arXiv subjects

Abigail Bodner

Publications and source records attributed to Abigail Bodner.

5 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.

physics.flu-dyn↗

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.

physics.flu-dyn↗

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.

physics.flu-dyn↗

arXiv2026

A theoretical model for oceanic submesoscales under next-order effects of strain and turbulence

Submesoscale currents in the oceanic mixed layer, comprising fronts, eddies, and filaments, are characterized by $\textit{O}(1)$ Rossby numbers (Ro). These features, which constantly interact with background mesoscale flows and boundary layer turbulence (BLT), are critical for mediating vertical exchange between the surface and the ocean interior. Despite growing insight into their generation and evolution, the modification of initially balanced submesoscale dynamics by finite-Ro effects under the combined influence of mesoscale strain and BLT remains unresolved. In this study, we address this question through a perturbation analysis of two-dimensional, geostrophically adjusted oceanic fronts and filaments, adapting the analytical models of \citet{shakespeare_generalized_2013} and \citet{bodner_breakdown_2020}. This framework allows for a systematic exploration across a broad range of Rossby numbers Ro, Ekman numbers Ek, and strain parameters. The first-order solution under pure mesoscale strain exhibits clear frontogenesis and closely mirrors the full model dynamics during early inertial periods, despite the absence of an exponential collapse. Under BLT perturbation, the first-order solution confirms the distinct frontogenetic and frontolytic tendencies associated with eddy viscosity and diffusivity, respectively; however, no transition between these regimes is observed across the explored Ro and Ek parameter space for vertical mixing. When both strain and BLT perturbations are present, turbulent fluxes can strengthen, weaken, or even reverse strain-induced frontogenesis depending on the parameter regime. These results suggest that mixed-layer parameterizations must carefully account for the spatial variability of BLT within submesoscale currents to accurately capture frontal evolution under mesoscale strain.

physics.flu-dyn↗

arXiv2023

A Data-Driven Approach for Parameterizing Submesoscale Vertical Buoyancy Fluxes in the Ocean Mixed Layer

Parameterizations of O(1-10)km submesoscale flows in General Circulation Models (GCMs) represent the effects of unresolved vertical buoyancy fluxes in the ocean mixed layer. These submesoscale flows interact non-linearly with mesoscale and boundary layer turbulence, and it is challenging to account for all the relevant processes in physics-based parameterizations. In this work, we present a data-driven approach for the submesoscale parameterization, that relies on a Convolutional Neural Network (CNN) trained to predict mixed layer vertical buoyancy fluxes as a function of relevant large-scale variables. The data used for training is given from 12 regions sampled from the global high-resolution MITgcm-LLC4320 simulation. When compared with the baseline of a submesoscale physics-based parameterization, the CNN demonstrates high offline skill across all regions, seasons, and filter scales tested in this study. During seasons when submesoscales are most active, which generally corresponds to winter and spring months, we find that the CNN prediction skill tends to be lower than in summer months. The CNN exhibits strong dependency on the mixed layer depth and on the large scale strain field, a variable closely related to frontogenesis, which is currently missing from the submesoscale parameterizations in GCMs.

physics.ao-ph↗