# A Machine Learning Surrogate Modeling Benchmark for Temperature Field Reconstruction of Heat-Source Systems

arXiv: https://arxiv.org/abs/2108.08298 · HTML: https://mlsanity.com/paper/2108.08298/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 56 references that are in the map.
- First posted on arXiv 17 Aug 2021.

## Builds on (most cited first, 15 of 15)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Feature Pyramid Networks for Object Detection](https://mlsanity.com/paper/1612.03144/) (2016)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [SegNet: A Deep Convolutional Encoder-Decoder Architecture for Image Segmentation](https://mlsanity.com/paper/1511.00561/) (2015)
- [Image Transformer](https://mlsanity.com/paper/1802.05751/) (2018)
- [DeepGCNs: Can GCNs Go as Deep as CNNs?](https://mlsanity.com/paper/1904.03751/) (2019)
- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [Data-Driven Sparse Sensor Placement for Reconstruction](https://mlsanity.com/paper/1701.07569/) (2017)
- [Global field reconstruction from sparse sensors with Voronoi tessellation-assisted deep learning](https://mlsanity.com/paper/2101.00554/) (2021)
- [Statistical Loss and Analysis for Deep Learning in Hyperspectral Image Classification](https://mlsanity.com/paper/1912.12385/) (2019)
- [FeatureNMS: Non-Maximum Suppression by Learning Feature Embeddings](https://mlsanity.com/paper/2002.07662/) (2020)
- [Deep Manifold Embedding for Hyperspectral Image Classification](https://mlsanity.com/paper/1912.11264/) (2019)
- [Convex Optimization of Launch Vehicle Ascent Trajectory with Heat-Flux and Splash-Down Constraints](https://mlsanity.com/paper/2008.13239/) (2020)

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

- [RecFNO: a resolution-invariant flow and heat field reconstruction method from sparse observations via Fourier neural operator](https://mlsanity.com/paper/2302.09808/) (2023)
- [Causal reasoning in typical computer vision tasks](https://mlsanity.com/paper/2307.13992/) (2023)
- [Multi-fidelity prediction of fluid flow and temperature field based on transfer learning using Fourier Neural Operator](https://mlsanity.com/paper/2304.06972/) (2023)
- [Uncertainty Guided Ensemble Self-Training for Semi-Supervised Global Field Reconstruction](https://mlsanity.com/paper/2302.11940/) (2023)
- [Deep Intrinsic Decomposition with Adversarial Learning for Hyperspectral Image Classification](https://mlsanity.com/paper/2310.18549/) (2023)
- [FR-Mamba: Time-Series Physical Field Reconstruction Based on State Space Model](https://mlsanity.com/paper/2505.16083/) (2025)
- [Learning to Reconstruct Temperature Field from Sparse Observations with Implicit Physics Priors](https://mlsanity.com/paper/2512.01196/) (2025)
- [MTL-FNO: A Lightweight Multi-Task Fourier Neural Operator for Sparse Field Reconstruction](https://mlsanity.com/paper/2605.26718/) (2026)

## Abstract (arXiv)

Temperature field reconstruction of heat source systems (TFR-HSS) with limited monitoring sensors occurred in thermal management plays an important role in real time health detection system of electronic equipment in engineering. However, prior methods with common interpolations usually cannot provide accurate reconstruction performance as required. In addition, there exists no public dataset for widely research of reconstruction methods to further boost the reconstruction performance and engineering applications. To overcome this problem, this work develops a machine learning modelling benchmark for TFR-HSS task. First, the TFR-HSS task is mathematically modelled from real-world engineering problem and four types of numerically modellings have been constructed to transform the problem into discrete mapping forms. Then, this work proposes a set of machine learning modelling methods, including the general machine learning methods and the deep learning methods, to advance the state-of-the-art methods over temperature field reconstruction. More importantly, this work develops a novel benchmark dataset, namely Temperature Field Reconstruction Dataset (TFRD), to evaluate these machine learning modelling methods for the TFR-HSS task. Finally, a performance analysis of typical methods is given on TFRD, which can be served as the baseline results on this benchmark.