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arXiv:2404.08737

Potential of quantum scientific machine learning applied to weather modelling

Ben Jaderberg, Antonio A. Gentile, Atiyo Ghosh, Vincent E. Elfving, C. R. Jones, Davide Vodola, John Manobianco, Horst Weiß

Published Apr 12, 2024• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2404.08737

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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.
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.
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Weather forecasting plays a critical role across various sectors, supporting strategic planning and reducing the impact of hazardous climatic conditions. However, the inherently chaotic and nonlinear nature of atmospheric systems limits the performance of conventional forecasting approaches, often resulting in prediction inaccuracies and heightened risk. This study proposes a quantum-driven predictive framework that exploits the computational strengths of Quantum Machine Learning (QML) and hybrid quantum–classical optimization to enhance the accuracy and efficiency of modern forecasting models. The framework employs Quantum Neural Networks (QNNs) combined with Variational Quantum Circuits (VQCs) to learn complex spatial–temporal dynamics embedded within large meteorological datasets. Through quantum feature encoding, key atmospheric indicators—including temperature, humidity, wind velocity, and barometric pressure—are projected into high-dimensional Hilbert spaces, enabling more expressive pattern extraction and robust predictive behavior. Simulation results reveal that the quantum-augmented approach surpasses traditional deep learning architectures in both training convergence and forecast precision when applied to extensive weather records. The hybrid design further supports scalability by intelligently distributing computational workloads between classical processors and quantum hardware. Overall, this research demonstrates the transformative potential of quantum computing in atmospheric modeling, offering a foundation for future real-time forecasting systems capable of managing the increasing complexity of global climate patterns.
Weather forecasting is a major challenge because of the unpredictable nature of atmospheric systems and the large number of interacting variables. Although traditional machine learning models have been used for weather prediction, they cannot capture the complex, nonlinear dynamics of weather. Recently, Quantum Machine Learning (QML) shows ability to improve computational speed and pattern recognition. Its practical application in weather prediction, however, is not well exploited. This work methodically analyzes QML algorithms for predicting weather states and compares their predictive performance with that of classical machine learning. We assembled extensive hourly meteorological data for Sylhet City, Bangladesh (24.9172∘N,91.8319∘24.9172^{\circ} \mathrm{N}, 91.8319^{\circ}24.9172∘N,91.8319∘E) over 185 days from Microsoft and IBM weather sites, totaling 4,504 data points. The dataset combines the main atmospheric parameters as temperature, real feel temperature, humidity, precipitation probability, visibility, dew point, and air pressure, from Microsoft and IBM weather sites. Four QML algorithms, including Quantum Random Forest (QRF), Quantum Decision Tree (QDT), Quantum Support Vector Machine (QSVM), and Quantum Neural Network (QNN) are trained and tested for five weather state classification, and compared to their classical counterparts named SVM, Random Forest, Decision Tree, and Neural Network. All quantum experiments were run on Qiskit simulators due to current hardware limitations. Results show that classical models performed slightly better than quantum models, and the difference was not very large.
Quantum computing promises to speed up some of the most challenging problems in science and engineering. Quantum algorithms have been proposed showing theoretical advantages in applications ranging from chemistry to logistics optimization. Many problems appearing in science and engineering can be rewritten as a set of differential equations. Quantum algorithms for solving differential equations have shown a provable advantage in the fault-tolerant quantum computing regime, where deep and wide quantum circuits can be used to solve large linear systems like partial differential equations (PDEs) efficiently. Recently, variational approaches to solving non-linear PDEs also with near-term quantum devices were proposed. One of the most promising general approaches is based on recent developments in the field of scientific machine learning for solving PDEs. We extend the applicability of near-term quantum computers to more general scientific machine learning tasks, including the discovery of differential equations from a dataset of measurements. We use differentiable quantum circuits (DQCs) to solve equations parameterized by a library of operators, and perform regression on a combination of data and equations. Our results show a promising path to Quantum Model Discovery (QMoD), on the interface between classical and quantum machine learning approaches. We demonstrate successful parameter inference and equation discovery using QMoD on different systems including a second-order, ordinary differential equation and a non-linear, partial differential equation.
Quantum Machine Learning (QML):An emerging research area that integrates principles of quantum computing with machine learning algorithms to enhance computational efficiency, scalability, and learning capability for complex data-driven problems. Cloud-Based Quantum Computing:A computing paradigm that provides remote access to quantum processors and simulators through cloud platforms, enabling scalable, cost-effective, and accessible quantum experimentation without the need for dedicated quantum hardware. Hybrid Quantum–Classical Models:Machine learning architectures that combine classical data preprocessing and optimization techniques with quantum circuits to leverage the strengths of both classical and quantum computation. Weather Forecasting:The process of predicting atmospheric conditions such as temperature, humidity, pressure, and wind speed using data-driven models and computational techniques. Variational Quantum Circuits (VQC):Parameterized quantum circuits optimized using classical algorithms, widely used in quantum machine learning for classification and regression tasks on Noisy Intermediate-Scale Quantum (NISQ) devices. NISQ Devices:Current-generation quantum computers characterized by limited qubit counts and noise, which influence the performance and accuracy of present-day quantum algorithms.