arXiv subjects

Jonathan F. MacArt

Publications and source records attributed to Jonathan F. MacArt.

At least 19 recordsLinked to original sources

arXiv2026

A physics-constrained machine-learning sub-grid-scale modeling approach for turbulent premixed flames

A physics-embedded training framework is used to close the sub-grid-scale dynamics of turbulent premixed flames. The trained model augments the resolved flow equations and is trained to match its predicted flow field to trusted data. An end-to-end optimization of the coupled resolved equations and embedded model leads to a model that is robust and effective for a freely propagating premixed flame in turbulence, modeled by a single-species, single-step, and irreversible chemical reaction. Important constraints are built into the training formulation for conservation, scalar boundedness, and equivariance. The model is scaled based on the residual of the resolved flow equations to focus its influence where the closure is needed. It outperforms other cases considered --- no-model, dynamic closure, and the same machine learning model trained directly to fit the residual data --- for a long-time simulation, correcting the turbulence dissipation and flame kinematics. Finally, it is shown how the prediction-based training better informs the model than the precise residual data.

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arXiv2026

Solver-in-the-loop training of deep learning closures for large-eddy simulation of turbulent premixed jet flames

Large-eddy simulation (LES) turbulence models often fail to capture the effects of chemical heat release and the resulting modulation of turbulence in premixed flames, underscoring the need for a framework that remains accurate across a broad range of physical regimes. We develop an augmented eddy-viscosity closure, based on deep neural networks calibrated jointly with the LES solution using adjoint-based optimization and differentiable programming, ensuring consistency with the governing partial differential equations (PDEs). Several objective functions and training methods are examined, and each model is assessed for its capability to interpolate and extrapolate across a wide range of Damköhler numbers. Relative to the Smagorinsky-model baseline, the best neural network model improves a posteriori errors in the LES primitive variables by 25-50% and in the resolved Reynolds stress and scalar flux by more than 60%. Crucially, the model generalizes across Damköhler number regimes, maintaining stability and accuracy even for out-of-sample conditions. These results demonstrate that PDE-consistent deep learning closures can recover both mean fields and resolved turbulence statistics in LES of turbulent premixed flames and can therefore provide a broadly applicable framework for turbulent combustion modeling.

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arXiv2026

Deep Learning-based Algebraic Reynolds Stress Closures for RANS Simulations of Turbulent Flows

Turbulence is ubiquitous in engineering and science, yet direct simulation is prohibitively expensive. The Reynolds-averaged Navier-Stokes (RANS) equations provide savings exceeding ten orders of magnitude but introduce unclosed terms (the closure problem). Offline-trained machine-learning (ML) closures suffer distribution shift in predictive simulations, while ML methods that bypass the governing equations struggle to generalise from scarce high-fidelity data. We develop a physics-derived deep learning closure model for RANS, the Deep Algebraic Reynolds Stress Model (DARSM), which can be trained on small datasets and accurately generalise across Reynolds numbers, to unseen geometries, and to different flow regimes. A neural network maps flow invariants to empirical parameters in an implicit algebraic Reynolds stress equation, derived from the Reynolds stress transport equations under the weak-equilibrium assumption, imposing physics-based structure on the ML closure. End-to-end optimisation through the governing PDEs and the coupled implicit closure eliminates distribution shift, but both unrolled and implicit automatic differentiation fail on the stiff coupled solver. We derive adjoint equations that exploit the solver's implicit-explicit structure for efficient optimisation. On canonical square-duct and periodic-hill benchmarks, DARSM reduces average test velocity error over baseline RANS by $2$-$4\times$ across Reynolds number, geometries, and flow regimes, with peak case-level reductions of $12\times$. The model trained on attached, anisotropy-dominated flows (square duct) accurately generalises without retraining to separated flows (periodic hills), a regime change in the underlying physics. DARSM also outperforms five established ML methods: offline training, tensor-basis neural networks, field-inversion machine learning, DeepONets, and physics-informed neural networks.

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arXiv2026

Model synthesis and identifiability analysis of stiff chemical reaction systems with inVAErt networks

We consider the problem of learning data-driven replicas for stiff systems of ordinary differential equations arising in chemical kinetics that can be evaluated with high computational efficiency. We first focus on training emulators for families of reaction equations under varying reaction rates, using conditional residual networks or long-short term memory architectures. We then apply a recently proposed data-driven framework known as ``inVAErt networks'' to address the ill-posed inverse problem of inferring reaction rates, integration time, and possibly initial conditions from a target set of species concentrations - a problem that has received relatively little attention in the literature. The proposed approach is demonstrated on chemical systems with reversible and irreversible kinetics, spanning 2 to 20 differential equations, 3 to 20 chemical species, and 3 to 25 reaction rate parameters. Relative root mean squared errors produced by the proposed emulators range from $10^{-5}$ for lower-dimensional systems to $10^{-4}$ and $10^{-3}$ for an air pollution model and a hydrogen-air reaction system, respectively. Manifolds of non-identifiable reaction rates recovered by the proposed approach can be analytically verified for simple systems and are consistent with local identifiability analysis in higher dimensions.

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arXiv2025

Dynamic mixed turbulence modeling using a super-resolution generative adversarial approach

A dynamic mixed super-resolution model (DMSRM) for large-eddy simulations (LESs) is proposed, which combines the traditional dynamic mixed model (DMM) formulation with the generation of super-resolved velocity fields from which the subfilter-scale (SFS) stress tensor can be computed. A data-driven super-resolution generative adversarial network (SR-GAN) is employed to upsample the grid-filtered velocity fields by a factor of two, enabling the evaluation of both scale-similarity and the dynamic Smagorinsky contributions. A priori analyses of forced homogeneous isotropic turbulence show that the SR-GAN accurately reconstructs fine-scale flow features and generalizes well across different filter sizes and higher Reynolds number flow configurations, even for unseen input fields. The DMSRM reproduces SFS stresses and energy dissipation more accurately than the traditional DMM. A posteriori LES calculations further confirm that DMSRM predicts the energy spectrum and intermittency more accurately than DMM, even for different LES grid-scale resolutions and for higher Reynolds numbers than those used for training. Unlike DMM, DMSRM yields realistic backscatter and physically consistent SFS energy dissipation. These improvements arise from the physically accurate super-resolved fields generated by the SR-GAN, from which SFS stresses are directly computed. The result is a closure that accurately reproduces stress magnitudes and dissipation while reducing reliance on additional dissipation from the dynamic term. The DMSRM formulation achieves a balance of physical fidelity, robustness, and computational efficiency, offering a promising alternative to traditional DMMs for turbulence LES modeling.

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arXiv2025

Physics-Based Machine Learning Closures and Wall Models for Hypersonic Transition-Continuum Boundary Layer Predictions

Modeling rarefied hypersonic flows remains a fundamental challenge due to the breakdown of classical continuum assumptions in the transition-continuum regime, where the Knudsen number ranges from approximately 0.1 to 10. Conventional Navier-Stokes-Fourier (NSF) models with empirical slip-wall boundary conditions fail to accurately predict nonequilibrium effects such as velocity slip, temperature jump, and shock structure deviations. We develop a physics-constrained machine learning framework that augments transport models and boundary conditions to extend the applicability of continuum solvers in nonequilibrium hypersonic regimes. We employ deep learning PDE models (DPMs) for the viscous stress and heat flux embedded in the governing PDEs and trained via adjoint-based optimization. We evaluate these for two-dimensional supersonic flat-plate flows across a range of Mach and Knudsen numbers. Additionally, we introduce a wall model based on a mixture of skewed Gaussian approximations of the particle velocity distribution function. This wall model replaces empirical slip conditions with physically informed, data-driven boundary conditions for the streamwise velocity and wall temperature. Our results show that a trace-free anisotropic viscosity model, paired with the skewed-Gaussian distribution function wall model, achieves significantly improved accuracy, particularly at high-Mach and high-Knudsen number regimes. Strategies such as parallel training across multiple Knudsen numbers and inclusion of high-Mach data during training are shown to enhance model generalization. Increasing model complexity yields diminishing returns for out-of-sample cases, underscoring the need to balance degrees of freedom and overfitting. This work establishes data-driven, physics-consistent strategies for improving hypersonic flow modeling for regimes in which conventional continuum approaches are invalid.

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arXiv2025

Active Control of Turbulent Airfoil Flows Using Adjoint-based Deep Learning

We train active neural-network flow controllers using a deep learning PDE augmentation method to optimize lift-to-drag ratios in turbulent airfoil flows at Reynolds number $5\times10^4$ and Mach number 0.4. Direct numerical simulation and large eddy simulation are employed to model compressible, unconfined flow over two- and three-dimensional semi-infinite NACA 0012 airfoils at angles of attack $α= 5^\circ$, $10^\circ$, and $15^\circ$. Control actions, implemented through a blowing/suction jet at a fixed location and geometry on the upper surface, are adaptively determined by a neural network that maps local pressure measurements to optimal jet total pressure, enabling a sensor-informed control policy that responds spatially and temporally to unsteady flow conditions. The sensitivities of the flow to the neural network parameters are computed using the adjoint Navier-Stokes equations, which we construct using automatic differentiation applied to the flow solver. The trained flow controllers significantly improve the lift-to-drag ratios and reduce flow separation for both two- and three-dimensional airfoil flows, especially at $α= 5^\circ$ and $10^\circ$. The 2D-trained models remain effective when applied out-of-sample to 3D flows, which demonstrates the robustness of the adjoint-trained control approach. The 3D-trained models capture the flow dynamics even more effectively, which leads to better energy efficiency and comparable performance for both adaptive (neural network) and offline (simplified, constant-pressure) controllers. These results underscore the effectiveness of this learning-based approach in improving aerodynamic performance.

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arXiv2025

ZipGAN: Super-Resolution-based Generative Adversarial Network Framework for Data Compression of Direct Numerical Simulations

The advancement of high-performance computing has enabled the generation of large direct numerical simulation (DNS) datasets of turbulent flows, driving the need for efficient compression/decompression techniques that reduce storage demands while maintaining fidelity. Traditional methods, such as the discrete wavelet transform (DWT), cannot achieve compression ratios of 8 or higher for complex turbulent flows without introducing significant encoding/decoding errors. On the other hand, a super-resolution-based generative adversarial network (SR-GAN), called ZipGAN, can accurately reconstruct fine-scale features, preserving velocity gradients and structural details, even at a compression ratio of 512, thanks to the more efficient representation of the data in a compact latent space. Additional benefits are ascribed to adversarial training. The high GAN training time is significantly reduced with a progressive transfer learning approach and, once trained, they can be applied independently of the Reynolds number. It is demonstrated that ZipGAN can enhance dataset temporal resolution without additional simulation overhead by generating high-quality intermediate fields from compressed snapshots. The ZipGAN discriminator can reliably evaluate the quality of decoded fields, ensuring fidelity even in the absence of original DNS fields. Hence, ZipGAN compression/decompression method presents a highly efficient and scalable alternative for large-scale DNS storage and transfer, offering substantial advantages over the DWT methods in terms of compression efficiency, reconstruction fidelity, and temporal resolution enhancement.

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arXiv2025

oRANS: Online optimisation of RANS machine learning models with embedded DNS data generation

Deep learning (DL) has demonstrated promise for accelerating and enhancing the accuracy of flow physics simulations, but progress is constrained by the scarcity of high-fidelity training data, which is costly to generate and inherently limited to a small set of flow conditions. Consequently, closures trained in the conventional offline paradigm tend to overfit and fail to generalise to new regimes. We introduce an online optimisation framework for DL-based Reynolds-averaged Navier--Stokes (RANS) closures which seeks to address the challenge of limited high-fidelity datasets. Training data is dynamically generated by embedding a direct numerical simulation (DNS) within a subdomain of the RANS domain. The RANS solution supplies boundary conditions to the DNS, while the DNS provides mean velocity and turbulence statistics that are used to update a DL closure model during the simulation. This feedback loop enables the closure to adapt to the embedded DNS target flow, avoiding reliance on precomputed datasets and improving out-of-distribution performance. The approach is demonstrated for the stochastically forced Burgers equation and for turbulent channel flow at $Re_τ=180$, $270$, $395$ and $590$ with varying embedded domain lengths $1\leq L_0/L\leq 8$. Online-optimised RANS models significantly outperform both offline-trained and literature-calibrated closures, with accurate training achieved using modest DNS subdomains. Performance degrades primarily when boundary-condition contamination dominates or when domains are too short to capture low-wavenumber modes. This framework provides a scalable route to physics-informed machine learning closures, enabling data-adaptive reduced-order models that generalise across flow regimes without requiring large precomputed training datasets.

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arXiv2025

OGF: An Online Gradient Flow Method for Optimizing the Statistical Steady-State Time Averages of Unsteady Turbulent Flows

Turbulent flows are chaotic and unsteady, but their statistical distribution converges to a statistical steady state. Engineering quantities of interest typically take the form of time-average statistics such as $ \frac{1}{t} \int_0^t f ( u(x,τ; θ) ) dτ\overset{t \rightarrow \infty}{\rightarrow} F(x; θ)$, where $u(x,t; θ)$ are solutions of the Navier--Stokes equations with parameters $θ$. Optimizing over $F(x; θ)$ has many engineering applications including geometric optimization, flow control, and closure modeling. However, this remains an open challenge, as existing computational approaches are incapable of scaling to physically representative numbers of grid points. The fundamental obstacle is the chaoticity of turbulent flows: gradients calculated with the adjoint method diverge exponentially as $t \rightarrow \infty$. We develop a new online gradient-flow (OGF) method that is scalable to large degree-of-freedom systems and enables optimizing for the steady-state statistics of chaotic, unsteady, turbulence-resolving simulations. The method forward-propagates an online estimate for the gradient of $F(x; θ)$ while simultaneously performing online updates of the parameters $θ$. A key feature is the fully online nature of the algorithm to facilitate faster optimization progress and its combination with a finite-difference estimator to avoid the divergence of gradients due to chaoticity. The proposed OGF method is demonstrated for optimizations over three chaotic ordinary and partial differential equations: the Lorenz-63 equation, the Kuramoto--Sivashinsky equation, and Navier--Stokes solutions of compressible, forced, homogeneous isotropic turbulence. In each case, the OGF method successfully reduces the loss based on $F(x; θ)$ by several orders of magnitude and accurately recovers the optimal parameters.

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arXiv2025

Optimization of Second-Order Transport Models for Transition-Continuum Flows

Modeling transition-continuum hypersonic flows poses significant challenges due to thermodynamic nonequilibrium and the associated breakdown of the continuum assumption. Standard continuum models such as the Navier-Stokes equations are inaccurate for these flows, and molecular models can be inefficient due to the large number of computational particles required at moderately high densities. We explore computational modeling of transition-continuum flows using a second-order constitutive theory that provides closures for the terms representing the molecular transport of momentum and energy. We optimize the second-order model parameters for one-dimensional viscous shocks using an adjoint-based optimization method, with the objective function comprising the primitive flow variables. Target data is obtained from moments of distribution functions obtained by solving the Boltzmann equation. We compare results using optimized second-order models, the unoptimized second-order model, and the first-order Navier-Stokes model for Mach numbers $M\in[1.1,10]$ and observe improvements to the shock profiles and shock thickness calculations. We validate the optimized models by comparing the predicted viscous stress and heat flux, which are not included in the objective function, to those obtained by integrating the distribution function. The close match to these moments indicates that the satisfactory performance of the optimized second-order models is consistent with the nonequilibrium flow physics.

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arXiv2025

Neural network-augmented eddy viscosity closures for turbulent premixed jet flames

Extending gradient-type turbulence closures to turbulent premixed flames is challenging due to the significant influence of combustion heat release. We incorporate a deep neural network (DNN) into Reynolds-averaged Navier--Stokes (RANS) models for the turbulent viscosity and thermal conductivity as nonlinear functions of the local flow state and thermochemical gradients. Our models are optimized over the RANS partial differential equations (PDEs) using an adjoint-based data assimilation procedure. Because we directly target the RANS solution, as opposed to the unclosed terms, successfully trained models are guaranteed to improve the in-sample accuracy of the DNN-augmented RANS predictions. We demonstrate the learned closures for in- and out-of-sample $\textit{a posteriori}$ RANS predictions of compressible, premixed, turbulent jet flames with turbulent Damköhler numbers spanning the gradient- and counter-gradient transport regimes. The DNN-augmented RANS predictions have one to two orders of magnitude lower spatiotemporal mean-squared error than those using a baseline $k$--$ε$ model, even for Damköhler numbers far from those used for training. This demonstrates the accuracy, stability, and generalizability of the PDE-constrained modeling approach for turbulent jet flames over this relatively wide Damköhler number range.

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arXiv2025

Understanding Latent Timescales in Neural Ordinary Differential Equation Models for Advection-Dominated Dynamical Systems

The neural ordinary differential equation (ODE) framework has emerged as a powerful tool for developing accelerated surrogate models of complex physical systems governed by partial differential equations (PDEs). A popular approach for PDE systems employs a two-step strategy: a nonlinear dimensionality reduction using an autoencoder, followed by time integration in the latent space using a neural ODE. This study examines the applicability of such autoencoder-based neural ODE architectures to systems where advection dominates the dynamics. In addition to predictive performance, this work investigates the mechanisms behind model acceleration by analyzing how the autoencoder and neural ODE components influence latent system time-scales. These effects are quantified through eigenvalue analysis of dynamical system Jacobians. Specifically, the study evaluates the sensitivity of model accuracy and discovered latent time-scales to key training choices: decoupled versus end-to-end training, latent space dimensionality, and training trajectory length. A central finding is the crucial role of training trajectory length (i.e., the number of rollout steps included in the loss function), which directly impacts the recovered latent time-scales. Longer trajectories lead to larger limiting time-scales in the latent system, and the most accurate models are shown to capture the largest time-scales of the original system. These insights are demonstrated across a diverse set of unsteady, advection-driven fluid dynamics problems: (1) the Kuramoto-Sivashinsky equations, (2) hydrogen-air channel detonations governed by the compressible reacting Navier-Stokes equations, and (3) 2D atmospheric flows.

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arXiv2025

Sampling-based Distributed Training with Message Passing Neural Network

In this study, we introduce a domain-decomposition-based distributed training and inference approach for message-passing neural networks (MPNN). Our objective is to address the challenge of scaling edge-based graph neural networks as the number of nodes increases. Through our distributed training approach, coupled with Nyström-approximation sampling techniques, we present a scalable graph neural network, referred to as DS-MPNN (D and S standing for distributed and sampled, respectively), capable of scaling up to $O(10^5)$ nodes. We validate our sampling and distributed training approach on two cases: (a) a Darcy flow dataset and (b) steady RANS simulations of 2-D airfoils, providing comparisons with both single-GPU implementation and node-based graph convolution networks (GCNs). The DS-MPNN model demonstrates comparable accuracy to single-GPU implementation, can accommodate a significantly larger number of nodes compared to the single-GPU variant (S-MPNN), and significantly outperforms the node-based GCN.

cs.LG↗

arXiv2024

Online Optimisation of Machine Learning Collision Models to Accelerate Direct Molecular Simulation of Rarefied Gas Flows

We develop an online optimisation algorithm for in situ calibration of collision models in simulations of rarefied gas flows. The online optimised collision models are able to achieve similar accuracy to Direct Molecular Simulation (DMS) at significantly reduced computational cost for 1D normal shocks in argon across a wide range of temperatures and Mach numbers. DMS is a method of simulating rarefied gases which numerically integrates the trajectories of colliding molecules. It often achieves similar fidelity to Molecular Dynamics (MD) simulations, which fully resolve the trajectories of all particles at all times. However, DMS is substantially more computationally expensive than the popular Direct Simulation Monte Carlo (DSMC) method, which uses simple phenomenological models of the collisions. We aim to accelerate DMS by replacing the computationally costly Classical Trajectory Calculations (CTC) with a neural network collision model. A key feature of our approach is that the machine learning (ML) collision model is optimised online during the simulation on a small dataset of CTC trajectories generated in situ during simulations. The online Machine Learning DMS (ML-DMS) is able to reproduce the accuracy of MD and CTC-DMS for 1D normal shocks in argon at a significantly lower computational cost (by a factor of $\sim5$--$15$), at a wide range of physical conditions (Mach numbers $1.55\leq \text{Ma}\leq 50 $, densities $\sim 10^{-4}\text{kg}\text{m}^{-3}$ to $1\text{kg}\text{m}^{-3}$, and temperatures 16K to 300K). We also derive an online optimisation method for calibration of DSMC collision models given a model of the interatomic forces. In our numerical evaluations for 1D normal shocks, the online optimisation method matches or significantly improves the accuracy of VHS (Variable Hard Sphere) DSMC with respect to CTC-DMS (with a $\sim20 \times$ lower computational cost).

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arXiv2024

Influence of adversarial training on super-resolution turbulence reconstruction

Supervised super-resolution deep convolutional neural networks (CNNs) have gained significant attention for their potential in reconstructing velocity and scalar fields in turbulent flows. Despite their popularity, CNNs currently lack the ability to accurately produce high-frequency and small-scale features, and tests of their generalizability to out-of-sample flows are not widespread. Generative adversarial networks (GANs), which consist of two distinct neural networks (NNs), a generator and discriminator, are a promising alternative, allowing for both semi-supervised and unsupervised training. The difference in the flow fields produced by these two NN architectures has not been thoroughly investigated, and a comprehensive understanding of the discriminator's role has yet to be developed. This study assesses the effectiveness of the unsupervised adversarial training in GANs for turbulence reconstruction in forced homogeneous isotropic turbulence. GAN-based architectures are found to outperform supervised CNNs for turbulent flow reconstruction for in-sample cases. The reconstruction accuracy of both architectures diminishes for out-of-sample cases, though the GAN's discriminator network significantly improves the generator's out-of-sample robustness using either an additional unsupervised training step with large eddy simulation input fields and a dynamic selection of the most suitable upsampling factor. These enhance the generator's ability to reconstruct small-scale gradients, turbulence intermittency, and velocity-gradient probability density functions. The extrapolation capability of the GAN-based model is demonstrated for out-of-sample flows at higher Reynolds numbers. Based on these findings, incorporating discriminator-based training is recommended to enhance the reconstruction capability of super-resolution CNNs.

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arXiv2023

Deep Learning Closure of the Navier-Stokes Equations for Transition-Continuum Flows

The predictive accuracy of the Navier-Stokes equations is known to degrade at the limits of the continuum assumption, thereby necessitating expensive and often highly approximate solutions to the Boltzmann equation. While tractable in one spatial dimension, their high dimensionality makes multi-dimensional Boltzmann calculations impractical for all but canonical configurations. It is therefore desirable to augment the Navier-Stokes equations in these regimes. We present an application of a deep learning method to extend the validity of the Navier-Stokes equations to the transition-continuum flows. The technique encodes the missing physics via a neural network, which is trained directly from Boltzmann solutions. While standard DL methods can be considered ad-hoc due to the absence of underlying physical laws, at least in the sense that the systems are not governed by known partial differential equations, the DL framework leverages the a-priori known Boltzmann physics while ensuring that the trained model is consistent with the Navier-Stokes equations. The online training procedure solves adjoint equations, constructed using algorithmic differentiation, which efficiently provide the gradient of the loss function with respect to the learnable parameters. The model is trained and applied to predict stationary, one-dimensional shock thickness in low-pressure argon.

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arXiv2023

Adjoint-based machine learning for active flow control

We develop neural-network active flow controllers using a deep learning PDE augmentation method (DPM). The sensitivities for optimization are computed using adjoints of the governing equations without restriction on the terms that may appear in the objective function. In 1D Burgers' examples with analytic control functions, DPM-based control is comparably effective to supervised learning for in-sample solutions and more effective for out-of-sample solutions. The influence of the optimization time interval is analyzed, the results of which influence algorithm design and hyperparameter choice, balancing control efficacy with computational cost. We later develop adjoint-based controllers for two flows. First, we compare the drag-reduction performance and optimization cost of adjoint controllers and deep reinforcement learning (DRL) controllers for 2D, incompressible, confined cylinder flow at Re=100, with synthetic body forces along the cylinder boundary. The required model complexity for the DRL controller is 4k times that required for the DPM controller. In these tests, the DPM controller is 4.85 times more effective and 63.2 times less computationally intensive to train than the DRL controller. Second, we test DPM control for compressible, unconfined cylinder flow and extrapolate the controller to out-of-sample Reynolds numbers. We also train a simplified, steady controller based on the DPM control law. Both controllers stabilize the vortex shedding with a 99% drag reduction, demonstrating the robustness of the learning approach. For out-of-sample flows, both controllers successfully reduce drag and stabilize vortex shedding, indicating that the DPM-based approach results in a stable model. A key attractive feature is the flexibility of adjoint-based optimization, which permits optimization over arbitrarily defined control laws without the need to match a priori known functions.

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