# Fourier Neural Operators for Arbitrary Resolution Climate Data Downscaling

arXiv: https://arxiv.org/abs/2305.14452 · HTML: https://mlsanity.com/paper/2305.14452/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 39 references that are in the map.
- First posted on arXiv 23 May 2023.

## Builds on (most cited first, 21 of 21)

- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks](https://mlsanity.com/paper/1809.00219/) (2018)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [Video Frame Synthesis using Deep Voxel Flow](https://mlsanity.com/paper/1702.02463/) (2017)
- [Delving Deeper into Convolutional Networks for Learning Video Representations](https://mlsanity.com/paper/1511.06432/) (2015)
- [Stochastic Super-Resolution for Downscaling Time-Evolving Atmospheric Fields with a Generative Adversarial Network](https://mlsanity.com/paper/2005.10374/) (2020)
- [Building high accuracy emulators for scientific simulations with deep neural architecture search](https://mlsanity.com/paper/2001.08055/) (2020)
- [Increasing the accuracy and resolution of precipitation forecasts using deep generative models](https://mlsanity.com/paper/2203.12297/) (2022)
- [Hard-Constrained Deep Learning for Climate Downscaling](https://mlsanity.com/paper/2208.05424/) (2022)
- [Achieving Conservation of Energy in Neural Network Emulators for Climate Modeling](https://mlsanity.com/paper/1906.06622/) (2019)
- [Physics-Guided Architecture (PGA) of Neural Networks for Quantifying Uncertainty in Lake Temperature Modeling](https://mlsanity.com/paper/1911.02682/) (2019)
- [ClimAlign: Unsupervised statistical downscaling of climate variables via normalizing flows](https://mlsanity.com/paper/2008.04679/) (2020)
- [Climbing down Charney's ladder: Machine Learning and the post-Dennard era of computational climate science](https://mlsanity.com/paper/2005.11862/) (2020)
- [RainNet: A Large-Scale Imagery Dataset and Benchmark for Spatial Precipitation Downscaling](https://mlsanity.com/paper/2012.09700/) (2020)
- [Physics-Informed Learning of Aerosol Microphysics](https://mlsanity.com/paper/2207.11786/) (2022)

## Built on by (most cited first, 26 of 26)

- [Generative Diffusion-based Downscaling for Climate](https://mlsanity.com/paper/2404.17752/) (2024)
- [Application-Driven Innovation in Machine Learning](https://mlsanity.com/paper/2403.17381/) (2024)
- [AI Foundation Models for Weather and Climate: Applications, Design, and Implementation](https://mlsanity.com/paper/2309.10808/) (2023)
- [Precipitation Downscaling with Spatiotemporal Video Diffusion](https://mlsanity.com/paper/2312.06071/) (2023)
- [Knowledge-guided Machine Learning: Current Trends and Future Prospects](https://mlsanity.com/paper/2403.15989/) (2024)
- [Masked Autoencoders are PDE Learners](https://mlsanity.com/paper/2403.17728/) (2024)
- [DiffFNO: Diffusion Fourier Neural Operator](https://mlsanity.com/paper/2411.09911/) (2024)
- [Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning](https://mlsanity.com/paper/2506.10973/) (2025)
- [Hierarchical Neural Operator Transformer with Learnable Frequency-aware Loss Prior for Arbitrary-scale Super-resolution](https://mlsanity.com/paper/2405.12202/) (2024)
- [Local Off-Grid Weather Forecasting with Multi-Modal Earth Observation Data](https://mlsanity.com/paper/2410.12938/) (2024)
- [Evaluating the transferability potential of deep learning models for climate downscaling](https://mlsanity.com/paper/2407.12517/) (2024)
- [Longitudinal Flow Matching for Trajectory Modeling](https://mlsanity.com/paper/2510.03569/) (2025)
- [Climate Variable Downscaling with Conditional Normalizing Flows](https://mlsanity.com/paper/2405.20719/) (2024)
- [Conformal Prediction for Generative Models via Adaptive Cluster-Based Density Estimation](https://mlsanity.com/paper/2601.22298/) (2026)
- [On Global Applicability and Location Transferability of Generative Deep Learning Models for Precipitation Downscaling](https://mlsanity.com/paper/2512.01400/) (2025)
- [Towards a Foundation Model for the Martian Atmosphere](https://mlsanity.com/paper/2605.28851/) (2026)
- [Is Zero-Shot Super-Resolution Possible in Operator Learning?](https://mlsanity.com/paper/2606.00296/) (2026)
- [FLAME: Physics-Guided Neural Operators for Onboard Satellite Methane Detection in Hyperspectral Imagery](https://mlsanity.com/paper/2606.01577/) (2026)
- [Multi-modal Representation Learning for Cross-modal Prediction of Continuous Weather Patterns from Discrete Low-Dimensional Data](https://mlsanity.com/paper/2401.16936/) (2024)
- [Weakly-Constrained 4D Var for Downscaling with Uncertainty using Data-Driven Surrogate Models](https://mlsanity.com/paper/2503.02665/) (2025)
- [Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems](https://mlsanity.com/paper/2505.24578/) (2025)
- [Vision Transformers for Multi-Variable Climate Downscaling: Emulating Regional Climate Models with a Shared Encoder and Multi-Decoder Architecture](https://mlsanity.com/paper/2506.22447/) (2025)
- [Multiscale Neural PDE Surrogates for Prediction and Downscaling: Application to Ocean Currents](https://mlsanity.com/paper/2507.18067/) (2025)
- [Downscaling climate projections to 1 km with single-image super resolution](https://mlsanity.com/paper/2509.21399/) (2025)
- [Physics-Informed Super-Resolution of Atmospheric Data](https://mlsanity.com/paper/2607.18877/) (2026)
- [Generalizable Neural Downscaling of Earth System Model Wind Fields via Continuous Dynamics Modeling](https://mlsanity.com/paper/2610.03757/) (2026)

## Abstract (arXiv)

Climate simulations are essential in guiding our understanding of climate change and responding to its effects. However, it is computationally expensive to resolve complex climate processes at high spatial resolution. As one way to speed up climate simulations, neural networks have been used to downscale climate variables from fast-running low-resolution simulations, but high-resolution training data are often unobtainable or scarce, greatly limiting accuracy. In this work, we propose a downscaling method based on the Fourier neural operator. It trains with data of a small upsampling factor and then can zero-shot downscale its input to arbitrary unseen high resolution. Evaluated both on ERA5 climate model data and on the Navier-Stokes equation solution data, our downscaling model significantly outperforms state-of-the-art convolutional and generative adversarial downscaling models, both in standard single-resolution downscaling and in zero-shot generalization to higher upsampling factors. Furthermore, we show that our method also outperforms state-of-the-art data-driven partial differential equation solvers on Navier-Stokes equations. Overall, our work bridges the gap between simulation of a physical process and interpolation of low-resolution output, showing that it is possible to combine both approaches and significantly improve upon each other.