Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Quantum machine learning-based parameterisation for atmospheric boundary layer turbulence

Lena Hannah Dogra, Janis Klamt, Veronika Eyring, Mierk Schwabe

Published Aug 5, 2026• 0 citations
Publisher

Abstract

The advent of quantum computing has opened unprecedented promises to tackle humanity' s most pressing challenges: computationally intractable problems might come within reach through quantum advantages. It is imperative for the field of climate modeling to explore possible uses of this emerging technology. Global climate models have successfully projected different future scenarios, but the spread in projections remains large, with subgrid-scale parameterizations being the main origin of these uncertainties. While machine learning models improve these parameterizations, quantum computing could bring decisive further improvements. Atmospheric turbulence affects the climate because it determines the rates of exchange of heat, moisture, and momentum between the Earth surface and the atmosphere, but has been especially hard to predict and model. Here, we develop a quantum machine learning-based subgrid-scale parameterization for the turbulent vertical heat flux. The training data are coarse-grained data from large-eddy-simulations of a dry convective boundary layer in an idealized setup without topography. Training various quantum and classical neural network models, we find that quantum models based on parametrized circuits with just 2 or 3 qubits achieve accuracies similar to classical models with the same number of trainable parameters. In contrast, the Smagorinsky closure applied to the coarse target resolution deviates strongly from the highly resolved flux. Both our quantum and classical models generalize well to unseen atmospheric conditions. Finally, the feature importances in our quantum models are on average more stable with respect to the random initial parameters, highlighting the possibility to exploit quantum advantages in climate and Earth system models.

DOI
10.22541/essoar.15007068/v1

Related papers

Quantum neural networks for cloud cover parameterizations in climate models

Lorenzo Pastori, Arthur Grundner, Veronika Eyring +1 more

Long-term climate projections require running global Earth system models on timescales of hundreds of years and have relatively coarse resolution (from 40 to 160 km in the horizontal) due to their high computational costs. Unresolved subgrid-scale processes, such as clouds, are described in a semi-empirical manner by so called parameterizations, which are a major source of uncertainty in climate projections. Machine learning models trained on short high-resolution climate simulations are promising candidates to replace conventional parameterizations. In this work, we explore the potential of quantum machine learning (QML), and in particular quantum neural networks (QNNs), to develop cloud cover parameterizations. QNNs differ from their classical counterparts, and their potentially high expressivity turns them into promising tools for accurate data-driven schemes to be used in climate models. We perform an extensive comparative analysis between several QNNs and classical neural networks (NNs), by training both ansatzes on data coming from high-resolution simulations with the ICOsahedral Non-hydrostatic weather and climate model (ICON). Our results show that the overall performance of the investigated QNNs is comparable to that of classical NNs of similar size, i.e., with the same number of trainable parameters, with both ansatzes outperforming standard parameterizations used in climate models. Our study includes an analysis of the generalization ability of the models as well as the geometrical properties of their optimization landscape. We also investigate the effects of finite sampling noise, and show that the training and the predictions of the QNNs are stable even in this noisy setting. These results demonstrate the applicability of QML to learn meaningful patterns in climate data, and are thus relevant for a broad range of problems within the climate modeling community.

arXiv:2502.10131•Machine Learning Earth•Feb 24, 2026•2 citations

Quantum Machine Learning Parameterization of the Boundary Layer Height

Juan de Dios Rodriguez Garrido

Accurate representation of the atmospheric Boundary Layer Height (BLH) remains challenging in numerical weather and climate modeling, especially when turbulent processes occur at scales below the model grid resolution. This thesis investigates whether Quantum Machine Learning (QML) models can be used to build compact BLH parameterizations from coarse-grained ICON-XPP atmospheric columns. The work develops a complete offline pipeline for QML-compatible BLH prediction. Starting from high-dimensional atmospheric profiles, several dimensionality reduction and feature-engineering strategies are evaluated to obtain compact representations suitable for Quantum Neural Networks (QNNs). Two complementary 8-dimensional input representations are selected: SAE8D, a supervised autoencoder latent space optimized for predictive performance, and FtEng8D, a physically interpretable feature-engineered space based on stability, humidity-gradient and wind-shear diagnostics. Several QNN architectures are then trained and compared against parameter-matched classical Multi-Layer Perceptron (MLP) baselines. The QNN experiments analyze the effect of circuit depth, ansatz family, readout, data re-uploading and training-set size. The final full-dataset evaluation shows that the selected QNN remains competitive with a fixed MLP under the same parameter budget. The MLP achieves slightly better average RMSE, R2 and MAE, while the QNN shows lower seed-to-seed variability and a bias closer to zero. The error analysis reveals that the final QNN performs best in the dominant low and moderate BLH regimes, but systematically underestimates rare deep-boundary-layer cases. SHAP-based interpretability analysis indicates that the QNN mainly relies in physically meaningful thermodynamic, stability and humidity-gradient features, supporting the plausibility of the learned parameterization. Overall, the results do not demonstrate a systematic quantum advantage over classical machine learning. However, they show that QML-compatible BLH parameterization is feasible when high-dimensional atmospheric columns are first compressed into carefully designed low-dimensional representations. The proposed QNN therefore provides a compact and physically motivated prototype for future quantum-compatible atmospheric parameterizations, with future work focusing on richer interpretable feature spaces, rare high-BLH regimes and online testing in ICON-XPP.

•Jul 2, 2026•0 citations

Potential of quantum scientific machine learning applied to weather modelling

Ben Jaderberg, Antonio A. Gentile, Atiyo Ghosh +5 more

In this work we explore how quantum scientific machine learning can be used to tackle the challenge of weather modelling. Using parameterised quantum circuits as machine learning models, we consider two paradigms: supervised learning from weather data and physics-informed solving of the underlying equations of atmospheric dynamics. In the first case, we demonstrate how a quantum model can be trained to accurately reproduce real-world global stream function dynamics at a resolution of 4°. We detail a number of problem-specific classical and quantum architecture choices used to achieve this result. Subsequently, we introduce the barotropic vorticity equation (BVE) as our model of the atmosphere, which is a $3^{\text{rd}}$ order partial differential equation (PDE) in its stream function formulation. Using the differentiable quantum circuits algorithm, we successfully solve the BVE under appropriate boundary conditions and use the trained model to predict unseen future dynamics to high accuracy given an artificial initial weather state. Whilst challenges remain, our results mark an advancement in terms of the complexity of PDEs solved with quantum scientific machine learning.

arXiv:2404.08737•Apr 12, 2024•1 citation

Opportunities and challenges of quantum computing for climate modelling

Mierk Schwabe, Lorenzo Pastori, Inés de Vega +6 more

Adaptation to climate change requires robust climate projections, yet the uncertainty in these projections performed by ensembles of Earth system models (ESMs) remains large. This is mainly due to uncertainties in the representation of subgrid-scale processes such as turbulence or convection that are partly alleviated at higher resolution. New developments in machine learning-based hybrid ESMs demonstrate great potential for systematically reduced errors compared to traditional ESMs. Building on the work of hybrid (physics + AI) ESMs, we here discuss the additional potential of further improving and accelerating climate models with quantum computing. We discuss how quantum computers could accelerate climate models by solving the underlying differential equations faster, how quantum machine learning could better represent subgrid-scale phenomena in ESMs even with currently available noisy intermediate-scale quantum devices, how quantum algorithms aimed at solving optimisation problems could assist in tuning the many parameters in ESMs, a currently time-consuming and challenging process, and how quantum computers could aid in the analysis of climate models. We also discuss hurdles and obstacles facing current quantum computing paradigms. Strong interdisciplinary collaboration between climate scientists and quantum computing experts could help overcome these hurdles and harness the potential of quantum computing for this urgent topic.

arXiv:2502.10488•Feb 14, 2025•1 citation

Opportunities and challenges of quantum computing for climate modeling

Mierk Schwabe, Lorenzo Pastori, Inés de Vega +6 more

Abstract Adaptation to climate change requires robust climate projections, yet the uncertainty in these projections performed by ensembles of Earth system models (ESMs) remains large. This is mainly due to uncertainties in the representation of subgrid-scale processes such as turbulence or convection that are partly alleviated at higher resolution. New developments in machine learning-based hybrid ESMs demonstrate great potential for systematically reduced errors compared to traditional ESMs. Building on the work of hybrid (physics + AI) ESMs, we here discuss the additional potential of further improving and accelerating climate models with quantum computing. We discuss how quantum computers could accelerate climate models by solving the underlying differential equations faster, how quantum machine learning could better represent subgrid-scale phenomena in ESMs even with currently available noisy intermediate-scale quantum devices, how quantum algorithms aimed at solving optimization problems could assist in tuning the many parameters in ESMs, a currently time-consuming and challenging process, and how quantum computers could aid in the analysis of climate models. We also discuss hurdles and obstacles facing current quantum computing paradigms. Strong interdisciplinary collaboration between climate scientists and quantum computing experts could help overcome these hurdles and harness the potential of quantum computing for this urgent topic.

Environmental Data Science•Jan 1, 2025•12 citations

Potential of quantum scientific machine learning applied to weather modeling

Ben Jaderberg, Antonio A. Gentile, Atiyo Ghosh +5 more

In this paper we explore how quantum scientific machine learning can be used to tackle the challenge of weather modeling. Using parametrized quantum circuits as machine learning models, we consider two paradigms: supervised learning from weather data and physics-informed solving of the underlying equations of atmospheric dynamics. In the first case, we demonstrate how a quantum model can be trained to accurately reproduce real-world global stream function dynamics at a resolution of ${4}^{\ensuremath{\circ}}$. We detail a number of problem-specific classical and quantum architecture choices used to achieve this result. Subsequently, we introduce the barotropic vorticity equation (BVE) as our model of the atmosphere, which is a third-order partial differential equation (PDE) in its stream function formulation. Using the differentiable quantum circuits algorithm, we successfully solve the BVE under appropriate boundary conditions and use the trained model to predict unseen future dynamics to high accuracy given an artificial initial weather state. While challenges remain, our results mark an advancement in terms of the complexity of PDEs solved with quantum scientific machine learning.

Physical Review A•Nov 18, 2024•16 citations
The advent of quantum computing has opened unprecedented promises to tackle humanity' s most pressing challenges: computationally intractable problems might come within reach through quantum advantages. It is imperative for the field of climate modeling to explore possible uses of this emerging technology. Global climate models have successfully projected different future scenarios, but the spread in projections remains large, with subgrid-scale parameterizations being the main origin of these uncertainties. While machine learning models improve these parameterizations, quantum computing could bring decisive further improvements. Atmospheric turbulence affects the climate because it determines the rates of exchange of heat, moisture, and momentum between the Earth surface and the atmosphere, but has been especially hard to predict and model. Here, we develop a quantum machine learning-based subgrid-scale parameterization for the turbulent vertical heat flux. The training data are coarse-grained data from large-eddy-simulations of a dry convective boundary layer in an idealized setup without topography. Training various quantum and classical neural network models, we find that quantum models based on parametrized circuits with just 2 or 3 qubits achieve accuracies similar to classical models with the same number of trainable parameters. In contrast, the Smagorinsky closure applied to the coarse target resolution deviates strongly from the highly resolved flux. Both our quantum and classical models generalize well to unseen atmospheric conditions. Finally, the feature importances in our quantum models are on average more stable with respect to the random initial parameters, highlighting the possibility to exploit quantum advantages in climate and Earth system models.
Long-term climate projections require running global Earth system models on timescales of hundreds of years and have relatively coarse resolution (from 40 to 160 km in the horizontal) due to their high computational costs. Unresolved subgrid-scale processes, such as clouds, are described in a semi-empirical manner by so called parameterizations, which are a major source of uncertainty in climate projections. Machine learning models trained on short high-resolution climate simulations are promising candidates to replace conventional parameterizations. In this work, we explore the potential of quantum machine learning (QML), and in particular quantum neural networks (QNNs), to develop cloud cover parameterizations. QNNs differ from their classical counterparts, and their potentially high expressivity turns them into promising tools for accurate data-driven schemes to be used in climate models. We perform an extensive comparative analysis between several QNNs and classical neural networks (NNs), by training both ansatzes on data coming from high-resolution simulations with the ICOsahedral Non-hydrostatic weather and climate model (ICON). Our results show that the overall performance of the investigated QNNs is comparable to that of classical NNs of similar size, i.e., with the same number of trainable parameters, with both ansatzes outperforming standard parameterizations used in climate models. Our study includes an analysis of the generalization ability of the models as well as the geometrical properties of their optimization landscape. We also investigate the effects of finite sampling noise, and show that the training and the predictions of the QNNs are stable even in this noisy setting. These results demonstrate the applicability of QML to learn meaningful patterns in climate data, and are thus relevant for a broad range of problems within the climate modeling community.
Accurate representation of the atmospheric Boundary Layer Height (BLH) remains challenging in numerical weather and climate modeling, especially when turbulent processes occur at scales below the model grid resolution. This thesis investigates whether Quantum Machine Learning (QML) models can be used to build compact BLH parameterizations from coarse-grained ICON-XPP atmospheric columns. The work develops a complete offline pipeline for QML-compatible BLH prediction. Starting from high-dimensional atmospheric profiles, several dimensionality reduction and feature-engineering strategies are evaluated to obtain compact representations suitable for Quantum Neural Networks (QNNs). Two complementary 8-dimensional input representations are selected: SAE8D, a supervised autoencoder latent space optimized for predictive performance, and FtEng8D, a physically interpretable feature-engineered space based on stability, humidity-gradient and wind-shear diagnostics. Several QNN architectures are then trained and compared against parameter-matched classical Multi-Layer Perceptron (MLP) baselines. The QNN experiments analyze the effect of circuit depth, ansatz family, readout, data re-uploading and training-set size. The final full-dataset evaluation shows that the selected QNN remains competitive with a fixed MLP under the same parameter budget. The MLP achieves slightly better average RMSE, R2 and MAE, while the QNN shows lower seed-to-seed variability and a bias closer to zero. The error analysis reveals that the final QNN performs best in the dominant low and moderate BLH regimes, but systematically underestimates rare deep-boundary-layer cases. SHAP-based interpretability analysis indicates that the QNN mainly relies in physically meaningful thermodynamic, stability and humidity-gradient features, supporting the plausibility of the learned parameterization. Overall, the results do not demonstrate a systematic quantum advantage over classical machine learning. However, they show that QML-compatible BLH parameterization is feasible when high-dimensional atmospheric columns are first compressed into carefully designed low-dimensional representations. The proposed QNN therefore provides a compact and physically motivated prototype for future quantum-compatible atmospheric parameterizations, with future work focusing on richer interpretable feature spaces, rare high-BLH regimes and online testing in ICON-XPP.
In this work we explore how quantum scientific machine learning can be used to tackle the challenge of weather modelling. Using parameterised quantum circuits as machine learning models, we consider two paradigms: supervised learning from weather data and physics-informed solving of the underlying equations of atmospheric dynamics. In the first case, we demonstrate how a quantum model can be trained to accurately reproduce real-world global stream function dynamics at a resolution of 4°. We detail a number of problem-specific classical and quantum architecture choices used to achieve this result. Subsequently, we introduce the barotropic vorticity equation (BVE) as our model of the atmosphere, which is a 3rd3^{\text{rd}}3rd order partial differential equation (PDE) in its stream function formulation. Using the differentiable quantum circuits algorithm, we successfully solve the BVE under appropriate boundary conditions and use the trained model to predict unseen future dynamics to high accuracy given an artificial initial weather state. Whilst challenges remain, our results mark an advancement in terms of the complexity of PDEs solved with quantum scientific machine learning.
Adaptation to climate change requires robust climate projections, yet the uncertainty in these projections performed by ensembles of Earth system models (ESMs) remains large. This is mainly due to uncertainties in the representation of subgrid-scale processes such as turbulence or convection that are partly alleviated at higher resolution. New developments in machine learning-based hybrid ESMs demonstrate great potential for systematically reduced errors compared to traditional ESMs. Building on the work of hybrid (physics + AI) ESMs, we here discuss the additional potential of further improving and accelerating climate models with quantum computing. We discuss how quantum computers could accelerate climate models by solving the underlying differential equations faster, how quantum machine learning could better represent subgrid-scale phenomena in ESMs even with currently available noisy intermediate-scale quantum devices, how quantum algorithms aimed at solving optimisation problems could assist in tuning the many parameters in ESMs, a currently time-consuming and challenging process, and how quantum computers could aid in the analysis of climate models. We also discuss hurdles and obstacles facing current quantum computing paradigms. Strong interdisciplinary collaboration between climate scientists and quantum computing experts could help overcome these hurdles and harness the potential of quantum computing for this urgent topic.
Abstract Adaptation to climate change requires robust climate projections, yet the uncertainty in these projections performed by ensembles of Earth system models (ESMs) remains large. This is mainly due to uncertainties in the representation of subgrid-scale processes such as turbulence or convection that are partly alleviated at higher resolution. New developments in machine learning-based hybrid ESMs demonstrate great potential for systematically reduced errors compared to traditional ESMs. Building on the work of hybrid (physics + AI) ESMs, we here discuss the additional potential of further improving and accelerating climate models with quantum computing. We discuss how quantum computers could accelerate climate models by solving the underlying differential equations faster, how quantum machine learning could better represent subgrid-scale phenomena in ESMs even with currently available noisy intermediate-scale quantum devices, how quantum algorithms aimed at solving optimization problems could assist in tuning the many parameters in ESMs, a currently time-consuming and challenging process, and how quantum computers could aid in the analysis of climate models. We also discuss hurdles and obstacles facing current quantum computing paradigms. Strong interdisciplinary collaboration between climate scientists and quantum computing experts could help overcome these hurdles and harness the potential of quantum computing for this urgent topic.
In this paper we explore how quantum scientific machine learning can be used to tackle the challenge of weather modeling. Using parametrized quantum circuits as machine learning models, we consider two paradigms: supervised learning from weather data and physics-informed solving of the underlying equations of atmospheric dynamics. In the first case, we demonstrate how a quantum model can be trained to accurately reproduce real-world global stream function dynamics at a resolution of ${4}^{\ensuremath{\circ}}$. We detail a number of problem-specific classical and quantum architecture choices used to achieve this result. Subsequently, we introduce the barotropic vorticity equation (BVE) as our model of the atmosphere, which is a third-order partial differential equation (PDE) in its stream function formulation. Using the differentiable quantum circuits algorithm, we successfully solve the BVE under appropriate boundary conditions and use the trained model to predict unseen future dynamics to high accuracy given an artificial initial weather state. While challenges remain, our results mark an advancement in terms of the complexity of PDEs solved with quantum scientific machine learning.