Physics informed neural networks for solving inverse thermal wave coupled boundary-value problems
Bibliographic record
Abstract
• Casting BVPs for steady-state amplitude and phase of a dynamic TW field with spatially variant cooling. • Introducing PINNs to solve the BVP of TWs. • Developing a dimensionless BVP framework for the PINN loss function. • Presenting a novel method for filtering the DC component of TWs in thermal diffusivity measurement. As one of the essential parameters in thermophysical analysis, effective measurement of thermal diffusivity is necessary. This paper utilizes the Physics-Informed Neural Networks (PINN) framework to simulate the diffusion of thermal waves. The governing equations / boundary-value problem (BVP) for the thermal waves are expressed in a coupled partial differential form, derived using the method of separation of variables. The inverse problem associated with the coupled partial differential equations is solved using a dimensionless equation / BVP with a loss function that incorporates physical information. Even in the presence of experimental system errors, the neural network (NN) method introduced in this work (“new NN method”) was shown to be capable of robustly solving the thermal wave inverse problem without nonlinear DC components at different spatial locations, for determining the unknown thermal diffusivity of green (unsintered) metal powder compact materials. The results indicate that the coupled partial differential equations for the amplitude and phase of thermal waves within the PINN framework represent a promising strategy for determining thermophysical parameters.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".