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This arXiv paper applies physics-informed neural networks (PINNs) to estimate spatially varying heat transfer coefficients in jet impingement cooling, and compares them with an adjoint-FEM inverse method. Its main findings are modest: PINN variants perform comparably at Re = 5000, and generalized representations help at Re = 15000, with errors around 14%. Transfer learning cuts target training time by roughly 51-85%, but its effect on accuracy depends on source-target compatibility. For ML readers, the useful takeaway is the cost-accuracy trade-off in PINN-based inverse problems, not a general claim of superiority.
Generalized PINN-Based Inverse Estimation of Spatially Varying Heat Transfer Coefficients with Transfer Learning
arXiv:2610.14008v1 Announce Type: new Abstract: This study investigates generalized boundary representations and transfer learning for physics-informed neural-network (PINN) estimation of spatially varying convective heat transfer coefficients (HTCs) in jet impingement cooling. Piecewise-linear (PWL) and neural-network boundary estimators are inferred from transient interior-temperature measurements and evaluated against CFD-CHT reference HTC profiles at Reynolds numbers of 5000, 10000 and 15000. A discrete Adjoint-FEM formulation with gradient regularization based on the $H^1$-seminorm provides an independent inverse-method comparison. Transfer learning is investigated under two source-target conditions: transfer between noise levels at the same Reynolds number, and transfer from a controlled Gaussian-profile problem to CFD-CHT-derived target problems at different Reynolds numbers. For the representative Re = 5000 target with 5% measurement noise, quadratic, PWL, and neural-network PINNs achieve relative HTC-profile errors of 5.08, 5.31 and 5.19%, respectively, while generalized representations reduce the error for the Re = 15000 target from 16.76% for the quadratic PINN to 14.41% and 14.46%. Transfer learning reduces target-training time by 57.86-81.71% for fixed-Reynolds-number transfer and by 50.59-84.94% for Gaussian-to-CHT transfer. Its effect on reconstruction accuracy is target dependent: fixed-profile PWL transfer remains within 0.30 percentage points of scratch training, whereas Gaussian-to-CHT transfer produces differences of 0.10-1.52 percentage points across targets and representations. These results demonstrate that generalized PINN representations can accommodate spatially varying HTC profiles without a prescribed quadratic form, while transfer learning can substantially reduce target-training cost for repeated inverse estimation, with the resulting reconstruction accuracy depending on source-target compatibility.
Abstract:This study investigates generalized boundary representations and transfer learning for physics-informed neural-network (PINN) estimation of spatially varying convective heat transfer coefficients (HTCs) in jet impingement cooling. Piecewise-linear (PWL) and neural-network boundary estimators are inferred from transient interior-temperature measurements and evaluated against CFD-CHT reference HTC profiles at Reynolds numbers of 5000, 10000 and 15000. A discrete Adjoint-FEM formulation with gradient regularization based on the $H^1$-seminorm provides an independent inverse-method comparison. Transfer learning is investigated under two source-target conditions: transfer between noise levels at the same Reynolds number, and transfer from a controlled Gaussian-profile problem to CFD-CHT-derived target problems at different Reynolds numbers. For the representative Re = 5000 target with 5% measurement noise, quadratic, PWL, and neural-network PINNs achieve relative HTC-profile errors of 5.08, 5.31 and 5.19%, respectively, while generalized representations reduce the error for the Re = 15000 target from 16.76% for the quadratic PINN to 14.41% and 14.46%. Transfer learning reduces target-training time by 57.86-81.71% for fixed-Reynolds-number transfer and by 50.59-84.94% for Gaussian-to-CHT transfer. Its effect on reconstruction accuracy is target dependent: fixed-profile PWL transfer remains within 0.30 percentage points of scratch training, whereas Gaussian-to-CHT transfer produces differences of 0.10-1.52 percentage points across targets and representations. These results demonstrate that generalized PINN representations can accommodate spatially varying HTC profiles without a prescribed quadratic form, while transfer learning can substantially reduce target-training cost for repeated inverse estimation, with the resulting reconstruction accuracy depending on source-target compatibility.
Machine Learning (cs.LG); Computational Engineering, Finance, and Science (cs.CE); Numerical Analysis (math.NA); Optimization and Control (math.OC); Fluid Dynamics (physics.flu-dyn)
I.2.6; G.1.8; J.2; G.1.10; G.1.6
arXiv:2610.14008 [cs.LG]
(or arXiv:2610.14008v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.14008 arXiv-issued DOI via DataCite (pending registration)
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