Quantum Machine Learning for Climate Modelling

Technical Summary: Quantum Machine Learning for Climate Modelling

Problem Statement
Earth System Models (ESMs) are essential for projecting future climate change but operate at coarse resolutions (tens of kilometers) that cannot resolve critical subgrid-scale processes such as cloud microphysics, turbulence, and convection. These unresolved processes are currently handled by empirical parameterizations, which introduce significant uncertainties and biases into climate projections. While classical Machine Learning (ML) has shown promise in replacing these parameterizations with data-driven models, challenges remain regarding generalization beyond training regimes and the physical consistency of learned relationships. This paper investigates whether Quantum Machine Learning (QML), specifically Quantum Neural Networks (QNNs), can offer advantages in developing parameterizations for cloud cover, a critical component of ESMs.

Methodology
The authors developed a hybrid quantum-classical approach to parameterize cloud cover for the ICON climate model.

• Data Generation: Training data were derived from high-resolution (2.5 km horizontal) global simulations using the ICON model within the DYAMOND project. Unlike previous works using multiscale modeling frameworks (MMF), this approach used the same model for data generation and the target application, avoiding assumptions of scale separation.
• Preprocessing: High-resolution data were coarse-grained to 80 km to match the target ESM resolution. A grid cell was defined as cloudy if specific cloud condensate exceeded a threshold. The target variable was the fractional cloud cover (0 to 1).
• Input Features: The models utilized coarse state variables including specific humidity ($q_v$), specific cloud water/ice content ($q_c, q_i$), air temperature ($T$), pressure ($p$), horizontal wind magnitude ($h_w$), geometric height ($z_g$), and latitude ($\phi$).
• Model Architecture:
  • QNN: A parameterized quantum circuit was employed where the number of qubits equaled the number of input features (6 or 8). The architecture involved data re-uploading (encoding input features as rotation angles in multiple layers), interleaved with variational blocks containing entangling gates and trainable parameters. The output was derived from the expectation values of Pauli-Z operators, processed through a simple linear layer (weighted average with bias) to predict cloud cover.
  • Classical NN: For comparison, a classical neural network with three hidden layers (12, 6, 2 nodes) and non-linear activation functions (leaky-ReLU or tanh) was constructed. Crucially, the classical NN was designed to have a comparable number of free parameters (203) to the QNN (200–201) to ensure a fair comparison of expressivity rather than parameter count.
• Training and Explainability: Models were trained for 200 epochs using Mean Squared Error (MSE) and gradient descent (via the parameter-shift rule for QNNs). To analyze the physical consistency of the learned relationships, the authors applied SHAP (SHapley Additive exPlanations) values, a model-agnostic explainability method, to assess feature importance stability across multiple training instances.

Key Results

• Predictive Performance: The QNN achieved performance comparable to the classical NN with a similar number of parameters, with the classical NN showing a slight edge. Both ML approaches significantly outperformed the traditional Xu-Randall parameterization scheme used in climate models.
• Noise Robustness: Simulations incorporating shot noise demonstrated that the QNN maintains stable performance provided the number of shots ($n_{shots}$) exceeds $10^4$. Below this threshold, training becomes unstable due to gradient noise, though variance regularization techniques can mitigate this.
• Learning Consistency (Explainability): A critical finding emerged from the SHAP analysis. While both models achieved similar accuracy, the feature importances learned by the classical NNs varied significantly across different training instances (random initializations). In contrast, the QNNs exhibited highly stable feature importances. Specifically, the QNNs consistently identified specific humidity and temperature as the most critical features, aligning with physical expectations. The classical NNs occasionally learned inconsistent or potentially unphysical relationships regarding feature importance.

Significance and Claims
The paper claims that QNNs can serve as viable alternatives to classical NNs for climate parameterization, offering performance on par with classical counterparts while demonstrating superior robustness in learning consistent physical relationships. The authors posit that the QNNs' ability to converge on stable feature importances suggests they may be less prone to learning spurious correlations compared to classical networks, a crucial trait for climate modeling where generalization to changing climates is vital.

The work demonstrates that QML can be effectively developed on current Noisy Intermediate-Scale Quantum (NISQ) devices (or simulators) for climate applications. The authors suggest that while running QML parameterizations online in climate models currently faces computational overheads, "surrogates" or shadows of trained QML models could be used for operational deployment, retaining the benefits of the quantum training phase without requiring real-time quantum hardware. Future work is proposed to extend these methods to larger problem sizes, quantum convolutional neural networks (to avoid barren plateaus), and more complex parameterizations like boundary layer turbulence.