Data-Driven Integration Kernels for Interpretable Nonlocal Operator Learning

2026-03-11

AI Summary

This study addresses the poor interpretability and overfitting issues of existing machine learning models in capturing non-local dependencies in climate processes. The authors propose a kernel-based neural network architecture that explicitly decouples non-local information aggregation from local nonlinear prediction by introducing learnable continuous weighted integral kernels. This design enables efficient multi-scale feature integration across horizontal, vertical, and temporal dimensions while rendering the non-local dependency structure explicitly interpretable. Moreover, it substantially reduces model parameters. Evaluated on South Asian monsoon precipitation forecasting, the proposed model achieves predictive performance comparable to state-of-the-art baselines with significantly fewer parameters, demonstrating its superior generalization capability and modeling efficiency.

Technology Category

• Machine Learning: Kernel Methods
• Natural Language Processing: Interpretability, Analysis, and Evaluation of NLP Models
• Computer Vision: Large Vision Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Large pretrained models with web data

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.

Problem

• nonlocal operator learning
• interpretability
• overfitting
• climate modeling
• data-driven kernels

Innovation

• data-driven integration kernels
• interpretable nonlocal operator learning
• spatiotemporal weighting functions
• structured neural networks
• climate process modeling