Unified Finite Volume Physics Informed Deep Learning to Solve Heat Transfer Problems
Bibliographic record
Abstract
As an alternative for the conventional numerical solver, the emerged physics informed neural network (PINN) has the capacity to solve partial differential equations (PDEs) with noisy data or partially missing physics.Thus, it has gained popularity in fluid dynamics, e.g., solving the heat transfer problems.Nevertheless, PINN struggles with low accuracy and high computational cost when the PDE solution contains multiple scales or steep gradients, which hinders its applications to high-Reynolds-number flows.To remedy the limitations, we propose a PINN approach that unifies the sub-domain decomposition, finite volume discretization and conventional numerical solver, termed as unified finite volume PINN (UFV-PINN).The output by neural network (NN) over the boundaries of agglomerated sub-domains functions as boundary conditions (BCs).Based on this, the conventional numerical solver further solves the PDEs.The gap between NN prediction and the solution by the conventional solver within the subdomain is taken as the new loss term to enforce the conservation law of PDE.As illustration, the steady-state Reynolds-averaged Navier-Stokes (RANS) equations and advection-diffusion equation (ADE) are solved.Numerical experiments are conducted to compare the performance of the proposed UFV-PINN and the standard-PINN, as well as the conventional finite volume (FV) solver.Results indicate that UFV-PINN obtains comparable accuracy to the numerical FV solver, while outperforms the standard-PINN to a large degree in terms of accuracy, computational time, and memory consumption.The proposed UFV-PINN is promising to serve as a powerful diagnostic tool in thermal fluids or surrogate model for thermal design.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| 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) | 0.002 | 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".