Generalizable turbulence closures across bluff-body shapes by PINN-based solver-agnostic training
Abstract
Data-driven turbulence closures are commonly calibrated by embedding a CFD solver within an inverse procedure that requires a converged flow solution at every optimization iteration, which is fragile and costly. We instead formulate closure identification as a PDE-constrained, data-driven inverse problem within a physics-informed neural network (PINN), and subsequently stabilize the inferred closure for deployment in a numerical solver. This separation eliminates the training cost of repeated CFD solves and associated adjoint or ensemble evaluations, providing substantial flexibility to investigate alternative closure forms. Using this flexibility, we develop four closures: three model the Reynolds stress on a realizable tensor basis---a local map, a non-local model transporting the turbulent kinetic energy and recovering the out-of-plane normal stress, and the same with a learned length scale ℓ---and a fourth models the Reynolds force F=−∇·τ directly, free of the realizability constraint. All four are trained across six two-dimensional bluff-body wakes at Re=104 and deployed frozen in a standard finite-element solver, stabilized primarily by input-gradient smoothing. Under a strict leave-one-shape-out (LOSO) protocol, all four reduce the field errors of a steady SST k-ω baseline, most strongly on the mean velocity. The learned-length-scale closure is most accurate on the stress fields, while the force model generalizes best on the mean velocity and drag (LOSO drag error ∼ 7%). The closures also train efficiently on Particle Image Velocimetry data, enabling geometries intractable for DNS.
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BibTeX
@misc{zhang2026generalizable,
title = {{Generalizable turbulence closures across bluff-body shapes by PINN-based solver-agnostic training}},
author = {Zhen Zhang and Theo Käufer and Louise Ronglan and Michael S. Triantafyllou and George Em Karniadakis},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.04491},
eprint = {2607.04491},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.04491},
}
RIS
TY - UNPB
TI - Generalizable turbulence closures across bluff-body shapes by PINN-based solver-agnostic training
AU - Zhen Zhang
AU - Theo Käufer
AU - Louise Ronglan
AU - Michael S. Triantafyllou
AU - George Em Karniadakis
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2607.04491
UR - https://arxiv.org/abs/2607.04491
AB - Data-driven turbulence closures are commonly calibrated by embedding a CFD solver within an inverse procedure that requires a converged flow solution at every optimization iteration, which is fragile and costly. We instead formulate closure identification as a PDE-constrained, data-driven inverse problem within a physics-informed neural network (PINN), and subsequently stabilize the inferred closure for deployment in a numerical solver. This separation eliminates the training cost of repeated CFD solves and associated adjoint or ensemble evaluations, providing substantial flexibility to investigate alternative closure forms. Using this flexibility, we develop four closures: three model the Reynolds stress on a realizable tensor basis---a local map, a non-local model transporting the turbulent kinetic energy and recovering the out-of-plane normal stress, and the same with a learned length scale ℓ---and a fourth models the Reynolds force F=−∇·τ directly, free of the realizability constraint. All four are trained across six two-dimensional bluff-body wakes at Re=10^4 and deployed frozen in a standard finite-element solver, stabilized primarily by input-gradient smoothing. Under a strict leave-one-shape-out (LOSO) protocol, all four reduce the field errors of a steady SST k-ω baseline, most strongly on the mean velocity. The learned-length-scale closure is most accurate on the stress fields, while the force model generalizes best on the mean velocity and drag (LOSO drag error ∼ 7%). The closures also train efficiently on Particle Image Velocimetry data, enabling geometries intractable for DNS.
ER -