# Multi-fidelity surrogate modeling for temperature field prediction using deep convolution neural network

arXiv: https://arxiv.org/abs/2301.06674 · HTML: https://mlsanity.com/paper/2301.06674/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 44 references that are in the map.
- First posted on arXiv 17 Jan 2023.

## Builds on (most cited first, 12 of 12)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [On the Variance of the Adaptive Learning Rate and Beyond](https://mlsanity.com/paper/1908.03265/) (2019)
- [Lookahead Optimizer: k steps forward, 1 step back](https://mlsanity.com/paper/1907.08610/) (2019)
- [Survey of multifidelity methods in uncertainty propagation, inference, and optimization](https://mlsanity.com/paper/1806.10761/) (2018)
- [Transfer learning based multi-fidelity physics informed deep neural network](https://mlsanity.com/paper/2005.10614/) (2020)
- [Physics-informed Convolutional Neural Networks for Temperature Field Prediction of Heat Source Layout without Labeled Data](https://mlsanity.com/paper/2109.12482/) (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)
- [Statistical Loss and Analysis for Deep Learning in Hyperspectral Image Classification](https://mlsanity.com/paper/1912.12385/) (2019)
- [Deep Adaptive Arbitrary Polynomial Chaos Expansion: A Mini-data-driven Semi-supervised Method for Uncertainty Quantification](https://mlsanity.com/paper/2107.10428/) (2021)

## Built on by (most cited first, 7 of 7)

- [Multi-fidelity prediction of fluid flow and temperature field based on transfer learning using Fourier Neural Operator](https://mlsanity.com/paper/2304.06972/) (2023)
- [Self-Attention to Operator Learning-based 3D-IC Thermal Simulation](https://mlsanity.com/paper/2510.15968/) (2025)
- [Introducing a microstructure-embedded autoencoder approach for reconstructing high-resolution solution field data from a reduced parametric space](https://mlsanity.com/paper/2405.01975/) (2024)
- [A Kernel-based Resource-efficient Neural Surrogate for Multi-fidelity Prediction of Aerodynamic Field](https://mlsanity.com/paper/2512.10287/) (2025)
- [Enhanced multi-fidelity modelling for digital twin and uncertainty quantification](https://mlsanity.com/paper/2306.14430/) (2023)
- [Machine-learning-based multipoint optimization of fluidic injection parameters for improving nozzle performance](https://mlsanity.com/paper/2409.12707/) (2024)
- [Learning to Reconstruct Temperature Field from Sparse Observations with Implicit Physics Priors](https://mlsanity.com/paper/2512.01196/) (2025)

## Abstract (arXiv)

Temperature field prediction is of great importance in the thermal design of systems engineering, and building the surrogate model is an effective way for the task. Generally, large amounts of labeled data are required to guarantee a good prediction performance of the surrogate model, especially the deep learning model, which have more parameters and better representational ability. However, labeled data, especially high-fidelity labeled data, are usually expensive to obtain and sometimes even impossible. To solve this problem, this paper proposes a pithy deep multi-fidelity model (DMFM) for temperature field prediction, which takes advantage of low-fidelity data to boost the performance with less high-fidelity data. First, a pre-train and fine-tune paradigm are developed in DMFM to train the low-fidelity and high-fidelity data, which significantly reduces the complexity of the deep surrogate model. Then, a self-supervised learning method for training the physics-driven deep multi-fidelity model (PD-DMFM) is proposed, which fully utilizes the physics characteristics of the engineering systems and reduces the dependence on large amounts of labeled low-fidelity data in the training process. Two diverse temperature field prediction problems are constructed to validate the effectiveness of DMFM and PD-DMFM, and the result shows that the proposed method can greatly reduce the dependence of the model on high-fidelity data.