# Multi-fidelity prediction of fluid flow and temperature field based on transfer learning using Fourier Neural Operator

arXiv: https://arxiv.org/abs/2304.06972 · HTML: https://mlsanity.com/paper/2304.06972/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 64 references that are in the map.
- First posted on arXiv 14 Apr 2023.

## Builds on (most cited first, 10 of 10)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flows](https://mlsanity.com/paper/1810.08217/) (2018)
- [Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networks](https://mlsanity.com/paper/1905.13166/) (2019)
- [Global field reconstruction from sparse sensors with Voronoi tessellation-assisted deep learning](https://mlsanity.com/paper/2101.00554/) (2021)
- [Transfer Learning on Multi-Fidelity Data](https://mlsanity.com/paper/2105.00856/) (2021)
- [A Deep Neural Network Surrogate Modeling Benchmark for Temperature Field Prediction of Heat Source Layout](https://mlsanity.com/paper/2103.11177/) (2021)
- [Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models](https://mlsanity.com/paper/2106.05722/) (2021)
- [A Machine Learning Surrogate Modeling Benchmark for Temperature Field Reconstruction of Heat-Source Systems](https://mlsanity.com/paper/2108.08298/) (2021)
- [Multi-fidelity surrogate modeling for temperature field prediction using deep convolution neural network](https://mlsanity.com/paper/2301.06674/) (2023)

## Built on by (most cited first, 10 of 10)

- [Towards Foundation Models for Scientific Machine Learning: Characterizing Scaling and Transfer Behavior](https://mlsanity.com/paper/2306.00258/) (2023)
- [In-Context Operator Learning with Data Prompts for Differential Equation Problems](https://mlsanity.com/paper/2304.07993/) (2023)
- [PDE Generalization of In-Context Operator Networks: A Study on 1D Scalar Nonlinear Conservation Laws](https://mlsanity.com/paper/2401.07364/) (2024)
- [Self-Attention to Operator Learning-based 3D-IC Thermal Simulation](https://mlsanity.com/paper/2510.15968/) (2025)
- [Multi-fidelity Fourier Neural Operator for Fast Modeling of Large-Scale Geological Carbon Storage](https://mlsanity.com/paper/2308.09113/) (2023)
- [Evaluation of Deep Neural Operator Models toward Ocean Forecasting](https://mlsanity.com/paper/2308.11814/) (2023)
- [SuperWing: a comprehensive transonic wing dataset for data-driven aerodynamic design](https://mlsanity.com/paper/2512.14397/) (2025)
- [Spatiotemporal wall pressure forecast of a rectangular cylinder with physics-aware DeepU-Fourier neural network](https://mlsanity.com/paper/2508.03183/) (2025)
- [Banach neural operator for Navier-Stokes equations](https://mlsanity.com/paper/2512.09070/) (2025)
- [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)

## Abstract (arXiv)

Data-driven prediction of fluid flow and temperature distribution in marine and aerospace engineering has received extensive research and demonstrated its potential in real-time prediction recently. However, usually large amounts of high-fidelity data are required to describe and accurately predict the complex physical information, while in reality, only limited high-fidelity data is available due to the high experiment/computational cost. Therefore, this work proposes a novel multi-fidelity learning method based on the Fourier Neural Operator by jointing abundant low-fidelity data and limited high-fidelity data under transfer learning paradigm. First, as a resolution-invariant operator, the Fourier Neural Operator is first and gainfully applied to integrate multi-fidelity data directly, which can utilize the scarce high-fidelity data and abundant low-fidelity data simultaneously. Then, the transfer learning framework is developed for the current task by extracting the rich low-fidelity data knowledge to assist high-fidelity modeling training, to further improve data-driven prediction accuracy. Finally, three typical fluid and temperature prediction problems are chosen to validate the accuracy of the proposed multi-fidelity model. The results demonstrate that our proposed method has high effectiveness when compared with other high-fidelity models, and has the high modeling accuracy of 99% for all the selected physical field problems. Significantly, the proposed multi-fidelity learning method has the potential of a simple structure with high precision, which can provide a reference for the construction of the subsequent model.