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

TL;DR

This work addresses persistent grid-to-station biases in weather forecasting by reframing meteorological fields as continuous neural functions learned from discretized grids. It introduces the Kolmogorov–Arnold Neural Interpolator (KANI), a hypernetwork-enabled implicit representation that uses a conv encoder, a weight generator, and a KAN-based reconstructor to fuse gridded fields, coordinates, time, and topography into a continuous, multi-scale meteorological state. By leveraging sparse in-situ observations and topographic textures, KANI achieves zero-shot downscaling and systematic bias correction without high-resolution supervision, delivering substantial accuracy gains for temperature and wind speed across CONUS regions. The approach demonstrates strong cross-resolution generalization and offers a scalable, physically informed paradigm for meteorological post-processing with potential broader applicability to other geophysical fields.

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.

Figures (9)

• Figure 1: Visualization of systematic bias correction and zero-shot downscaling results using the proposed KANI method for input meteorological fields a). Through supervision from sparse in-situ observations b), KANI can reconstruct meteorological fields that are more consistent with actual observations, achieving zero-shot downscaling without requiring high-resolution grid supervision. Moreover, the validation accuracy against in-situ stations progressively improves with increasing resolution of the reconstructed fields, significantly exceeding the validation accuracy of the input fields c).
• Figure 2: Illustration of our proposed Kolmogorov–Arnold Neural Interpolator (KANI) architecture a), which mainly consists of three parts: a convolutional encoder to encode the input grid meteorological field. A weight generator produces the weights of the target MLP layers based on the high-level features extracted from the input field. And the KAN-based reconstructor to learn the nonlinear mapping between the embedded input both from meteorological states and auxiliary inputs b) and corresponding reconstruct states at the grid scale and the station scale. Once trained, KANI can accomplish different target tasks by inputting auxiliary information at different scales c).
• Figure 3: The study area in this paper and the distribution of corresponding in-situ observations.
• Figure 4: The illustration of proposed KANI for correcting the grid-station systematic bias for the input meteorological field. As shown in the figure, significant biases (different color distributions) exist between the input fields and their interpolated observations presented in the second column compared to the ground truth observations shown in the first column. Through KANI's correction, we achieve predictions more consistent with ground truth at in-situ station locations and generalize these corrections across the entire field based on topography texture patterns, thereby accomplishing the goal of bias correction.
• Figure 5: Illustration of the zero-shot downscaling result by inputting high-resolution coordinates and corresponding topography information into trained KANI.