex multiscale flows](https://mlsanity.com/paper/2602.15592/) (2026)
- [AI Needs Physics More Than Physics Needs AI](https://mlsanity.com/paper/2512.16344/) (2025)
- [Fast-Forward Lattice Boltzmann: Learning Kinetic Behaviour with Physics-Informed Neural Operators](https://mlsanity.com/paper/2509.22411/) (2025)
- [Quantum Generative Models for Computational Fluid Dynamics: A First Exploration of Latent Space Learning in Lattice Boltzmann Simulations](https://mlsanity.com/paper/2512.22672/) (2025)
- [Quantum Statistical Memory Advantage Reveals Predictive Structure in Chaotic Invariant Measures](https://mlsanity.com/paper/2606.13422/) (2026)
- [Quantum simulation of real-world nonlinear dynamics via Koopman method](https://mlsanity.com/paper/2607.07338/) (2026)
- [Explainable quantum-compressed machine learning for complex fluid flows](https://mlsanity.com/paper/2607.21688/) (2026)

## Abstract (arXiv)

We introduce a quantum-informed machine learning (QIML) framework for modelling the long-term behaviour of high-dimensional chaotic systems. QIML combines a one-time, offline-trained quantum generative model with a classical autoregressive predictor for spatiotemporal field generation. The quantum model learns a quantum prior (Q-Prior) that guides the representation of small-scale interactions and improves the modelling of fine-scale dynamics. We evaluate QIML on the Kuramoto-Sivashinsky equation, two-dimensional Kolmogorov flow, and the three-dimensional turbulent channel flow used as a realistic inflow condition. Across these systems, QIML improves predictive distribution accuracy by up to 17.25% and full-spectrum fidelity by up to 29.36% relative to classical baselines. For turbulent channel inflow, the Q-Prior is trained on a superconducting quantum processor and proves essential: without it, predictions become unstable, whereas QIML produces physically consistent long-term forecasts that outperform leading PDE solvers. Beyond accuracy, QIML offers a memory advantage by compressing multi-megabyte datasets into a kilobyte-scale Q-Prior, enabling scalable integration of quantum resources into scientific modelling.