arXiv subjects

Mierk Schwabe

Publications and source records attributed to Mierk Schwabe.

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

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

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↗

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

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↗

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

Interpretable multiscale Machine Learning-Based Parameterizations of Convection for ICON

Machine learning (ML)-based parameterizations have been developed for Earth System Models (ESMs) with the goal to better represent subgrid-scale processes or to accelerate computations. ML-based parameterizations within hybrid ESMs have successfully learned subgrid-scale processes from short high-resolution simulations. However, most studies used a particular ML method to parameterize the subgrid tendencies or fluxes originating from the compound effect of various small-scale processes (e.g., radiation, convection, gravity waves) in mostly idealized settings or from superparameterizations. Here, we use a filtering technique to explicitly separate convection from these processes in simulations with the Icosahedral Non-hydrostatic modelling framework (ICON) in a realistic setting and benchmark various ML algorithms against each other offline. We discover that an unablated U-Net, while showing the best offline performance, learns reverse causal relations between convective precipitation and subgrid fluxes. While we were able to connect the learned relations of the U-Net to physical processes this was not possible for the non-deep learning-based Gradient Boosted Trees. The ML algorithms are then coupled online to the host ICON model. Our best online performing model, an ablated U-Net excluding precipitating tracer species, indicates higher agreement for simulated precipitation extremes and mean with the high-resolution simulation compared to the traditional scheme. However, a smoothing bias is introduced both in water vapor path and mean precipitation. Online, the ablated U-Net significantly improves stability compared to the non-ablated U-Net and runs stable for the full simulation period of 180 days. Our results hint to the potential to significantly reduce systematic errors with hybrid ESMs.

physics.ao-ph↗

arXiv2023

Particle-resolved study of the onset of turbulence

The transition from laminar to turbulent flow is an immensely important topic that is still being studied. Here we show that complex plasmas, i.e., microparticles immersed in a low temperature plasma, make it possible to study the particle-resolved onset of turbulence under the influence of damping, a feat not possible with conventional systems. We performed three-dimensional (3D) molecular dynamics (MD) simulations of complex plasmas flowing past an obstacle and observed 3D turbulence in the wake and fore-wake region of this obstacle. We found that we could reliably trigger the onset of turbulence by changing key parameters such as the flow speed and particle charge, which can be controlled in experiments, and show that the transition to turbulence follows the conventional pathway involving the intermittent emergence of turbulent puffs. The power spectra for fully developed turbulence in our simulations followed the -5/3 power law of Kolmogorovian turbulence in both time and space. We demonstrate that turbulence in simulations with damping occurs after the formation of shock fronts, such as bow shocks and Mach cones. By reducing the strength of damping in the simulations, we could trigger a transition to turbulence in an undamped system. This work opens the pathway to detailed experimental and simulation studies of the onset of turbulence on the level of the carriers of the turbulent interactions, i.e., the microparticles.

physics.plasm-ph↗

arXiv2021

Spontaneous dust pulse formation in the afterglow of complex plasmas under microgravity conditions

A new type of nonlinear dust pulse structures has been observed in afterglow complex plasma under microgravity condition on board the International Space Station (ISS). The dust pulses are triggered spontaneously as the plasma is switched off and the particles start to flow through each other (uni-directional or counter-streaming) in the presence of a low-frequency external electric excitation. The pulses are oblique with respect to the microparticle cloud and appear to be symmetric with respect to the central axis. A possible explanation of this observation with the spontaneous development of a double layer in the afterglow of complex plasma is described.

physics.plasm-ph↗

arXiv2020

Penetration of a supersonic particle at the interface in a binary complex plasma

The penetration of a supersonic particle at the interface was studied in a binary complex plasma. Inspired by the experiments performed in the PK-3 Plus Laboratory on board the International Space Station, Langevin dynamics simulations were carried out. The evolution of Mach cone at the interface was observed, where a kink of the lateral wake front was observed at the interface. By comparing the evolution of axial and radial velocity, we show that the interface solitary wave is non-linear. The dependence of the background particle dynamics in the vicinity of the interface on the penetration direction reveals that the disparity of the mobility may be the cause of various interface effects.

physics.plasm-ph↗

arXiv2019

3D Particle Positions from Computer Stereo Vision in PK-4

Complex plasmas consist of microparticles embedded in a low-temperature plasma containing ions, electrons and neutral particles. The microparticles form a dynamical system that can be used to study a multitude of effects on the level of the constituent particles. The microparticles are usually illuminated with a sheet of laser light, and the scattered light can be observed with digital cameras. Some complex plasma microgravity research facilities use two cameras with an overlapping field of view. An overlapping field of view can be used to combine the resulting images into one and trace the particles in the larger field of view. In previous work this was discussed for the images recorded by the PK-4 Laboratory on board the International Space Station. In that work the width of the laser sheet was, however, not taken into account. In this paper, we will discuss how to improve the transformation of the features into a joint coordinate system, and possibly extract information on the 3D position of particles in the overlap region.

cs.CV↗

arXiv2018

Dissipative solitary wave at the interface of a binary complex plasma

The propagation of a dissipative solitary wave across an interface is studied in a binary complex plasma. The experiments were performed under microgravity conditions in the PK-3 Plus Laboratory on board the International Space Station using microparticles with diameters of 1.55 micrometre and 2.55 micrometre immersed in a low-temperature plasma. The solitary wave was excited at the edge of a particle-free region and propagated from the sub-cloud of small particles into that of big particles. The interfacial effect was observed by measuring the deceleration of particles in the wave crest. The results are compared with a Langevin dynamics simulation, where the waves were excited by a gentle push on the edge of the sub-cloud of small particles. Reflection of the wave at the interface is induced by increasing the strength of the push. By tuning the ion drag force exerted on big particles in the simulation, the effective width of the interface is adjusted. We show that the strength of reflection increases with narrower interfaces.

physics.plasm-ph↗