arXiv subjects

Veronika Eyring

Publications and source records attributed to Veronika Eyring.

At least 19 recordsLinked to original sources

arXiv2026

Shadow models of a quantum model for cloud cover and the influence of finite sampling noise

Quantum computing is a quickly growing field that is promising various advantages compared to conventional computing. However, currently stand-alone quantum applications are scarce and hybrid (quantum-classical) computing is needed, especially in quantum machine learning (QML). Due to current limitations of quantum computing hardware and the coupling between HPC and quantum devices, integrating a trained (QML) model in classical applications is challenging. In this case, it is helpful to couple so-called shadows of the QML model instead, i.e., classical models that imitate the input-output relations of QML models such that quantum resources are only needed during the training stage. Here we consider constructive shadowing processes without an explicit training or regression stage to avoid rendering the QML model redundant, and apply them to a previously developed QML model for cloud cover [1] to allow for an efficient coupling to a climate model. We compare classical interpolation methods to an approximation of the quantum Fourier model, the representation of the circuit as a partial Fourier series. The encoding strategy in [1] allows the use of the discrete Fourier transform to efficiently reconstruct the circuits classically. Truncating the partial Fourier series further reduces the size of the shadow models. Both methods have the effect of mitigating finite sampling noise under certain conditions, which yields a motivation to use shadow models also beyond the era of limited hardware availability. Further, we compute the shadow models on the quantum system Euro-Q-Exa, based on the IQM Radiance system with superconducting qubits, where error mitigating effects can also be observed, albeit it is still difficult to distinguish them from errors connected to the calibration of the system.

quant-ph↗

arXiv2026

Fisher Information, Training and Bias in Fourier Regression Models

Motivated by the growing interest in quantum machine learning, in particular quantum neural networks (QNNs), we study how recently introduced evaluation metrics based on the Fisher information matrix (FIM) are effective for predicting their training and prediction performance. We exploit the equivalence between a broad class of QNNs and Fourier models, and study the interplay between the \emph{effective dimension} and the \emph{bias} of a model towards a given task, investigating how these affect the model's training and performance. We show that for a model that is completely agnostic, or unbiased, towards the function to be learned, a higher effective dimension likely results in a better trainability and performance. On the other hand, for models that are biased towards the function to be learned a lower effective dimension is likely beneficial during training. To obtain these results, we derive an analytical expression of the FIM for Fourier models and identify the features controlling a model's effective dimension. This allows us to construct models with tunable effective dimension and bias, and to compare their training. We furthermore introduce a tensor network representation of the considered Fourier models, which could be a tool of independent interest for the analysis of QNN models. Overall, these findings provide an explicit example of the interplay between geometrical properties, model-task alignment and training, which are relevant for the broader machine learning community.

cs.LG↗

arXiv2026

How Hard Is Quantum Advantage? A Cloud Microphysics Stress Test for Variational Quantum Models

Quantum machine learning (QML) could have the potential to leverage advantages of quantum over classical computing but still lacks strong evidence of actual improvements and scalability, partly due to phenomena such as barren plateaus. In this paper, we employ a hybrid quantum neural network (QNN) on a dataset on cloud microphysics, containing processes for phase transitions of water in the atmosphere and its related temperature changes, which are highly relevant for accurate climate predictions and projections. To reach optimal performance of our QNNs, we employ a rich and trainable frequency spectrum together with expressivity enhancing classical postprocessing. We find that our QNNs strongly benefit from extensive hyperparameter optimization and thereby demonstrate the feasibility of applying QNNs to complex physical systems. At the same time, the QNNs are outperformed by classical baselines in the form of simple fully-connected neural networks. We discuss identified bottlenecks of this class of quantum models to learn the full complexity of the cloud microphysics dataset to show that there is a need to further understand and improve variational quantum models for machine learning such that they might fill the gap where classical models fail or are inefficient.

quant-ph↗

arXiv2026

From stable online coupling to decade-long climate simulations: A machine learning parameterization for cloud microphysics in ICON

The representation of cloud microphysics and its nonlinear character and scale-dependence is a remaining source of uncertainty in Earth system models (ESMs). Here, we develop and couple online a machine learning (ML)-based cloud microphysics parameterization with the Icosahedral non-hydrostatic modeling framework (ICON). The primary challenge is achieving numerically stable, long-term online coupling when transitioning from training with km-scale data to application in coarse-scale simulations, where the coupled system encounters atmospheric states and feedbacks not seen during training. The training data is obtained from a global convection-permitting ICON simulation at 5 km resolution. The ML microphysics scheme uses a two-stage design: a classifier to identify active grid cells and a regressor to predict cloud microphysical tendencies. Physical constraints such as enforcing mass positivity and overshoot prevention prove essential for numerical stability in the coupled system. We demonstrate that achieving stable online coupling requires enforcing physical constraints and careful dataset curation, and that strong offline performance alone is insufficient. The coupled model maintains numerical stability over decade-long simulations with a performance in reproducing the observed climate comparable to the classical graupel scheme. The ML-based scheme eliminates two microphysics-specific tuning parameters of the classical graupel scheme, though systematic improvements in long-term mean-state biases are not yet realized. This study demonstrates that stable, decade-long climate simulations with an ML-based cloud microphysics scheme trained on convection-permitting data are feasible, providing a foundation for future hybrid ESMs.

physics.ao-ph↗

arXiv2026

PhysMetrics.Weather: An Evaluation Framework for Physical Consistency in ML Weather Models

Machine learning weather prediction (MLWP) models have achieved impressive forecasting performance at a small fraction of the computational costs required for traditional physics-based methods. However, they are primarily (1) data-driven and (2) evaluated using pixel-wide error metrics (e.g., RMSE), so there are no guarantees that their forecasts are consistent with known physical laws. We introduce PhysMetrics$.$Weather, an evaluation framework that assesses the physical realism of MLWP models across three types of metrics: conservation, spectral, and dynamical. By quantifying physical realism, this tool guides the development of physics-informed architectures and helps evaluate whether MLWP models are reliable for operational use. Our framework is available on Github at https://github.com/Emmakast/PhysMetrics.Weather.

cs.LG↗

arXiv2026

Beyond the Training Data: Confidence-Guided Mixing of Parameterizations in a Hybrid AI-Climate Model

Persistent systematic errors in Earth system models (ESMs) arise from difficulties in representing the full diversity of subgrid, multiscale atmospheric convection and turbulence. Machine learning (ML) parameterizations trained on short high-resolution simulations show strong potential to reduce these errors. However, stable long-term atmospheric simulations with hybrid (physics + ML) ESMs remain difficult, as neural networks (NNs) trained offline often destabilize online runs. Training convection parameterizations directly on coarse-grained data is challenging, notably because scales cannot be cleanly separated. This issue is mitigated using data from superparameterized simulations, which provide clearer scale separation. Yet, transferring a parameterization from one ESM to another remains difficult due to distribution shifts that induce large inference errors. Here, we present a proof-of-concept where a ClimSim-trained, physics-informed NN convection parameterization is successfully transferred to ICON-A. The scheme is (a) trained on adjusted ClimSim data with subtracted radiative tendencies, and (b) integrated into ICON-A. The NN parameterization predicts its own error, enabling mixing with a conventional convection scheme when confidence is low, thus making the hybrid AI-physics model tunable with respect to observations and reanalysis through mixing parameters. This improves process understanding by constraining convective tendencies across column water vapor, lower-tropospheric stability, and geographical conditions, yielding interpretable regime behavior. In AMIP-style setups, several hybrid configurations outperform the default convection scheme (e.g., improved precipitation statistics). With additive input noise during training, both hybrid and pure-ML schemes lead to stable simulations and remain physically consistent for at least 20 years.

physics.ao-ph↗

arXiv2026

Interpretable Neural Networks to Predict Momentum Fluxes of Orographic Gravity Waves

State-of-the-art Earth system models (ESMs) cannot explicitly resolve many small-scale atmospheric processes such as atmospheric gravity waves, and thus must represent, or parameterise, their effects on the resolved state. Machine learning (ML) has the potential to improve these parameterisations. In our study, we train neural networks (NNs) on ERA5 reanalysis data to predict momentum fluxes of orographic gravity waves as a function of the state variables at the resolution of a coarse ESM. Employing a full year of data, we extract inertia-gravity waves using the software MODES, which applies linear theory for wave filtering, and train ML models on data coarse-grained to the ESM's target resolution. We consider four different cases: the full spectrum of inertia-gravity waves resolved in ERA5, or just the part of the spectrum that is subgrid-scale in the target ESM, both over all land or just over mountainous terrain. Our NNs successfully predict momentum fluxes, with a global coefficient of determination ($R^2$) ranging from 0.72 to 0.56, depending on the case, when evaluated offline with data from another year. An analysis of our models using SHAP values, an explainable AI technique, suggests that the networks learned physically meaningful relationships. In addition, we give a comparison with the physics-based parameterisation scheme by Lott and Miller. This work forms the basis for the development of operational ML-based parameterisations to improve the representation of gravity waves and their effects in climate models.

physics.ao-ph↗

arXiv2026

Quantum-Enhanced Convergence of Physics-Informed Neural Networks

Partial differential equations (PDEs) form the backbone of simulations of many natural phenomena, for example in climate modeling, material science, and even financial markets. The application of physics-informed neural networks to accelerate the solution of PDEs is promising, but not competitive with numerical solvers yet. Here, we show how quantum computing can improve the ability of physics-informed neural networks to solve partial differential equations. For this, we develop hybrid networks consisting of quantum circuits combined with classical layers and systematically test them on various non linear PDEs and boundary conditions in comparison with purely classical networks. We demonstrate that the advantage of using quantum networks lies in their ability to achieve an accurate approximation of the solution in substantially fewer training epochs, particularly for more complex problems. These findings provide the basis for targeted developments of hybrid quantum neural networks with the goal to significantly accelerate numerical modeling.

quant-ph↗

arXiv2026

Physics-Constrained Adaptive Flow Matching for Climate Downscaling

Regional climate information at kilometer scales is essential for assessing the impacts of climate change, but generating it with global climate models is too expensive due to their high computational costs. Machine learning models offer a fast alternative, yet they often violate basic physical laws and degrade when applied to climates outside of their training distribution. We present Physics-Constrained Adaptive Flow Matching (PC-AFM), a generative downscaling model that addresses both problems. Building on the Adaptive Flow Matching (AFM) model of Fotiadis et al. (2025) as our baseline, we add soft conservation constraints that keep the downscaled output consistent with the large-scale input for precipitation and humidity, and use gradient surgery via the ConFIG algorithm to prevent these constraints from interfering with the generative objective. We train the model on Central Europe climate data, evaluate it on a 10-time downscaling task (63km to 6.3km) over six variables (near-surface temperature, precipitation, specific humidity, surface pressure, and horizontal wind components) across a comprehensive set of metrics including bias, ensemble skill scores, power spectra, and conservation error, and test the generalization on two held-out climate regions. Within the training distribution, PC-AFM reduces conservation errors and improves ensemble calibration while matching the baseline on standard skill metrics. Outside the training distribution, where unconstrained models develop large systematic errors by extrapolating learned statistics, PC-AFM halves precipitation wet bias, reduces conservation error and improves extreme-quantile accuracy, all without any information about the target climate at inference time. These results indicate that physical consistency is a practical requirement for deploying generative downscaling models in real-world applications.

physics.ao-ph↗

arXiv2025

Quantum Bayesian Optimization for the Automatic Tuning of Lorenz-96 as a Surrogate Climate Model

In this work, we propose a hybrid quantum-inspired heuristic for automatically tuning the Lorenz-96 model -- a simple proxy to describe atmospheric dynamics, yet exhibiting chaotic behavior. Building on the history matching framework by Lguensat et al. (2023), we fully automate the tuning process with a new convergence criterion and propose replacing classical Gaussian process emulators with quantum counterparts. We benchmark three quantum kernel architectures, distinguished by their quantum feature map circuits. A dimensionality argument implies, in principle, an increased expressivity of the quantum kernels over their classical competitors. For each kernel type, we perform an extensive hyperparameter optimization of our tuning algorithm. We confirm the validity of a quantum-inspired approach based on statevector simulation by numerically demonstrating the superiority of two studied quantum kernels over the canonical classical RBF kernel. Finally, we discuss the pathway towards real quantum hardware, mainly driven by a transition to shot-based simulations and evaluating quantum kernels via randomized measurements, which can mitigate the effect of gate errors. The very low qubit requirements and moderate circuit depths, together with a minimal number of trainable circuit parameters, make our method particularly NISQ-friendly.

quant-ph↗

arXiv2025

Quantum Machine Learning for Climate Modelling

Quantum machine learning (QML) is making rapid progress, and QML-based models hold the promise of quantum advantages such as potentially higher expressivity and generalizability than their classical counterparts. Here, we present work on using a quantum neural net (QNN) to develop a parameterization of cloud cover for an Earth system model (ESM). ESMs are needed for predicting and projecting climate change, and can be improved in hybrid models incorporating both traditional physics-based components as well as machine learning (ML) models. We show that a QNN can predict cloud cover with a performance similar to a classical NN with the same number of free parameters and significantly better than the traditional scheme. We also analyse the learning capability of the QNN in comparison to the classical NN and show that, at least for our example, QNNs learn more consistent relationships than classical NNs.

quant-ph↗

arXiv2025

Reduced Cloud Cover Errors in a Hybrid AI-Climate Model Through Equation Discovery And Automatic Tuning

Cloud-related parameterizations remain a leading source of uncertainty in climate projections. Although machine learning holds promise for Earth system models (ESMs), many data-driven parameterizations lack interpretability, physical consistency, and smooth integration into ESMs. Here, a two-step method is presented to improve a climate model with data-driven parameterizations. First, we incorporate a physically consistent cloud cover parameterization -- derived from storm-resolving simulations via symbolic regression, preserving interpretability while enhancing accuracy -- into the ICON global atmospheric model. Second, we apply the gradient-free Nelder-Mead optimizer to automatically recalibrate the hybrid model against Earth observations, tuning in nested stages (2-, 7-, 30- and 365-day runs) to ensure stability and tractability. The tuned hybrid model substantially reduces long-standing biases in cloud cover -- particularly over the Southern Ocean (by 75%) and subtropical stratocumulus regions (by 44%) -- and remains robust under +4K surface warming. These results demonstrate that interpretable machine-learned parameterizations, paired with practical tuning, can efficiently and transparently strengthen ESM fidelity.

physics.ao-ph↗

arXiv2025

Representing Subgrid-Scale Cloud Effects in a Radiation Parameterization using Machine Learning: MLe-radiation v1.0

Improvements of Machine Learning (ML)-based radiation emulators remain constrained by the underlying assumptions to represent horizontal and vertical subgrid-scale cloud distributions, which continue to introduce substantial uncertainties. In this study, we introduce a method to represent the impact of subgrid-scale clouds by applying ML to learn processes from high-resolution model output with a horizontal grid spacing of 5km. In global storm resolving models, clouds begin to be explicitly resolved. Coarse-graining these high-resolution simulations to the resolution of coarser Earth System Models yields radiative heating rates that implicitly include subgrid-scale cloud effects, without assumptions about their horizontal or vertical distributions. We define the cloud radiative impact as the difference between all-sky and clear-sky radiative fluxes, and train the ML component solely on this cloud-induced contribution to heating rates. The clear-sky tendencies remain being computed with a conventional physics-based radiation scheme. This hybrid design enhances generalization, since the machine-learned part addresses only subgrid-scale cloud effects, while the clear-sky component remains responsive to changes in greenhouse gas or aerosol concentrations. Applied to coarse-grained data offline, the ML-enhanced radiation scheme reduces errors by a factor of 4-10 compared with a conventional coarse-scale radiation scheme. This shows the potential of representing subgrid-scale cloud effects in radiation schemes with ML for the next generation of Earth System Models.

physics.ao-ph↗

arXiv2025

Transferring climate change physical knowledge

Precise and reliable climate projections are required for climate adaptation and mitigation, but Earth system models still exhibit great uncertainties. Several approaches have been developed to reduce the spread of climate projections and feedbacks, yet those methods cannot capture the nonlinear complexity inherent in the climate system. Using a Transfer Learning approach, we show that Machine Learning can be used to optimally leverage and merge the knowledge gained from global temperature maps simulated by Earth system models and observed in the historical period to reduce the spread of global surface air temperature fields projected in the 21st century. We reach an uncertainty reduction of more than 50% with respect to state-of-the-art approaches while giving evidence that our method provides improved regional temperature patterns together with narrower projections uncertainty, urgently required for climate adaptation.

physics.ao-ph↗

arXiv2025

Opportunities and challenges of quantum computing for climate modelling

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.

quant-ph↗

arXiv2025

Simulating Atmospheric Processes in Earth System Models and Quantifying Uncertainties with Deep Learning Multi-Member and Stochastic Parameterizations

Deep learning is a powerful tool to represent subgrid processes in climate models, but many application cases have so far used idealized settings and deterministic approaches. Here, we develop stochastic parameterizations with calibrated uncertainty quantification to learn subgrid convective and turbulent processes and surface radiative fluxes of a superparameterization (SP) embedded in an Earth System Model (ESM). We explore three methods to construct stochastic parameterizations: 1) a single Deep Neural Network (DNN) with Monte Carlo Dropout; 2) a multi-member parameterization; and 3) a Variational Encoder Decoder with latent space perturbation. We show that the multi-member (MM) parameterization improves the representation of convective processes, especially in the planetary boundary layer, compared to individual DNNs. The respective uncertainty quantification illustrates that methods 2) and 3) are advantageous compared to a dropout-based DNN parameterization regarding the spread of convective processes. Hybrid simulations with our best-performing MM parameterizations remained challenging and crash within the first days. Therefore, we develop a pragmatic partial coupling strategy relying on the SP for condensate emulation. Partial coupling reduces the computational efficiency of hybrid Earth-like simulations but enables model stability over 5 months with our MM parameterizations. However, our hybrid simulations exhibit biases in thermodynamic fields and differences in precipitation patterns. Despite this, the MM parameterizations enable improvements in reproducing tropical extreme precipitation compared to a traditional convection parameterization. Despite these challenges, our results indicate the potential of a new generation of MM machine learning parameterizations leveraging uncertainty quantification to improve the representation of stochasticity of subgrid effects.

physics.ao-ph↗

arXiv2025

Quantum Neural Networks for Cloud Cover Parameterizations in Climate 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.

quant-ph↗

arXiv2024

Towards Physically Consistent Deep Learning For Climate Model Parameterizations

Climate models play a critical role in understanding and projecting climate change. Due to their complexity, their horizontal resolution of about 40-100 km remains too coarse to resolve processes such as clouds and convection, which need to be approximated via parameterizations. These parameterizations are a major source of systematic errors and large uncertainties in climate projections. Deep learning (DL)-based parameterizations, trained on data from computationally expensive short, high-resolution simulations, have shown great promise for improving climate models in that regard. However, their lack of interpretability and tendency to learn spurious non-physical correlations result in reduced trust in the climate simulation. We propose an efficient supervised learning framework for DL-based parameterizations that leads to physically consistent models with improved interpretability and negligible computational overhead compared to standard supervised training. First, key features determining the target physical processes are uncovered. Subsequently, the neural network is fine-tuned using only those relevant features. We show empirically that our method robustly identifies a small subset of the inputs as actual physical drivers, therefore removing spurious non-physical relationships. This results in by design physically consistent and interpretable neural networks while maintaining the predictive performance of unconstrained black-box DL-based parameterizations.

cs.LG↗