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

arXiv: https://arxiv.org/abs/2501.14404 · HTML: https://mlsanity.com/paper/2501.14404/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 36 references that are in the map.
- First posted on arXiv 24 Jan 2025.

## Builds on (most cited first, 19 of 19)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Skillful Precipitation Nowcasting using Deep Generative Models of Radar](https://mlsanity.com/paper/2104.00954/) (2021)
- [U-KAN Makes Strong Backbone for Medical Image Segmentation and Generation](https://mlsanity.com/paper/2406.02918/) (2024)
- [FengWu: Pushing the Skillful Global Medium-range Weather Forecast beyond 10 Days Lead](https://mlsanity.com/paper/2304.02948/) (2023)
- [KAN 2.0: Kolmogorov-Arnold Networks Meet Science](https://mlsanity.com/paper/2408.10205/) (2024)
- [A Brief Review of Hypernetworks in Deep Learning](https://mlsanity.com/paper/2306.06955/) (2023)
- [DeepSD: Generating High Resolution Climate Change Projections through Single Image Super-Resolution](https://mlsanity.com/paper/1703.03126/) (2017)
- [Stochastic Super-Resolution for Downscaling Time-Evolving Atmospheric Fields with a Generative Adversarial Network](https://mlsanity.com/paper/2005.10374/) (2020)
- [A Survey on Kolmogorov-Arnold Network](https://mlsanity.com/paper/2411.06078/) (2024)
- [DiffDA: a Diffusion Model for Weather-scale Data Assimilation](https://mlsanity.com/paper/2401.05932/) (2024)
- [FengWu-GHR: Learning the Kilometer-scale Medium-range Global Weather Forecasting](https://mlsanity.com/paper/2402.00059/) (2024)
- [Precipitation Downscaling with Spatiotemporal Video Diffusion](https://mlsanity.com/paper/2312.06071/) (2023)
- [WeatherGNN: Exploiting Meteo- and Spatial-Dependencies for Local Numerical Weather Prediction Bias-Correction](https://mlsanity.com/paper/2310.05517/) (2023)
- [MambaDS: Near-Surface Meteorological Field Downscaling with Topography Constrained Selective State Space Modeling](https://mlsanity.com/paper/2408.10854/) (2024)
- [ADAF: An Artificial Intelligence Data Assimilation Framework for Weather Forecasting](https://mlsanity.com/paper/2411.16807/) (2024)
- [Local Off-Grid Weather Forecasting with Multi-Modal Earth Observation Data](https://mlsanity.com/paper/2410.12938/) (2024)
- [OMG-HD: A High-Resolution AI Weather Model for End-to-End Forecasts from Observations](https://mlsanity.com/paper/2412.18239/) (2024)
- [Verification against in-situ observations for Data-Driven Weather Prediction](https://mlsanity.com/paper/2305.00048/) (2023)

## Built on by (most cited first, 5 of 5)

- [MatrixKAN: Parallelized Kolmogorov-Arnold Network](https://mlsanity.com/paper/2502.07176/) (2025)
- [Localized Weather Prediction Using Kolmogorov-Arnold Network-Based Models and Deep RNNs](https://mlsanity.com/paper/2505.22686/) (2025)
- [Sparse Local Implicit Image Function for sub-km Weather Downscaling](https://mlsanity.com/paper/2510.20228/) (2025)
- [From AI Weather Prediction to Infrastructure Resilience: A Real-Time Correction-Downscaling Framework for Tropical Cyclone Impact Forecasting](https://mlsanity.com/paper/2603.12828/) (2026)
- [WindINR: Latent-State INR for Fast Local Wind Query and Correction in Complex Terrain](https://mlsanity.com/paper/2605.09511/) (2026)

## Abstract (arXiv)

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.