Distilling Machine Learning's Added Value: Pareto Fronts in Atmospheric Applications (2408.02161v2)

Abstract: The added value of machine learning for weather and climate applications is measurable through performance metrics, but explaining it remains challenging, particularly for large deep learning models. Inspired by climate model hierarchies, we propose that a full hierarchy of Pareto-optimal models, defined within an appropriately determined error-complexity plane, can guide model development and help understand the models' added value. We demonstrate the use of Pareto fronts in atmospheric physics through three sample applications, with hierarchies ranging from semi-empirical models with minimal parameters to deep learning algorithms. First, in cloud cover parameterization, we find that neural networks identify nonlinear relationships between cloud cover and its thermodynamic environment, and assimilate previously neglected features such as vertical gradients in relative humidity that improve the representation of low cloud cover. This added value is condensed into a ten-parameter equation that rivals deep learning models. Second, we establish a machine learning model hierarchy for emulating shortwave radiative transfer, distilling the importance of bidirectional vertical connectivity for accurately representing absorption and scattering, especially for multiple cloud layers. Third, we emphasize the importance of convective organization information when modeling the relationship between tropical precipitation and its surrounding environment. We discuss the added value of temporal memory when high-resolution spatial information is unavailable, with implications for precipitation parameterization. Therefore, by comparing data-driven models directly with existing schemes using Pareto optimality, we promote process understanding by hierarchically unveiling system complexity, with the hope of improving the trustworthiness of machine learning models in atmospheric applications.

• The paper introduces a novel framework using Pareto fronts to balance model error and complexity in atmospheric applications.
• It demonstrates how ML improves cloud cover parameterization, radiative transfer emulation, and tropical precipitation prediction through tailored architectures.
• These insights offer a pathway to develop interpretable and efficient operational models by synergizing domain-specific physics with advanced machine learning.

Distilling Machine Learning's Added Value: Pareto Fronts in Atmospheric Applications

The paper "Distilling Machine Learning's Added Value: Pareto Fronts in Atmospheric Applications" addresses the complexities and potential transformative impacts of ML within atmospheric sciences. The authors introduce the concept of Pareto-optimal model hierarchies in the context of error-complexity trade-offs to delineate the added value of ML models. The application of these hierarchies is demonstrated through three distinct atmospheric modeling problems: cloud cover parameterization, shortwave radiative transfer emulation, and tropical precipitation prediction.

Theoretical Framework

The authors propose defining full model hierarchies using Pareto optimality within an error-complexity space. This approach enables researchers to understand the nuanced benefits of increasing model complexity. In multi-objective optimization, a Pareto-optimal set consists of models where no other models can improve one metric without deteriorating another. In this paper, model complexity and performance error constitute the two primary evaluation metrics.

The categorization of ML benefits is rigorously detailed:

1. Functional Representation: The ability of a model to capture nonlinear relationships within atmospheric datasets.
2. Feature Assimilation: Integration of new, often neglected features which can significantly improve model performance.
3. Spatial Connectivity: The capability to leverage spatial information, crucial in applications like radiative transfer.
4. Temporal Connectivity: Harnessing temporal dependencies in data to improve predictions, as seen in precipitation modeling.

Case Studies

Cloud Cover Parameterization

One of the central challenges in climate modeling is the accurate parameterization of cloud cover. The authors compare various baselines, including the Sundqvist parameterization and polynomial regressions up to quadratic forms, against neural networks (NNs). The key findings highlight that NNs, through their ability to model complex nonlinear relationships and assimilate vertical gradients of humidity, notably improve cloud cover representations. Notably, they show that crucial improvements can be distilled into interpretable equations using symbolic regression—bridging the gap between ML complexity and human interpretation.

Shortwave Radiative Transfer

Radiative transfer modeling is computationally intensive but essential for accurate weather prediction. The paper evaluates different ML architectures to emulate shortwave radiative transfer models. The results emphasize that architectures preserving vertical connectivity, like U-nets and bidirectional recurrent neural networks (RNNs), exhibit superior performance over multilayer perceptrons (MLPs) and convolutional neural networks (CNNs) with limited kernels. RNNs, informed by the bidirectional nature of radiative transfer equations, demonstrate near-equivalent accuracy to U-nets with significantly less complexity—highlighting the value of leveraging domain-specific physical knowledge in ML models.

Tropical Precipitation Prediction

The representation of precipitation in tropical regions is pivotal yet challenging due to subgrid-scale processes. The authors show that including spatial granularity or temporal memory can markedly enhance model accuracy over baseline MLPs. Interestingly, NNs that leverage past timesteps of coarse data nearly match the performance of those using high-resolution spatial data. This finding suggests temporal memory as a valuable proxy for spatial detail, particularly beneficial when high-resolution data is unavailable or computationally prohibitive.

Implications and Future Directions

This paper underscores the importance of considering entire model hierarchies rather than seeking a singular 'best' model. Through rigorous application of Pareto optimality, researchers can systematically distill the added value of ML—transforming complex neural network models into interpretable, operationally viable solutions. The paper advocates for a multi-step approach that includes using Pareto-optimal fronts to explore incremental improvements, hypothesizing system-specific models, and ultimately distilling these into simpler, interpretable forms.

The implications are both theoretical and practical:

• Theoretical: The hierarchical approach aids in understanding the biophysical processes modeled, potentially unveiling new scientific insights.
• Practical: Operational models become more transparent and cost-effective, fostering trust and adoption in high-stakes applications like weather forecasting and climate change projections.

Future work could focus on expanding the complexity metrics beyond parameter count to include computational cost measures. This would align more closely with the practical constraints of deploying ML models in operational environments. Moreover, the approach could be extended to other domains within geosciences or even different scientific fields where modeling complex systems is essential.

In summary, the paper introduces a robust framework for extracting meaningful insights from ML in atmospheric sciences, advocating for a balanced consideration of complexity and accuracy through Pareto-optimal model hierarchies. This methodology not only elucidates the contributions of ML models but also promotes their operational integration, thereby enhancing their impact on both scientific discovery and practical applications.