# FNP: Fourier Neural Processes for Arbitrary-Resolution Data Assimilation

arXiv: https://arxiv.org/abs/2406.01645 · HTML: https://mlsanity.com/paper/2406.01645/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 61 references that are in the map.
- First posted on arXiv 3 Jun 2024.

## Builds on (most cited first, 30 of 30)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [Neural Processes](https://mlsanity.com/paper/1807.01622/) (2018)
- [Attentive Neural Processes](https://mlsanity.com/paper/1901.05761/) (2019)
- [WeatherBench: A benchmark dataset for data-driven weather forecasting](https://mlsanity.com/paper/2002.00469/) (2020)
- [FuXi: A cascade machine learning forecasting system for 15-day global weather forecast](https://mlsanity.com/paper/2306.12873/) (2023)
- [WeatherBench 2: A benchmark for the next generation of data-driven global weather models](https://mlsanity.com/paper/2308.15560/) (2023)
- [FengWu: Pushing the Skillful Global Medium-range Weather Forecast beyond 10 Days Lead](https://mlsanity.com/paper/2304.02948/) (2023)
- [Convolutional Conditional Neural Processes](https://mlsanity.com/paper/1910.13556/) (2019)
- [Score-based Data Assimilation](https://mlsanity.com/paper/2306.10574/) (2023)
- [Meta-Learning Stationary Stochastic Process Prediction with Convolutional Neural Processes](https://mlsanity.com/paper/2007.01332/) (2020)
- [Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review](https://mlsanity.com/paper/2303.10462/) (2023)
- [DiffDA: a Diffusion Model for Weather-scale Data Assimilation](https://mlsanity.com/paper/2401.05932/) (2024)
- [Latent Space Data Assimilation by using Deep Learning](https://mlsanity.com/paper/2104.00430/) (2021)
- [Convolutional conditional neural processes for local climate downscaling](https://mlsanity.com/paper/2101.07950/) (2021)
- [Deep Generative Data Assimilation in Multimodal Setting](https://mlsanity.com/paper/2404.06665/) (2024)
- [Integrating Recurrent Neural Networks with Data Assimilation for Scalable Data-Driven State Estimation](https://mlsanity.com/paper/2109.12269/) (2021)
- [Towards an end-to-end artificial intelligence driven global weather forecasting system](https://mlsanity.com/paper/2312.12462/) (2023)
- [ExtremeCast: Boosting Extreme Value Prediction for Global Weather Forecast](https://mlsanity.com/paper/2402.01295/) (2024)
- [Fuxi-DA: A Generalized Deep Learning Data Assimilation Framework for Assimilating Satellite Observations](https://mlsanity.com/paper/2404.08522/) (2024)
- [Environmental Sensor Placement with Convolutional Gaussian Neural Processes](https://mlsanity.com/paper/2211.10381/) (2022)
- [Evidential Conditional Neural Processes](https://mlsanity.com/paper/2212.00131/) (2022)
- [Latent assimilation with implicit neural representations for unknown dynamics](https://mlsanity.com/paper/2309.09574/) (2023)
- [Observation Error Covariance Specification in Dynamical Systems for Data assimilation using Recurrent Neural Networks](https://mlsanity.com/paper/2111.06447/) (2021)
- [Sim2Real for Environmental Neural Processes](https://mlsanity.com/paper/2310.19932/) (2023)
- [Spectral Convolutional Conditional Neural Processes](https://mlsanity.com/paper/2404.13182/) (2024)
- [GP-ConvCNP: Better Generalization for Convolutional Conditional Neural Processes on Time Series Data](https://mlsanity.com/paper/2106.04967/) (2021)

## Built on by (most cited first, 8 of 8)

- [FlowDAS: A Stochastic Interpolant-based Framework for Data Assimilation](https://mlsanity.com/paper/2501.16642/) (2025)
- [MambaDS: Near-Surface Meteorological Field Downscaling with Topography Constrained Selective State Space Modeling](https://mlsanity.com/paper/2408.10854/) (2024)
- [PhyDA: Physics-Guided Diffusion Models for Data Assimilation in Atmospheric Systems](https://mlsanity.com/paper/2505.12882/) (2025)
- [Align-DA: Align Score-based Atmospheric Data Assimilation with Multiple Preferences](https://mlsanity.com/paper/2505.22008/) (2025)
- [DAWP: A framework for global observation forecasting via Data Assimilation and Weather Prediction in satellite observation space](https://mlsanity.com/paper/2510.15978/) (2025)
- [DAMBench: A Multi-Modal Benchmark for Deep Learning-based Atmospheric Data Assimilation](https://mlsanity.com/paper/2511.01468/) (2025)
- [Earth-o1: A Grid-free Observation-native Atmospheric World Model](https://mlsanity.com/paper/2605.06337/) (2026)
- [Uncertainty-Calibrated Spatiotemporal Field Diffusion with Sparse Supervision](https://mlsanity.com/paper/2603.04431/) (2026)

## Abstract (arXiv)

Data assimilation is a vital component in modern global medium-range weather forecasting systems to obtain the best estimation of the atmospheric state by combining the short-term forecast and observations. Recently, AI-based data assimilation approaches have attracted increasing attention for their significant advantages over traditional techniques in terms of computational consumption. However, existing AI-based data assimilation methods can only handle observations with a specific resolution, lacking the compatibility and generalization ability to assimilate observations with other resolutions. Considering that complex real-world observations often have different resolutions, we propose the textitFourier Neural Processes (FNP) for textitarbitrary-resolution data assimilation in this paper. Leveraging the efficiency of the designed modules and flexible structure of neural processes, FNP achieves state-of-the-art results in assimilating observations with varying resolutions, and also exhibits increasing advantages over the counterparts as the resolution and the amount of observations increase. Moreover, our FNP trained on a fixed resolution can directly handle the assimilation of observations with out-of-distribution resolutions and the observational information reconstruction task without additional fine-tuning, demonstrating its excellent generalization ability across data resolutions as well as across tasks.