aiqbench analysis
This research introduces data-driven integration kernels to enhance the interpretability of nonlocal operator learning in climate modeling, effectively separating information aggregation from nonlinear prediction. By structuring neural networks this way, the framework captures complex spatiotemporal dependencies like South Asian monsoon patterns with fewer parameters while revealing exactly which locations and time steps drive forecasts. The approach directly addresses the "black box" problem in deep learning for scientific applications by making learned weighting functions explicit and understandable.
Data-Driven Integration Kernels for Interpretable Nonlocal Operator Learning
arXiv:2603.10305v4 Announce Type: replace 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 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/or 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 models achieve near-baseline performance with far fewer trainable parameters, indicating that much of the relevant nonlocal information can be captured through a small set of interpretable integrations when appropriate structural constraints are imposed.
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 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/or 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 models achieve near-baseline performance with far fewer trainable parameters, indicating that much of the relevant nonlocal information can be captured through a small set of interpretable integrations when appropriate structural constraints are imposed.
Machine Learning (cs.LG); Atmospheric and Oceanic Physics (physics.ao-ph)
arXiv:2603.10305 [cs.LG]
(or arXiv:2603.10305v4 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2603.10305 Focus to learn more arXiv-issued DOI via DataCite
Environ. Data Sci. 5 (2026) e31
https://doi.org/10.1017/eds.2026.10056 Focus to learn more DOI(s) linking to related resources
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Full text under the publisher's open licence · 332 words
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