arXiv subjects

Ryley McConkey

Publications and source records attributed to Ryley McConkey.

11 recordsLinked to original sources

arXiv2026

Rotational equivariance and locality in data-driven subgrid-scale closures

Data-driven subgrid-scale closures for large eddy simulation are of significant interest in many engineering and geoscience applications. In this context, several important questions remain about the role of rotational equivariance as an inductive bias for learned tensorial mappings. We investigate whether equivariance improves accuracy, parameter efficiency, and generalization for subgrid-scale modelling at realistic filter ratios. For turbulent channel flow, we compare data-augmented non-equivariant architectures to those with equivariance as an inductive bias. We compare both pointwise and nonlocal versions of these two model classes. All models are evaluated at matched parameter counts across spatiotemporal, anisotropy, and Reynolds number generalization. We show that non-augmented models learn a small degree of equivariance directly from turbulence data, especially when that data is more isotropic. The equivariant nonlocal architecture attains the highest correlation coefficient on every generalization test at approximately half the parameter count of its non-equivariant counterpart, while the pointwise architectures do not improve on the analytical Clark baseline. Additionally, the equivariant model is more data-efficient than a non-equivariant model. The benefit of equivariance grows with the receptive field of the model, indicating that equivariance and nonlocality are both useful for the subgrid-scale closure task at realistic dataset size, parameter counts, and filter size.

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arXiv2026

The Closure Challenge: a benchmark task for machine learning in turbulence modelling

We introduce a field-wide benchmark challenge for machine learning in Reynolds-averaged Navier-Stokes (RANS) turbulence modelling. Though open-source datasets exist for training data-driven turbulence closure models, the field has been notably lacking a standard benchmark metric and test dataset. The Closure Challenge is a curated collection of open-source datasets and evaluation code that remedies this problem. We provide a variety of high-fidelity training data in a standardized format, including mean velocity gradients. The test cases (periodic hills, square duct, and NASA wall-mounted hump) evaluate Reynolds number and geometry generalization, two key issues in the field. We present results from three early submissions to the challenge. This is an ongoing challenge, intended to continuously spur innovation in machine learning for turbulence modelling. Our goal is for this benchmark to become the standard evaluation for new machine learning frameworks in RANS. The Closure Challenge is available at https://github.com/rmcconke/closure-challenge-benchmark.

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arXiv2026

Turbulence teaches equivariance to neural networks

We show that the rotational nature of turbulence affects how neural networks learn mappings between quantities governed by the Navier-Stokes equations. We train super-resolution models at different wall-normal locations in a turbulent channel flow, where anisotropy varies naturally, and test their generalization to new coordinate frames, new anisotropy regimes, and a higher Reynolds number. Our findings inform both the design of equivariant machine learning models for turbulence and our understanding of how turbulence shapes what those models learn. First, mappings that better respect the rotational symmetries of the Navier-Stokes equations generalize better to new flows. Coordinate-frame generalization is therefore a key part of the broader generalization problem, since turbulent flows contain a wide range of local orientations. Second, turbulence itself partially teaches equivariance to learned mappings, an effect we call implicit data augmentation. The effect strengthens with dataset size and with isotropy, since a more isotropic dataset samples more orientations under which the Navier-Stokes equations are covariant. Implicit augmentation is also scale-dependent, with smaller scales exhibiting lower equivariance error. This scale-dependency is consistent with Kolmogorov's hypothesis of local isotropy. Third, enforcing equivariance as an architectural inductive bias is the limit of these effects: an exactly equivariant network outperforms unconstrained CNNs on all generalization tests, with roughly an order of magnitude fewer parameters. We expect these effects to apply broadly to learned mappings between tensorial flow quantities, making them relevant to most machine learning applications in turbulence.

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arXiv2025

Implicit Augmentation from Distributional Symmetry in Turbulence Super-Resolution

The immense computational cost of simulating turbulence has motivated the use of machine learning approaches for super-resolving turbulent flows. A central challenge is ensuring that learned models respect physical symmetries, such as rotational equivariance. We show that standard convolutional neural networks (CNNs) can partially acquire this symmetry without explicit augmentation or specialized architectures, as turbulence itself provides implicit rotational augmentation in both time and space. Using 3D channel-flow subdomains with differing anisotropy, we find that models trained on more isotropic mid-plane data achieve lower equivariance error than those trained on boundary layer data, and that greater temporal or spatial sampling further reduces this error. We show a distinct scale-dependence of equivariance error that occurs regardless of dataset anisotropy that is consistent with Kolmogorov's local isotropy hypothesis. These results clarify when rotational symmetry must be explicitly incorporated into learning algorithms and when it can be obtained directly from turbulence, enabling more efficient and symmetry-aware super-resolution.

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arXiv2025

Kolmogorov-Arnold Networks for Turbulence Anisotropy Mapping

This study evaluates the generalization performance and representation efficiency (parsimony) of a previously introduced Tensor Basis Kolmogorov-Arnold Network (TBKAN) architecture for data-driven turbulence modeling. The TBKAN framework replaces the multi-layer perceptron (MLP) used in either the standard or modified Tensor Basis Neural Network (TBNN) with a Kolmogorov-Arnold network (KAN), which significantly reduces the model complexity while providing a structure that potentially can be used with symbolic regression to provide a physical interpretability that is not available in a 'black box' MLP. While some prior work demonstrated TBKAN's feasibility for modeling a 'simple' flat plate boundary layer flow, this study extends the TBKAN architecture to model more complex benchmark flows, in particular, square duct and periodic hills flows which exhibit strong turbulence anisotropy, secondary motion, and flow separation and reattachment. A realizability-informed loss function is employed to constrain the model predictions, and, for the first time, TBKAN predictions are stably injected into the Reynolds-averaged Navier-Stokes equations to provide it a posteriori predictions of the mean velocity field.

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arXiv2025

Bayesian Optimization of the GEKO Turbulence Model for Predicting Flow Separation Over a Smooth Surface

This paper applies Bayesian-optimization-RANS (turbo-RANS) to improve Reynolds-averaged Navier-Stokes (RANS) turbulence models for a converging-diverging channel, a case with adverse pressure gradients and flow separation. Using Bayesian optimization, the Generalized $k$-$\omega$ (GEKO) model was calibrated by tuning $C_\text{SEP}$ and $C_\text{NW}$ with sparse direct numerical simulation (DNS) data at $Re = 12,600$. The calibration followed the Generalized Error Distribution-based Calibration Procedure (GEDCP), optimizing coefficients based on pressure recovery ($C_p$) and skin friction ($C_f$). The optimized model was evaluated beyond training data. Streamwise velocity ($U$) predictions at $Re = 12,600$ were compared to DNS to assess improvements in $C_p$ and $C_f$. To test robustness, comparisons were made against large-eddy simulation (LES) data at $Re = 20,580$ for velocity and skin friction. Results show that optimized GEKO (turbo-RANS) improves wall quantity predictions, particularly reattachment. Improved velocity profiles at both Reynolds numbers suggest Bayesian-optimized coefficients enhance adverse pressure gradient modeling. The model retains accuracy across different $Re$, showing turbo-RANS' potential in turbulence model corrections that generalize across flows. While skin friction predictions showed limited improvement due to constraints of two-equation models, this study highlights the role of machine learning-assisted RANS calibration in improving predictive accuracy for complex flows. The results suggest optimized coefficients from a single dataset can be applied across moderate $Re$ variations, improving turbo-RANS' applicability for turbulence model tuning.

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arXiv2024

Realizability-Informed Machine Learning for Turbulence Anisotropy Mappings

Within the context of machine learning-based closure mappings for RANS turbulence modelling, physical realizability is often enforced using ad-hoc postprocessing of the predicted anisotropy tensor. In this study, we address the realizability issue via a new physics-based loss function that penalizes non-realizable results during training, thereby embedding a preference for realizable predictions into the model. Additionally, we propose a new framework for data-driven turbulence modelling which retains the stability and conditioning of optimal eddy viscosity-based approaches while embedding equivariance. Several modifications to the tensor basis neural network to enhance training and testing stability are proposed. We demonstrate the conditioning, stability, and generalization of the new framework and model architecture on three flows: flow over a flat plate, flow over periodic hills, and flow through a square duct. The realizability-informed loss function is demonstrated to significantly increase the number of realizable predictions made by the model when generalizing to a new flow configuration. Altogether, the proposed framework enables the training of stable and equivariant anisotropy mappings, with more physically realizable predictions on new data. We make our code available for use and modification by others. Moreover, as part of this study, we explore the applicability of Kolmogorov-Arnold Networks (KAN) to turbulence modeling, assessing its potential to address non-linear mappings in the anisotropy tensor predictions and demonstrating promising results for the flat plate case.

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arXiv2024

turbo-RANS: Straightforward and Efficient Bayesian Optimization of Turbulence Model Coefficients

Industrial simulations of turbulent flows often rely on Reynolds-averaged Navier-Stokes (RANS) turbulence models, which contain numerous closure coefficients that need to be calibrated. In this work, we address this issue by proposing a semi-automated calibration of these coefficients using a new framework (referred to as turbo-RANS) based on Bayesian optimization. We introduce the generalized error and default coefficient preference (GEDCP) objective function, which can be used with integral, sparse, or dense reference data for the purpose of calibrating RANS turbulence closure model coefficients. Then, we describe a Bayesian optimization-based algorithm for conducting the calibration of these model coefficients. An in-depth hyperparameter tuning study is conducted to recommend efficient settings for the turbo-RANS optimization procedure. We demonstrate that the performance of the $k$-$ω$ shear stress transport (SST) and Generalized $k$-$ω$ (GEKO) turbulence models can be efficiently improved via turbo-RANS, for three example cases: predicting the lift coefficient of an airfoil; predicting the velocity and turbulent kinetic energy fields for a separated flow; and, predicting the wall pressure coefficient distribution for flow through a converging-diverging channel. This work is the first to propose and provide an open-source black-box calibration procedure for turbulence model coefficients based on Bayesian optimization. We propose a data-flexible objective function for the calibration target. Our open-source implementation of the turbo-RANS framework includes OpenFOAM, Ansys Fluent, STAR-CCM+, and solver-agnostic templates for user application.

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arXiv2022

On the generalizability of machine-learning-assisted anisotropy mappings for predictive turbulence modelling

Several machine learning frameworks for augmenting turbulence closure models have been recently proposed. However, the generalizability of an augmented turbulence model remains an open question. We investigate this question by systematically varying the training and test sets of several models. An optimal three-term tensor basis expansion is used to develop a model-agnostic data-driven turbulence closure approximation. Then, hyperparameter optimization was performed for a random forest, a neural network, and an eXtreme Gradient Boosting (XGBoost) model. We recommend XGBoost for data-driven turbulence closure modelling owing to its low-tuning cost and good performance. We also find that machine learning models generalize well to new parametric variations of flows seen in the training dataset, but lack generalizability to new flow types. This generalizability gap suggests that machine learning methods are most suited for developing specialized models for a given flow type, a problem often encountered in industrial applications.

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arXiv2022

Deep Structured Neural Networks for Turbulence Closure Modelling

Despite well-known limitations of Reynolds-averaged Navier-Stokes (RANS) simulations, this methodology remains the most widely used tool for predicting many turbulent flows, due to computational efficiency. Machine learning is a promising approach to improve the accuracy of RANS simulations. One major area of improvement is using machine learning models to represent the complex relationship between the mean flow field gradients and the Reynolds stress tensor. In the present work, modifications to improve the stability of previous optimal eddy viscosity approaches for RANS simulations are presented and evaluated. The optimal eddy viscosity is reformulated with a non-negativity constraint, which promotes numerical stability. We demonstrate that the new formulation of the optimal eddy viscosity improves the conditioning of the RANS equations for a periodic hills test case. To demonstrate the suitability of this proportional/orthogonal tensor decomposition for use in a physics-informed data-driven turbulence closure, we use two neural networks (structured on this specific tensor decomposition which is incorporated as an inductive bias into the network design) to predict the newly reformulated linear and non-linear parts of the Reynolds stress tensor. Injecting these network model predictions for the Reynolds stresses into a RANS simulation improves predictions of the velocity field, even when compared to a sophisticated (state of the art) physics-based turbulence closure model. Finally, we apply SHAP (SHapley Additive exPlanations) values to obtain insights from the learned representation for the inner workings of the neural network used to predict the optimal eddy viscosity from the input feature data.

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arXiv2021

A curated dataset for data-driven turbulence modelling

The recent surge in machine learning augmented turbulence modelling is a promising approach for addressing the limitations of Reynolds-averaged Navier-Stokes (RANS) models. This work presents the development of the first open-source dataset, curated and structured for immediate use in machine learning augmented turbulence closure modelling. The dataset features a variety of RANS simulations with matching direct numerical simulation (DNS) and large-eddy simulation (LES) data. Four turbulence models are selected to form the initial dataset: $k$-$\varepsilon$, $k$-$\varepsilon$-$ϕ_t$-$f$, $k$-$ω$, and $k$-$ω$ SST. The dataset consists of 29 cases per turbulence model, for several parametrically sweeping reference DNS/LES cases: periodic hills, square duct, parametric bumps, converging-diverging channel, and a curved backward-facing step. At each of the 895,640 points, various RANS features with DNS/LES labels are available. The feature set includes quantities used in current state-of-the-art models, and additional fields which enable the generation of new feature sets. The dataset reduces effort required to train, test, and benchmark new models. The dataset is available at https://doi.org/10.34740/kaggle/dsv/2044393 .

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