mlsanityData to 7 Oct 2026

Temperature Field Inversion of Heat-Source Systems via Physics-Informed Neural Networks

arXiv 2201.06880 ↗First posted 18 Jan 2022cs.LGcited by 8

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Abstract (arXiv)

Temperature field inversion of heat-source systems (TFI-HSS) with limited observations is essential to monitor the system health. Although some methods such as interpolation have been proposed to solve TFI-HSS, those existing methods ignore correlations between data constraints and physics constraints, causing the low precision. In this work, we develop a physics-informed neural network-based temperature field inversion (PINN-TFI) method to solve the TFI-HSS task and a coefficient matrix condition number based position selection of observations (CMCN-PSO) method to select optima positions of noise observations. For the TFI-HSS task, the PINN-TFI method encodes constrain terms into the loss function, thus the task is transformed into an optimization problem of minimizing the loss function. In addition, we have found that noise observations significantly affect reconstruction performances of the PINN-TFI method. To alleviate the effect of noise observations, the CMCN-PSO method is proposed to find optimal positions, where the condition number of observations is used to evaluate positions. The results demonstrate that the PINN-TFI method can significantly improve prediction precisions and the CMCN-PSO method can find good positions to acquire a more robust temperature field.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 7 of its 37 references that are in the map. First posted on arXiv 18 Jan 2022.

Builds on

7 of 37 references.

References · 7

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2019Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Datacited by 261
  3. 2019Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networkscited by 76
  4. 2018A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equationscited by 55
  5. 2020A Physics-Informed Machine Learning Approach for Solving Heat Transfer Equation in Advanced Manufacturing and Engineering Applicationscited by 53
  6. 2020Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker-Planck Equation and Physics-informed Neural Networkscited by 52
  7. 2021A Deep Neural Network Surrogate Modeling Benchmark for Temperature Field Prediction of Heat Source Layoutcited by 15

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Cited by year

Citing papers per year: 2022: 3; 2023: 1; 2024: 2; 2025: 2.

8 papers.

  1. 2024A finite element-based physics-informed operator learning framework for spatiotemporal partial differential equations on arbitrary domainscited by 15
  2. 2022Bayesian Physics-Informed Extreme Learning Machine for Forward and Inverse PDE Problems with Noisy Datacited by 12
  3. 2025Evolutionary Optimization of Physics-Informed Neural Networks: Evo-PINN Frontiers and Opportunitiescited by 10
  4. 2023Transfer learning for improved generalizability in causal physics-informed neural networks for beam simulationscited by 8
  5. 2022Physics-informed MTA-UNet: Prediction of Thermal Stress and Thermal Deformation of Satellitescited by 3
  6. 2022A physics and data co-driven surrogate modeling approach for temperature field prediction on irregular geometric domaincited by 2
  7. 2024A physics-driven sensor placement optimization methodology for temperature field reconstructioncited by 0
  8. 2025Learning to Reconstruct Temperature Field from Sparse Observations with Implicit Physics Priorscited by 0