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Data-Driven Integration Kernels for Interpretable Nonlocal Operator Learning

arXiv:2603.10305v1 Announce Type: new Abstract: Machine learning models can represent climate processes that are nonlocal in horizontal space, height, and time, often by combining information across these dimensions in highly nonlinear ways. While this can improve predictive skill, it makes learned relationships difficult to interpret and prone to overfitting as the extent of nonlocal information grows. We address this challenge by introducing data-driven integration kernels, a framework that adds structure to nonlocal operator learning by explicitly separating nonlocal information aggregation from local nonlinear prediction. Each spatiotemporal predictor field is first integrated using learnable kernels (defined as continuous weighting functions over horizontal space, height, and/or time), after which a local nonlinear mapping is applied only to the resulting kernel-integrated features and any optional local inputs. This design confines nonlinear interactions to a small set of integr

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Savannah L. Ferretti, Jerry Lin, Sara Shamekh, Jane W. Baldwin, Michael S. Pritchard, Tom Beucler · · 1 min read · 13 views
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arXiv:2603.10305v1 Announce Type: new Abstract: Machine learning models can represent climate processes that are nonlocal in horizontal space, height, and time, often by combining information across these dimensions in highly nonlinear ways. While this can improve predictive skill, it makes learned relationships difficult to interpret and prone to overfitting as the extent of nonlocal information grows. We address this challenge by introducing data-driven integration kernels, a framework that adds structure to nonlocal operator learning by explicitly separating nonlocal information aggregation from local nonlinear prediction. Each spatiotemporal predictor field is first integrated using learnable kernels (defined as continuous weighting functions over horizontal space, height, and/or time), after which a local nonlinear mapping is applied only to the resulting kernel-integrated features and any optional local inputs. This design confines nonlinear interactions to a small set of integrated features and makes each kernel directly interpretable as a weighting pattern that reveals which horizontal locations, vertical levels, and past timesteps contribute most to the prediction. We demonstrate the framework for South Asian monsoon precipitation using a hierarchy of neural network models with increasing structure, including baseline, nonparametric kernel, and parametric kernel models. Across this hierarchy, kernel-based models achieve near-baseline performance with far fewer trainable parameters, showing that much of the relevant nonlocal information can be captured through a small set of interpretable integrations when appropriate structural constraints are imposed.

Executive Summary

This article presents a novel approach to nonlocal operator learning, a machine learning framework that can represent complex climate processes. The authors introduce data-driven integration kernels, which separate nonlocal information aggregation from local nonlinear prediction, resulting in a more interpretable and structured model. The proposed framework is demonstrated on South Asian monsoon precipitation using a hierarchy of neural network models, showing that kernel-based models achieve near-baseline performance with significantly fewer trainable parameters. This approach has the potential to improve the understanding and prediction of climate processes, while also reducing the risk of overfitting. The authors' use of interpretable integrations and structural constraints is a key strength of the paper, allowing for a better understanding of the learned relationships.

Key Points

  • ▸ Introduction of data-driven integration kernels for nonlocal operator learning
  • ▸ Separation of nonlocal information aggregation from local nonlinear prediction
  • ▸ Improved interpretability and structure of the model

Merits

Strength

The proposed framework provides a structured approach to nonlocal operator learning, making it more interpretable and less prone to overfitting.

Strength

The use of learnable kernels allows for a flexible and adaptive aggregation of nonlocal information.

Strength

The hierarchy of neural network models demonstrates the effectiveness of the proposed framework in achieving near-baseline performance.

Demerits

Limitation

The proposed framework may not be generalizable to other climate processes or applications, as it is specifically designed for South Asian monsoon precipitation.

Limitation

The use of learnable kernels may require significant computational resources and training data.

Limitation

The interpretability of the integrations may not be sufficient for all users, as it requires a certain level of domain knowledge and expertise.

Expert Commentary

The proposed framework is a significant contribution to the field of nonlocal operator learning, as it provides a structured approach to aggregating nonlocal information. The use of learnable kernels and interpretable integrations is a key strength of the paper, allowing for a better understanding of the learned relationships. While the framework may have limitations, such as requiring significant computational resources and training data, it has the potential to improve the understanding and prediction of climate processes. As such, it is an important paper that warrants further investigation and development.

Recommendations

  • ✓ Further investigation is needed to evaluate the generalizability of the proposed framework to other climate processes and applications.
  • ✓ More research is required to improve the interpretability of the integrations and make them more accessible to users with limited domain knowledge.

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