mlsanityData to 7 Oct 2026

A Physics-Informed Machine Learning Approach for Solving Heat Transfer Equation in Advanced Manufacturing and Engineering Applications

arXiv 2010.02011 ↗First posted 28 Sep 2020cs.LGcited by 53

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Abstract (arXiv)

A physics-informed neural network is developed to solve conductive heat transfer partial differential equation (PDE), along with convective heat transfer PDEs as boundary conditions (BCs), in manufacturing and engineering applications where parts are heated in ovens. Since convective coefficients are typically unknown, current analysis approaches based on trial and error finite element (FE) simulations are slow. The loss function is defined based on errors to satisfy PDE, BCs and initial condition. An adaptive normalizing scheme is developed to reduce loss terms simultaneously. In addition, theory of heat transfer is used for feature engineering. The predictions for 1D and 2D cases are validated by comparing with FE results. It is shown that using engineered features, heat transfer beyond the training zone can be predicted. Trained model allows for fast evaluation of a range of BCs to develop feedback loops, realizing Industry 4.0 concept of active manufacturing control based on sensor data.

Key facts. Cited by 53 papers in the map (data through 7 Oct 2026). First posted on arXiv 28 Sep 2020.

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Citing papers per year: 2021: 10; 2022: 11; 2023: 9; 2024: 8; 2025: 7; 2026: 8.

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  1. 2021CAN-PINN: A Fast Physics-Informed Neural Network Based on Coupled-Automatic-Numerical Differentiation Methodcited by 93
  2. 2022AirfRANS: High Fidelity Computational Fluid Dynamics Dataset for Approximating Reynolds-Averaged Navier-Stokes Solutionscited by 77
  3. 2024From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learningcited by 73
  4. 2021Learning in Sinusoidal Spaces with Physics-Informed Neural Networkscited by 61
  5. 2023Group Equivariant Fourier Neural Operators for Partial Differential Equationscited by 42
  6. 2022A mixed formulation for physics-informed neural networks as a potential solver for engineering problems in heterogeneous domains: comparison with finite element methodcited by 33
  7. 2021Physics-informed Convolutional Neural Networks for Temperature Field Prediction of Heat Source Layout without Labeled Datacited by 31
  8. 2021Physics-informed neural network simulation of multiphase poroelasticity using stress-split sequential trainingcited by 26
  9. 2022Partial Differential Equations Meet Deep Neural Networks: A Surveycited by 25
  10. 2022Physics guided neural networks for modelling of non-linear dynamicscited by 20
  11. 2024A finite element-based physics-informed operator learning framework for spatiotemporal partial differential equations on arbitrary domainscited by 15
  12. 2023Learning Specialized Activation Functions for Physics-informed Neural Networkscited by 14
38 more
  1. 2021A Machine Learning Framework for Real-time Inverse Modeling and Multi-objective Process Optimization of Composites for Active Manufacturing Controlcited by 9
  2. 2022Temperature Field Inversion of Heat-Source Systems via Physics-Informed Neural Networkscited by 8
  3. 2023Transfer learning for improved generalizability in causal physics-informed neural networks for beam simulationscited by 8
  4. 2021Physics-informed Neural Network for Nonlinear Dynamics in Fiber Opticscited by 7
  5. 2023Digital Twins in Wind Energy: Emerging Technologies and Industry-Informed Future Directionscited by 7
  6. 2025PDE-Agent: A toolchain-augmented multi-agent framework for PDE solvingcited by 7
  7. 2022Physics-informed neural networks for non-Newtonian fluid thermo-mechanical problems: an application to rubber calendering processcited by 6
  8. 2021Applying physics-based loss functions to neural networks for improved generalizability in mechanics problemscited by 5
  9. 2022Self-scalable Tanh (Stan): Faster Convergence and Better Generalization in Physics-informed Neural Networkscited by 5
  10. 2022PhyGNNet: Solving spatiotemporal PDEs with Physics-informed Graph Neural Networkcited by 5
  11. 2021Residual fourier neural operator for thermochemical curing of compositescited by 4
  12. 2021A generic physics-informed neural network-based framework for reliability assessment of multi-state systemscited by 4
  13. 2024Physics-Constrained Learning for PDE Systems with Uncertainty Quantified Port-Hamiltonian Modelscited by 4
  14. 2025Sharp-PINNs: staggered hard-constrained physics-informed neural networks for phase field modelling of corrosioncited by 4
  15. 2021Theory-Guided Machine Learning for Process Simulation of Advanced Compositescited by 3
  16. 2022CP-PINNs: Data-Driven Changepoints Detection in PDEs Using Online Optimized Physics-Informed Neural Networkscited by 3
  17. 2023A Sequential Meta-Transfer (SMT) Learning to Combat Complexities of Physics-Informed Neural Networks: Application to Composites Autoclave Processingcited by 3
  18. 2023Probabilistic Physics-integrated Neural Differentiable Modeling for Isothermal Chemical Vapor Infiltration Processcited by 3
  19. 2024Densely Multiplied Physics Informed Neural Networkscited by 3
  20. 2024Physics and geometry informed neural operator network with application to acoustic scatteringcited by 3
  21. 2024Element-wise Multiplication Based Deeper Physics-Informed Neural Networkscited by 3
  22. 2023CoolPINNs: A Physics-informed Neural Network Modeling of Active Cooling in Vascular Systemscited by 2
  23. 2024Differentiable Neural-Integrated Meshfree Method for Forward and Inverse Modeling of Finite Strain Hyperelasticitycited by 2
  24. 2025A Survey of Physics-Informed AI for Complex Urban Systemscited by 2
  25. 2025Impact of Loss Weight and Model Complexity on Physics-Informed Neural Networks for Computational Fluid Dynamicscited by 2
  26. 2023Solving PDEs with Unmeasurable Source Terms Using Coupled Physics-Informed Neural Network with Recurrent Prediction for Soft Sensorscited by 1
  27. 2024Data assimilation and parameter identification for water waves using the nonlinear Schr"odinger equation and physics-informed neural networkscited by 1
  28. 2025Unraveling particle dark matter with Physics-Informed Neural Networkscited by 1
  29. 2026Ambient Physics: Training Neural PDE Solvers with Partial Observationscited by 1
  30. 2022Faster Optimization on Sparse Graphs via Neural Reparametrizationcited by 0
  31. 2022Interpretability and accessibility of machine learning in selected food processing, agriculture and health applicationscited by 0
  32. 2023Opening the Black Box: Towards inherently interpretable energy data imputation models using building physics insightcited by 0
  33. 2025BridgeNet: A Hybrid, Physics-Informed Machine Learning Framework for Solving High-Dimensional Fokker-Planck Equationscited by 0
  34. 2025Physics-Informed Neural Networks for Thermophysical Property Retrievalcited by 0
  35. 2026Enhancing Heat Sink Efficiency in MOSFETs using Physics Informed Neural Networks: A Systematic Study on Coolant Velocity Estimationcited by 0
  36. 2026Solving stiff dark matter equations via Jacobian Normalization with Physics-Informed Neural Networkscited by 0
  37. 2026Tackling multiphysics problems via finite element-guided physics-informed operator learningcited by 0
  38. 2026PiGRAND: Physics-informed Graph Neural Diffusion for Intelligent Additive Manufacturingcited by 0

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