Regional accuracy of physics-informed neural networks (PINNs) for recirculation in a deep lid-driven cavity
Abstract
Deep lid-driven cavities contain strong motion beneath the lid and much weaker recirculation at depth, so agreement in bulk velocity is an incomplete assessment of a computed flow. We examine data-free physics-informed neural networks (PINNs) for steady, two-dimensional incompressible flow in a cavity of depth-to-width ratio five at Reynolds numbers 100, 250, 500 and 1000. An established hard-constrained streamfunction formulation is combined with prescribed regional collocation, transferred initialization, and selected residual-scaling and envelope variants. Independent spectral/hp calculations with the same Gaussian-regularized lid provide the reference fields. For a cavity of depth-to-width ratio D/W=5 at Reynolds numbers Re=100, 250, 500, and 1000, evaluation on a common 121×605 grid gives interior relative velocity discrepancies of 5.130\%--7.850\%. Over the same cases, floor-region relative velocity discrepancies remain below 5\%, with absolute RMS discrepancies ranging from 1.255×10−10U to 2.332×10−9U, where U is the lid-velocity scale. In a separate 161×801 assessment at Rey=1000, the refined workflow lowers interior velocity discrepancy from 5.624\% to 2.658\% and gauge-aligned pressure RMS discrepancy from 2.793×10−3 to 1.167×10−3ρU2. The improvements compare accumulated training workflows and do not isolate regional sampling. Configuration rankings depend on both region and observable. These finite-budget comparisons establish where the retained workflows agree with the reference and where rotational-field discrepancies remain substantial.
Related
- Lazy training of quantum physics informed neural networks
- AKAPINN: Adaptive Kolmogorov-Arnold Physics-Informed Neural Networks for approximating solutions to quasilinear partial differential equations
- Solving Fredholm Integral Equations with Physics-Informed Neural Networks: Single-and double-network approaches
- Error Estimates in Physics-Informed Neural Networks to Heat-Wave Fluid-Structure Interactive System
- Lie Symmetry-Guided Adaptive Sampling for Physics-Informed Neural Networks
BibTeX
@misc{roohi2026regional,
title = {{Regional accuracy of physics-informed neural networks (PINNs) for recirculation in a deep lid-driven cavity}},
author = {Ehsan Roohi and Christopher J. McDevitt},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38814},
eprint = {2610.38814},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38814},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Regional accuracy of physics-informed neural networks (PINNs) for recirculation in a deep lid-driven cavity
AU - Ehsan Roohi
AU - Christopher J. McDevitt
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38814
UR - https://arxiv.org/abs/2610.38814
AB - Deep lid-driven cavities contain strong motion beneath the lid and much weaker recirculation at depth, so agreement in bulk velocity is an incomplete assessment of a computed flow. We examine data-free physics-informed neural networks (PINNs) for steady, two-dimensional incompressible flow in a cavity of depth-to-width ratio five at Reynolds numbers 100, 250, 500 and 1000. An established hard-constrained streamfunction formulation is combined with prescribed regional collocation, transferred initialization, and selected residual-scaling and envelope variants. Independent spectral/hp calculations with the same Gaussian-regularized lid provide the reference fields. For a cavity of depth-to-width ratio D/W=5 at Reynolds numbers Re=100, 250, 500, and 1000, evaluation on a common 121×605 grid gives interior relative velocity discrepancies of 5.130\%--7.850\%. Over the same cases, floor-region relative velocity discrepancies remain below 5\%, with absolute RMS discrepancies ranging from 1.255×10^−10U to 2.332×10^−9U, where U is the lid-velocity scale. In a separate 161×801 assessment at Rey=1000, the refined workflow lowers interior velocity discrepancy from 5.624\% to 2.658\% and gauge-aligned pressure RMS discrepancy from 2.793×10^−3 to 1.167×10^−3ρU^2. The improvements compare accumulated training workflows and do not isolate regional sampling. Configuration rankings depend on both region and observable. These finite-budget comparisons establish where the retained workflows agree with the reference and where rotational-field discrepancies remain substantial.
ER -