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NASA NTRS2024

Augmenting RANS Turbulence Models Guided by Field Inversion and Machine Learning

This report investigates the use of a data-driven approach, viz., Field Inversion and Machine Learning (FIML), to improve conventional RANS turbulence models like the Spalart-Allmaras model and the Menter SST k-ω model. One of the crucial aspects of using an ML-based approach with limited training data to produce corrections that are generalizable to a large range of flow configurations is to design appropriate “features” (inputs to the ML model). A model, based on guidance from the FIML methodology, is presented in analytical form. An additional list of potential features is provided. Although these were not used in the present correction, they were considered in the course of its development, and are included to fully document the complete process employed in the present work.

turbulence modeling↗

DOE OSTI2026

Hierarchical-embedding autoencoder with a predictor as efficient architecture for learning time-evolution in multi-scale turbulent flows

We introduce a scale-aware, data-driven deep learning modeling framework for accurately predicting the time evolution of multi-scale turbulent plasma and liquid flows. The approach is motivated by the idea of scale separation. Structures of vastly different length scales emerge in these systems, and interactions between these structures occur only locally. To exploit this structure, the flow state is transformed by a hierarchical, fully convolutional autoencoder, not into a single embedding layer as in conventional convolutional surrogate models, but into a series of embedding layers. A stepwise training strategy ensures that fine-scale features are encoded on a high-resolution grid, while larger structures are represented on progressively coarser layers. The time evolution predictor advances all embedding layers in sync, capturing local interactions between features at the same scale as well as between all scales. This approach enables efficient modeling of multi-scale systems since negligible interactions between distant, small-scale structures do not need to be directly modeled. Our hierarchical-embedding autoencoder with a predictor framework is evaluated on canonical examples of multi-scale turbulence: two-dimensional Kolmogorov flow and Hasegawa–Wakatani plasma turbulence. In both cases, the proposed framework significantly improves predictive accuracy relative to conventional convolutional network architectures. A significant improvement in prediction accuracy was observed for crucial statistical characteristics of the Hasegawa–Wakatani plasma as well as for individual trajectories of the Kolmogorov flow turbulence. Importantly, the model's rollout for the Hasegawa–Wakatani problem demonstrates a four-order-of-magnitude speedup compared to traditional numerical solvers.

Khrabry, Alexander I. [Princeton Univ., NJ (United↗

DOE OSTI2024

Physics-Reinforced Machine Learning Algorithms for Multiscale Closure Model Discovery

The central objective of this project was to address the challenge of modeling and simulating complex multiscale turbulence phenomena by leveraging physics-guided machine learning (PGML) and hybrid modeling approaches. By integrating physics-based methods with data-driven models, the research focused on achieving robust and scalable solutions for geophysical turbulence, enhancing numerical weather prediction and climate research tools. The project resulted in significant advancements in computational modeling paradigms, predictive tools for reduced-order modeling, and innovative algorithms for fluid dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRSDate not supplied

A Data-Driven Reduced Order Model of an Isolated Rotor

There are numerous conceptual design stage rotorcraft analysis tasks which demand a high-fidelity and low cost method for rotor load distribution predictions. Considering Urban Air Mobility (UAM) vehicles aim to operate in close proximity to buildings and with unique rotor configurations, there is a significant challenge in quickly and accurately modeling rotors operating in complex, turbulent flow fields. One potential path for deriving a high-fidelity, low cost rotor model is with data-driven surrogate modeling. In this study, an initial investigation is taken to apply a proper orthogonal decomposition (POD) based reduced order model (ROM) for the purpose of pressure distribution prediction. In this study, a POD ROM was derived to produce distributed pressure predictions on rotor blades subjected to topology change due to variation in twist and taper ratio. Rotor twist was varied between 0◦, 10◦, 20◦, and 30◦ while taper ratio was varied between 1.0, 0.9, 0.8, and 0.7. All rotors consisted of a single blade. The POD ROM was validated for three demonstration cases; a high thrust rotor in hover, a low thrust rotor in hover, and a rotor in forward flight with a flight speed of M = 0.1. Results showed highly accurate distributed load predictions could be achieved at minimal computational cost. Computational cost for hovering blade surface pressure modeling was reduced from 12 hours on 440 cores to 10−5 seconds on a single core. For blade in forward flight cost was reduced from 20 hours on 440 cores to 0.6 seconds on a single core. For cases of high thrust and low thrust rotors, POD ROM was used to undergo a design optimization of the rotor such that figure of merit was maximized. Total optimization time for each case was 1 minute.

Data-Driven↗

NASA NTRS2022

NASA Symposium on Turbulence Modeling: Roadblocks, and the Potential for Machine Learning

A three-day symposium sponsored by NASA was held in July 2022 in Suffolk, Virginia on the subject of Turbulence Modeling: Roadblocks, and the Potential for Machine Learning. This meeting brought together over 80 experts from academia, government, and industry to discuss critical issues for Reynolds-averaged Navier-Stokes turbulence and transition models, as well as to evaluate the results from a collaborative testing challenge based on data-driven methods and machine learning technology. This report puts this symposium in context with an earlier similar meeting and summarizes many of the questions, discussions, and conclusions that arose from it. Next steps are suggested.

machine learning↗

DOE OSTI2024

a priori uncertainty quantification of reacting turbulence closure models using Bayesian neural networks

While many physics-based closure model forms have been posited for the sub-filter scale (SFS) in large eddy simulation (LES), vast amounts of data available from direct numerical simulations (DNS) create opportunities to leverage data-driven modeling techniques. Albeit flexible, data-driven models still depend on the dataset and the functional form of the model chosen. Increased adoption of such models requires reliable uncertainty estimates both in the data-informed and out-of-distribution regimes. Here, in this work, we employ Bayesian neural networks (BNNs) to capture both epistemic and aleatoric uncertainties in a reacting flow model. In particular, we model the filtered progress variable scalar dissipation rate which plays a key role in the dynamics of turbulent premixed flames. We demonstrate that BNN models can provide unique insights about the structure of uncertainty of the data-driven closure models. We also propose a method for the incorporation of out-of-distribution information in a BNN, which can be used for out-of-distribution query detection. The efficacy of the model is demonstrated by a priori evaluation on a dataset consisting of a variety of flame conditions and fuels.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Learning Physically Interpretable Atmospheric Models From Data With WSINDy

The multiscale and turbulent nature of Earth's atmosphere has historically rendered accurate weather modeling a hard problem. Recently, there has been an explosion of interest surrounding data-driven approaches to weather modeling, which in many cases show improved forecasting accuracy and computational efficiency when compared to traditional methods. However, many of the current data-driven approaches employ highly parameterized neural networks, often resulting in uninterpretable models and limited gains in scientific understanding. In this work, we address the interpretability problem by explicitly discovering partial differential equations governing atmospheric phenomena, identifying symbolic mathematical models with direct physical interpretations. The purpose of this paper is to demonstrate that, in particular, the weak-form sparse identification of nonlinear dynamics (WSINDy) algorithm can learn effective atmospheric models from both simulated and assimilated data. Our approach adapts the standard WSINDy algorithm to work with high-dimensional fluid data of arbitrary spatial dimension.

58 GEOSCIENCES↗

DOE OSTI2026

Progress and innovations in the TCV tokamak research programme

Research on the Tokamak à Configuration Variable addresses a wide range of key questions relevant to ITER and future fusion power plants. Over the past two years, highly productive experimental campaigns have led to major advances across several areas: the ITER baseline scenario; pedestal properties in low-collisionality, peeling-limited conditions; and the development of high- β N , non-inductive regimes. Alternative high-confinement scenarios have likewise received significant attention, with remarkable progress in quasi-continuous exhaust operation, X-point radiator plasmas, and negative triangularity configurations. Substantial achievements were also made in the mitigation or benign termination of runaway electron beams, in elucidating fast-ion loss mechanisms, and in improving exhaust behaviour in both conventional and alternative divertor geometries. These experimental results have been strongly supported by advances in modelling and their direct application to the experiment, ranging from gyrokinetic simulations of core and pedestal turbulence to fluid-based studies of scrape-off layer and divertor physics in diverse geometries. Plasma control has taken on an increasingly important role, with model-based and data-driven approaches now closely intertwined with physics studies. This article provides a overview of these recent activities, together with a brief outlook on forthcoming upgrades and next steps.

EPFL↗

NASA NTRSDate not supplied

Intermittency Model for Coupled CFD-Stability Transition Analysis in Hypersonic Flow

Accurate prediction of aerothermodynamic loads on hypersonic vehicles requires precise modeling of surface quantities across the boundary layer transition zone. The peak heating loads and total heat transfer are determined by parameters such as the transition zone length and the magnitude of potential overshoots in heat flux and skin friction beyond their respective values in fully turbulent flows. While previous studies on CFD integrated transition modeling using linear stability correlations have shown promise in modeling these features, they did not develop an intermittency model for hypersonic flows. This paper presents a data-driven approach to develop a model of this type by correlating experimental transition data with the relevant flow parameters. The resulting model demonstrates significant improvements over previous low-speed models in terms of predicting heat transfer distributions during the transition process associated with first and second mode instabilities in axisymmetric high-speed flows. Separate correlations for flight and ground test conditions are developed, and the potential to combine these correlations is discussed.

Transition↗

DOE OSTI2024

Modeling and observations of North Atlantic cyclones: Implications for U.S. Offshore wind energy

To meet the Biden-Harris administration's goal of deploying 30 GW of offshore wind power by 2030 and 110 GW by 2050, expansion of wind energy into U.S. territorial waters prone to tropical cyclones (TCs) and extratropical cyclones (ETCs) is essential. This requires a deeper understanding of cyclone-related risks and the development of robust, resilient offshore wind energy systems. Here, this paper provides a comprehensive review of state-of-the-science measurement and modeling capabilities for studying TCs and ETCs, and their impacts across various spatial and temporal scales. We explore measurement capabilities for environments influenced by TCs and ETCs, including near-surface and vertical profiles of critical variables that characterize these cyclones. The capabilities and limitations of Earth system and mesoscale models are assessed for their effectiveness in capturing atmosphere–ocean–wave interactions that influence TC/ETC-induced risks under a changing climate. Additionally, we discuss microscale modeling capabilities designed to bridge scale gaps from the weather scale (a few kilometers) to the turbine scale (dozens to a few meters). We also review machine learning (ML)-based, data-driven models for simulating TC/ETC events at both weather and wind turbine scales. Special attention is given to extreme metocean conditions like extreme wind gusts, rapid wind direction changes, and high waves, which pose threats to offshore wind energy infrastructure. Finally, the paper outlines the research challenges and future directions needed to enhance the resilience and design of next-generation offshore wind turbines against extreme weather conditions.

17 WIND ENERGY↗

DOE OSTI2024

A framework for strategic discovery of credible neural network surrogate models under uncertainty

The widespread integration of deep neural networks in developing data-driven surrogate models for high-fidelity simulations of complex physical systems highlights the critical necessity for robust uncertainty quantification techniques and credibility assessment methodologies, ensuring the reliable deployment of surrogate models in consequential decision-making. Here, this study presents the Occam Plausibility Algorithm for surrogate models (OPAL-surrogate), providing a systematic framework to uncover predictive neural network-based surrogate models within the large space of potential models, including various neural network classes and choices of architecture and hyperparameters. The framework is grounded in hierarchical Bayesian inferences and employs model validation tests to evaluate the credibility and prediction reliability of the surrogate models under uncertainty. Leveraging these principles, OPAL-surrogate introduces a systematic and efficient strategy for balancing the trade-off between model complexity, accuracy, and prediction uncertainty. The effectiveness of OPAL-surrogate is demonstrated through two modeling problems, including the deformation of porous materials for building insulation and turbulent combustion flow for ablation of solid fuels within hybrid rocket motors.

42 ENGINEERING↗

DOE OSTI2025

A physics-constrained neural ordinary differential equations approach for robust learning of stiff chemical kinetics

The high computational cost associated with solving for detailed chemistry poses a significant challenge for predictive computational fluid dynamics (CFD) simulations of turbulent reacting flows. While deep learning techniques have been explored to develop faster surrogate models, they often fail to integrate reliably with CFD solvers. This instability arises because traditional deep learning approaches optimize for training error without ensuring compatibility with ordinary differential equation (ODE) solvers, resulting in accumulation of errors over time. Recently, neuralODE (NODE) based approaches have been shown to be a promising technique to emulate and accelerate detailed chemistry computations. Here, in the present work, we extend this NODE framework for stiff chemical kinetics by incorporating mass conservation constraints directly into the loss function during training. This ensures that the total mass as well as the individual elemental species masses are conserved in an a-posteriori manner. Proof-of-concept studies are performed with the novel physics-constrained NODE (PC-NODE) approach for homogeneous autoignition of hydrogen-air mixture over a range of composition and thermodynamic conditions. It is demonstrated that the PC-NODE framework not only improves the physical consistency of the resulting data-driven model with respect to mass conservation criteria, but also improves training efficiency. PC-NODE is shown to achieve 2–100× speedup relative to the hydrogen-air detailed chemical mechanism depending on the type of the ODE solver (implicit or explicit) used during autoregressive inference tests. Lastly, a-posteriori studies are performed wherein the trained PC-NODE model is coupled with a CFD solver. It is shown that higher accuracy is achieved with PC-NODE relative to the purely data-driven NODE approach. Moreover, PC-NODE also exhibits robustness and generalizability to unseen initial conditions from within (interpolative capability) as well as outside (extrapolative capability) the training regime.

computational combustion↗

DOE OSTI2025

Tropical Cyclone Super Resolution using conditional diffusion denoising probabilistic model from mesoscale simulation to LES

Accurate modeling of tropical cyclone wind fields is essential for the design, risk assessment, and operational planning of offshore energy infrastructure. While mesoscale simulations are widely used thanks to their computational efficiency, they lack the necessary resolution to capture key features such as wind shear and veer profiles as well as the distribution turbulent kinetic energy (TKE). High-fidelity large-eddy simulation (LES) models on the other hand, can resolve turbulent structures and provide a more accurate representation of the complex wind field, albeit at a higher computational cost. To address this modeling gap, we introduce a two-part generative framework to enhance the resolution and physics-capturing ability of mesoscale simulations. First, a reduced-order model based on Karhunen–Loève (KL) decomposition is used to extract dominant spatial modes from one-dimensional mean wind profiles. A multilayer perceptron (MLP) is trained to map mesoscale mode weights to their LES counterparts, enabling accurate reconstruction of vertical velocity profiles. Second, a conditional Diffusion Denoising Probabilistic Model (DDPM) is developed to super-resolve coarse and low-fidelity mesoscale velocity fields, recovering fine-scale turbulence structures and stress distributions. The framework is evaluated across different tropical cyclone intensity categories defined by the Saffir–Simpson scale and demonstrates strong performance in both interpolation and extrapolation tasks. The generated fields accurately reproduce spatial coherence, stress distributions, and spectral energy characteristics observed in LES data. By bridging the fidelity gap between mesoscale and LES outputs, this approach offers a scalable, data-driven solution for enhancing the representation of tropical cyclone wind fields, enabling more robust offshore energy infrastructure systems design in tropical-cyclone-prone areas.

17 WIND ENERGY↗

DOE OSTI2023

Code for the manuscript "Lagrangian Large Eddy Simulations vis Physics-informed Machine Learning"

We would like to disclose a code based on Python/Pytorch, in which we implement the data-driven physics-informed machine learning of Lagrangian large eddy simulation that is described in the manuscript "Lagrangian Large Eddy Simulations via Physics-Informed Machine Learning ". High-Reynolds number Homogeneous Isotropic Turbulence is fully described within the Navier-Stokes (NS) equations, which are notoriously difficult to solve numerically. Engineers, interested primarily in describing turbulence at a reduced range of resolved scales, have designed heuristics, known as Large Eddy Simulation (LES). LES is described in terms of the temporally evolving Eulerian velocity field defined over a spatial grid with the mean-spacing correspondent to the resolved scale. This classic Eulerian LES depends on assumptions about the effects of sub-grid scales on the resolved scales. Here, we take an alternative approach and design novel LES heuristics stated in terms of Lagrangian particles moving with the flow. Our \emph{Lagrangian LES}, thus L-LES, is described by equations generalizing the weakly compressible Smoothed Particle Hydrodynamics formulation with extended parametric and functional freedom, which is then resolved via Machine Learning training on Lagrangian data from Direct Numerical Simulations of the NS equations. The L-LES model includes physics-informed parameterization and functional form, by combining physics-based parameters and physics-inspired Neural Networks to describe the evolution of turbulence within the resolved range of scales. The sub-grid scale contributions are modeled separately with physical constraints to account for the effects from un-resolved scales. We build the resulting model under the Differentiable Programming framework to facilitate efficient training. We experiment with loss functions of different types, including physics-informed ones accounting for statistics of Lagrangian particles. We show that our Lagrangian LES model is capable of reproducing Eulerian and unique Lagrangian turbulence structures and statistics over a range of turbulent Mach numbers.

Tian, Yifeng↗

DOE OSTI2025

Challenge Problem 1: Preliminary Results of the Direct Numerical Simulation of Transient Flows

This report presents the first direct numerical simulations (DNS) of transient mixed convection in an idealized downcomer-like channel (Challenge Problem 1, Phase II). Using the GPU-accelerated NekRS solver, we modeled a sudden decay in driving pressure, mimicking loss-of-flow events, and tracked the resulting evolution of Reynolds number, boundary-layer structure, turbulence statistics, and heat-transfer metrics. Key findings include the systematic thickening and eventual asymmetry of velocity and thermal boundary layers under buoyant deceleration; minimal “memory” lag in Reynolds shear stress and TKE profiles when sampled at matching Re, yet clear shifts of peak locations toward the cooled wall; overshoots in transient eddy-viscosity and eddy-diffusivity (and corresponding sub-unity turbulent Prandtl numbers) on the cooled side; and a pronounced transient Nusselt-number enhancement driven by wall-temperature inertia and residual eddy mixing. These effects combined to offer a temporary cooling margin above steady-state predictions during reactor LOF transients. Future work will extend this work to a more complex “Case II” geometry (90° turn + lower plenum) and generate multi-Re/Pr datasets for data-driven turbulence closures.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Scientific machine learning for closure models in multiscale problems: A review

Here, closure problems are omnipresent when simulating multiscale systems, where some quantities and processes cannot be fully prescribed despite their effects on the simulation's accuracy. Recently, scientific machine learning approaches have been proposed as a way to tackle the closure problem, combining traditional (physics-based) modeling with data-driven (machine-learned) techniques, typically through enriching differential equations with neural networks. This paper reviews the different reduced model forms, distinguished by the degree to which they include known physics, and the different objectives of a priori and a posteriori learning. The importance of adhering to physical laws (such as symmetries and conservation laws) in choosing the reduced model form and choosing the learning method is discussed. The effect of spatial and temporal discretization and recent trends toward discretization-invariant models are reviewed. In addition, we make the connections between closure problems and several other research disciplines: inverse problems, Mori-Zwanzig theory, and multi-fidelity methods. In conclusion, much progress has been made with scientific machine learning approaches for solving closure problems, but many challenges remain. In particular, the generalizability and interpretability of learned models is a major issue that needs to be addressed further.

97 MATHEMATICS AND COMPUTING↗

NASA NTRSDate not supplied

Enhancements to Linear Stability-Based, CFD-integrated Transition Prediction for High-Speed Flows

Combining linear stability calculations with computational fluid dynamics (CFD) simulations has great potential for the automated modeling of high-speed flows, especially when adequate information about the configuration and the disturbance environment is available. However, a significant impediment to the applicability of this technique is the lack of an efficient method to calculate the crucial amplification ratio corresponding to the onset of transition in hypersonic flows. This ratio, also known as the "transition N-factor," is dependent upon the freestream disturbance environment as well as the surface properties of the test article. In response to the need for an engineering solution to predict the transition N-factor within conventional hypersonic wind tunnels, this paper presents a data-driven correlation that expands the existing correlations from straight circular cones with a narrow range of half angles to a broader array of axisymmetric configurations. Furthermore, when tested against a chosen dataset that was not used in its calibration, the suggested correlation shows good predictive accuracy with an RMS error of only 6.9%. Although similar accuracy may also be achieved via existing correlations based on similar datasets, predictions based on the proposed correlation have the advantage of not requiring an extensive amount of configuration-specific data. Practical applications often have access to the input parameters needed for this correlation, such as the freestream disturbance intensity, Mach number, and body-based slenderness Reynolds number. Additionally, this correlation outperforms the traditional assumption of a constant N-factor, particularly for configurations with blunted nose geometries. The development of this correlation is grounded in an extensive dataset encompassing conical models with body half-angles varying between 5 degrees and 16 degrees, Mach numbers ranging from 5 to 14, and nosetip-based Reynolds numbers approaching the transition reversal limit for blunt-nosed cones.

CFD↗

NASA NTRSDate not supplied

Enhancements to Linear Stability-Based, CFD-integrated Transition Prediction for High-Speed Flows

CFD↗