Seed variability and calibrated error bounds for physics-informed conjugate heat transfer surrogates

Abstract

Physics-informed neural networks are often proposed as fast surrogates for heat transfer problems too expensive to solve inside a design or control loop. Two questionsabout them are rarely answered: how much of the reported accuracy survives a change of random seed, and how large an error allowance a downstream decision rule needs to stay safe. Both are studied on nonlinear transient conjugate heat transfer in a convectively cooled wall with temperature-dependent properties. A finite volume reference solver is verified against a closed-form nonlinear steady solution, which it reproduces to better than one nanokelvin, and by the method of manufactured solutions. Four surrogate configurations, differing only in loss composition and in the number of reference solutions, are each trained from three random seeds. Adding the physics residual to four reference solutions cuts the mean peak-stress error by a factor of three and a half, and cuts the seed-to-seed standard deviation of the field error by a factor of forty-six. Used as an inequality constraint in a coolant scheduler, the surrogate violates the true structural limit on 14.4 percent of manoeuvres when no allowance is applied. A split-conformal allowance restores the nominal rate, and must be measured for each trained model.Version 3. The scope was narrowed and the title changed to match what the paper delivers. Every configuration is now trained over three random seeds instead of one, and all results are reported as mean and standard deviation. This produced a new result: the physics residual reduces the seed-to-seed standard deviation of the field error by a factor of 46, not only the mean by a factor of 3.5. The heuristic error allowance was replaced by split-conformal calibration, validated by measuring realised violation rates across four surrogates. The audit script now checks 104 quantitative claims, up from 68. The manuscript is formatted for Heat Transfer Engineering.