# Fourier neural operator for real-time simulation of 3D dynamic urban microclimate

arXiv: https://arxiv.org/abs/2308.03985 · HTML: https://mlsanity.com/paper/2308.03985/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 90 references that are in the map.
- First posted on arXiv 8 Aug 2023.

## Builds on (most cited first, 23 of 23)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [ClimaX: A foundation model for weather and climate](https://mlsanity.com/paper/2301.10343/) (2023)
- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [GraphCast: Learning skillful medium-range global weather forecasting](https://mlsanity.com/paper/2212.12794/) (2022)
- [Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers](https://mlsanity.com/paper/2111.13587/) (2021)
- [Towards Physics-informed Deep Learning for Turbulent Flow Prediction](https://mlsanity.com/paper/1911.08655/) (2019)
- [FengWu: Pushing the Skillful Global Medium-range Weather Forecast beyond 10 Days Lead](https://mlsanity.com/paper/2304.02948/) (2023)
- [Pangu-Weather: A 3D High-Resolution Model for Fast and Accurate Global Weather Forecast](https://mlsanity.com/paper/2211.02556/) (2022)
- [Learning Operators with Coupled Attention](https://mlsanity.com/paper/2201.01032/) (2022)
- [Physics-informed Autoencoders for Lyapunov-stable Fluid Flow Prediction](https://mlsanity.com/paper/1905.10866/) (2019)
- [Physics-Informed Probabilistic Learning of Linear Embeddings of Non-linear Dynamics With Guaranteed Stability](https://mlsanity.com/paper/1906.03663/) (2019)
- [Data-Driven Deep Learning of Partial Differential Equations in Modal Space](https://mlsanity.com/paper/1910.06948/) (2019)
- [Bayesian inference of chaotic dynamics by merging data assimilation, machine learning and expectation-maximization](https://mlsanity.com/paper/2001.06270/) (2020)
- [Deep-learning of Parametric Partial Differential Equations from Sparse and Noisy Data](https://mlsanity.com/paper/2005.07916/) (2020)
- [BCR-Net: a neural network based on the nonstandard wavelet form](https://mlsanity.com/paper/1810.08754/) (2018)

## Built on by (most cited first, 12 of 12)

- [Neural Operators for Accelerating Scientific Simulations and Design](https://mlsanity.com/paper/2309.15325/) (2023)
- [TANTE: Time-Adaptive Operator Learning via Neural Taylor Expansion](https://mlsanity.com/paper/2502.08574/) (2025)
- [Flow Straight and Fast in Hilbert Space: Functional Rectified Flow](https://mlsanity.com/paper/2509.10384/) (2025)
- [Invertible Koopman neural operator for data-driven modeling of partial differential equations](https://mlsanity.com/paper/2503.19717/) (2025)
- [Probabilistic Super-Resolution for Urban Micrometeorology via a Schr"odinger Bridge](https://mlsanity.com/paper/2510.12148/) (2025)
- [Fast 3D Surrogate Modeling for Data Center Thermal Management](https://mlsanity.com/paper/2511.11722/) (2025)
- [Debiased neural operators for estimating functionals](https://mlsanity.com/paper/2604.19296/) (2026)
- [A novel Fourier neural operator framework for classification of multi-sized images: Application to three dimensional digital porous media](https://mlsanity.com/paper/2402.11568/) (2024)
- [Coupling Machine Learning Local Predictions with a Computational Fluid Dynamics Solver to Accelerate Transient Buoyant Plume Simulations](https://mlsanity.com/paper/2409.07175/) (2024)
- [Real-time nonlinear inversion of magnetic resonance elastography with operator learning](https://mlsanity.com/paper/2510.03372/) (2025)
- [Shaping the Wind: Nested Potentials for Kinematically Admissible Urban Wind Prediction](https://mlsanity.com/paper/2610.07033/) (2026)
- [Conditional Flow Matching for Generation of 3D Multi-variable Instantaneous Urban Microclimate Fields](https://mlsanity.com/paper/2610.10430/) (2026)

## Abstract (arXiv)

Global urbanization has underscored the significance of urban microclimates for human comfort, health, and building/urban energy efficiency. They profoundly influence building design and urban planning as major environmental impacts. Understanding local microclimates is essential for cities to prepare for climate change and effectively implement resilience measures. However, analyzing urban microclimates requires considering a complex array of outdoor parameters within computational domains at the city scale over a longer period than indoors. As a result, numerical methods like Computational Fluid Dynamics (CFD) become computationally expensive when evaluating the impact of urban microclimates. The rise of deep learning techniques has opened new opportunities for accelerating the modeling of complex non-linear interactions and system dynamics. Recently, the Fourier Neural Operator (FNO) has been shown to be very promising in accelerating solving the Partial Differential Equations (PDEs) and modeling fluid dynamic systems. In this work, we apply the FNO network for real-time three-dimensional (3D) urban wind field simulation. The training and testing data are generated from CFD simulation of the urban area, based on the semi-Lagrangian approach and fractional stepping method to simulate urban microclimate features for modeling large-scale urban problems. Numerical experiments show that the FNO model can accurately reconstruct the instantaneous spatial velocity field. We further evaluate the trained FNO model on unseen data with different wind directions, and the results show that the FNO model can generalize well on different wind directions. More importantly, the FNO approach can make predictions within milliseconds on the graphics processing unit, making real-time simulation of 3D dynamic urban microclimate possible.