Kolmogorov Arnold Neural Interpolator for Downscaling and Correcting Meteorological Fields from In-Situ Observations

2025-01-24

AI Summary

Meteorological gridded forecasts exhibit systematic biases at station scales—particularly in complex terrain—where conventional discrete-grid models fail to capture the continuity of atmospheric fields. To address this, we propose a continuous neural function-based framework for bias correction and zero-shot super-resolution downscaling. Leveraging the Kolmogorov–Arnold representation theorem—a first in meteorological modeling—we construct a differentiable, continuous implicit neural representation (INR). We further design an optimization mechanism jointly constrained by terrain-texture embedding and sparse in-situ observations, enabling terrain-guided downscaling without high-resolution ground-truth supervision. Evaluated across three regions of the contiguous United States, our method improves station-scale temperature and wind speed forecast accuracy by 40.28% and 67.41%, respectively, significantly outperforming classical interpolation and data-driven baselines.

Technology Category

• Machine Learning: Representation Learning
• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Uncertainty Representations

Application Category

• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Obtaining accurate weather forecasts at station locations is a critical challenge due to systematic biases arising from the mismatch between multi-scale, continuous atmospheric characteristic and their discrete, gridded representations. Previous works have primarily focused on modeling gridded meteorological data, inherently neglecting the off-grid, continuous nature of atmospheric states and leaving such biases unresolved. To address this, we propose the Kolmogorov Arnold Neural Interpolator (KANI), a novel framework that redefines meteorological field representation as continuous neural functions derived from discretized grids. Grounded in the Kolmogorov Arnold theorem, KANI captures the inherent continuity of atmospheric states and leverages sparse in-situ observations to correct these biases systematically. Furthermore, KANI introduces an innovative zero-shot downscaling capability, guided by high-resolution topographic textures without requiring high-resolution meteorological fields for supervision. Experimental results across three sub-regions of the continental United States indicate that KANI achieves an accuracy improvement of 40.28% for temperature and 67.41% for wind speed, highlighting its significant improvement over traditional interpolation methods. This enables continuous neural representation of meteorological variables through neural networks, transcending the limitations of conventional grid-based representations.

Problem

• Weather Forecasting
• Atmospheric Continuity
• Complex Terrain

Innovation

• Kolmogorov Arnold Neural Interpolator
• Weather Forecasting Accuracy
• Terrain-Informed Neural Networks