Inherent Failure Modes of Physics-Informed Neural Networks for Buoyancy-Driven Flow: Role of Non-Dimensionalization in Network Training
Abstract
We investigate the influence of non-dimensionalization on the trainability and accuracy of physics-informed neural networks (PINNs) for buoyancy-driven flows. Using a differentially heated square cavity at Pr=0.71 and Ra=103--105, we compare thermal-diffusive and free-fall velocity scalings under identical training conditions. The free-fall scaling, with a unit buoyancy coefficient, achieves errors below 1.1\% in the mean Nusselt number for Ra≤104, whereas the diffusive scaling, with a buoyancy coefficient of Ra Pr, produces errors of 157--650\% and diverges at Ra=105. We identify a coefficient-induced gradient imbalance, with the dominant buoyancy-related contribution to the loss gradient scaling as (Ra Pr)2, and confirm it through direct gradient measurements. Neither sparse-data supervision nor adaptive loss weighting resolves the training difficulties under the tested conditions. For unsteady convection, the free-fall PINN accurately predicts long-time heat transfer but fails to capture the transient Nusselt-number overshoot. These findings establish non-dimensionalization as an important design consideration for improving PINN trainability in buoyancy-driven flows.
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BibTeX
@misc{chand2026inherent,
title = {{Inherent Failure Modes of Physics-Informed Neural Networks for Buoyancy-Driven Flow: Role of Non-Dimensionalization in Network Training}},
author = {Krishan Chand and Ahmad Peyvan and Haoxiang Luo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38889},
eprint = {2610.38889},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38889},
}
RIS
TY - UNPB
TI - Inherent Failure Modes of Physics-Informed Neural Networks for Buoyancy-Driven Flow: Role of Non-Dimensionalization in Network Training
AU - Krishan Chand
AU - Ahmad Peyvan
AU - Haoxiang Luo
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38889
UR - https://arxiv.org/abs/2610.38889
AB - We investigate the influence of non-dimensionalization on the trainability and accuracy of physics-informed neural networks (PINNs) for buoyancy-driven flows. Using a differentially heated square cavity at Pr=0.71 and Ra=10^3--10^5, we compare thermal-diffusive and free-fall velocity scalings under identical training conditions. The free-fall scaling, with a unit buoyancy coefficient, achieves errors below 1.1\% in the mean Nusselt number for Ra≤10^4, whereas the diffusive scaling, with a buoyancy coefficient of Ra Pr, produces errors of 157--650\% and diverges at Ra=10^5. We identify a coefficient-induced gradient imbalance, with the dominant buoyancy-related contribution to the loss gradient scaling as (Ra Pr)^2, and confirm it through direct gradient measurements. Neither sparse-data supervision nor adaptive loss weighting resolves the training difficulties under the tested conditions. For unsteady convection, the free-fall PINN accurately predicts long-time heat transfer but fails to capture the transient Nusselt-number overshoot. These findings establish non-dimensionalization as an important design consideration for improving PINN trainability in buoyancy-driven flows.
ER -