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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Differentiable Preisach Modeling for Characterization and Optimization of Particle Accelerator Systems with Hysteresis

Future improvements in particle accelerator performance are predicated on increasingly accurate online modeling of accelerators. Hysteresis effects in magnetic, mechanical, and material components of accelerators are often neglected in online accelerator models used to inform control algorithms, even though reproducibility errors from systems exhibiting hysteresis are not negligible in high precision accelerators. Here, we combine the classical Preisach model of hysteresis with machine learning techniques to efficiently create nonparametric, high-fidelity models of arbitrary systems exhibiting hysteresis. We experimentally demonstrate how these methods can be used in situ, where a hysteresis model of an accelerator magnet is combined with a Bayesian statistical model of the beam response, allowing characterization of magnetic hysteresis solely from beam-based measurements. Finally, we explore how using these joint hysteresis-Bayesian statistical models allows us to overcome optimization performance limitations that arise when hysteresis effects are ignored.

43 PARTICLE ACCELERATORS↗
DOE OSTI2025

Detecting Reactive Products in Carbon Capture Polymers with Chemical Shift Anisotropy and Machine Learning

Aminopolymers are attractive sorbents for CO 2 direct air capture applications due to their high density of amine groups, which can readily react with atmospheric levels of CO 2 to form chemisorbed species. The identity of these chemisorbed species and the functional groups that form upon oxidative degradation depends on both material properties and processing conditions, forming a variety of carbonyl-type sites such as ammonium carbamates, bicarbonates, carbonates, carbamic acids, ureas, and amides. 13 C solid-state nuclear magnetic resonance (NMR) is often used to help elucidate the identity of these reacted species, but it is challenging due to the narrow chemical shift range of carbonyl sites. Herein, we demonstrate the application of a two-dimensional (2D) chemical shift anisotropy (CSA) recoupling pulse sequence (ROCSA) to obtain CSA tensor values at each isotropic chemical shift, overcoming limitations of isotropic peak resolution. CSA tensor values describe the local chemical environment and can readily differentiate between the chemisorbed and degradation products. To aid identification, we also developed a k-nearest neighbor (kNN) classification model to distinguish the functional groups via their CSA tensor parameters. This methodology was demonstrated on poly(ethylenimine) in γ-Al 2 O 3 exposed to CO 2 and showed that the chemisorbed products are ammonium carbamate and a mixed carbamate–carbamic acid species. The sample was analyzed again after desorption at 100 °C inducing mild degradation, and the remaining products were strongly bound carbamate and urea species. In conclusion, the combination of 2D CSA measurements coupled with a kNN classification model enhances the ability to accurately identify chemisorbed or degradation products in complex carbon capture materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Machine Learning Techniques for Data Reduction of Climate Applications

Scientists conduct large-scale simulations to compute derived quantities-of-interest (QoI) from primary data. Often, QoI are linked to specific features, regions, or time intervals, such that data can be adaptively reduced without compromising the integrity of QoI. For many spatiotemporal applications, these QoI are binary in nature and represent presence or absence of a physical phenomenon. We present a pipelined compression approach that first uses neural-network-based techniques to derive regions where QoI are highly likely to be present. Then, we employ a Guaranteed Autoencoder (GAE) to compress data with differential error bounds. GAE uses QoI information to apply low-error compression to only these regions. This results in overall high compression ratios while still achieving downstream goals of simulation or data collections. Experimental results are presented for climate data generated from the E3SM Simulation model for downstream quantities such as tropical cyclone and atmospheric river detection and tracking. These results show that our approach is superior to comparable methods in the literature.

Li, Xiao [University of Florida]↗
DOE OSTI2023

Certifiably Robust Neural ODE With Learning-Based Barrier Function

Neural Ordinary Differential Equations (ODEs) have gained traction in many applications. While recent studies have focused on empirically increasing the robustness of neural ODEs against natural or adversarial attacks, certified robustness is still lacking. In this work, we propose a framework for training a neural ODE using barrier functions and demonstrate improved robustness for classification problems. Finally, we further provide the first generalization guarantee of robustness against adversarial attacks using a wait-and-judge scenario approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Predicting nonequilibrium Green’s function dynamics and photoemission spectra via nonlinear integral operator learning

Understanding the dynamics of nonequilibrium quantum many-body systems is an important research topic in a wide range of fields across condensed matter physics, quantum optics, and high-energy physics. However, numerical studies of large-scale nonequilibrium phenomena in realistic materials face serious challenges due to intrinsic high-dimensionality of quantum many-body problems and the absence of time-invariance. The nonequilibrium properties of many-body systems can be described by the dynamics of the correlator, or the Green's function of the system, whose time evolution is given by a high-dimensional system of integro-differential equations, known as the Kadanoff–Baym equations (KBEs). The time-convolution term in KBEs, which needs to be recalculated at each time step, makes it difficult to perform long-time numerical simulation. In this paper, we develop an operator-learning framework based on recurrent neural networks (RNNs) to address this challenge. We utilize RNNs to learn the nonlinear mapping between Green's functions and convolution integrals in KBEs. By using the learned operators as a surrogate model in the KBE solver, we obtain a general machine-learning scheme for predicting the dynamics of nonequilibrium Green's functions. Besides significant savings per each time step, the new methodology reduces the temporal computational complexity from $O(N_t^3)$ to $O(N_t)$ where N t is the number of steps taken in a simulation, thereby making it possible to study large many-body problems which are currently infeasible with conventional KBE solvers. Through various numerical examples, we demonstrate the effectiveness of the operator-learning based approach in providing accurate predictions of physical observables such as the reduced density matrix and time-resolved photoemission spectra. Moreover, our framework exhibits clear numerical convergence and can be easily parallelized, thereby facilitating many possible further developments and applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

A real-time machine learning-based disruption predictor in DIII-D

A disruption prediction algorithm, named DPRF (Disruption Prediction using Random Forests), has run in real-time in the DIII-D plasma control system (PCS) over more than 900 discharges. DPRF naturally provides a probability mapping associated to its predictions, i.e. the disruptivity signal, now incorporated in the DIII-D PCS. Here, we report on disruption prediction accomplishments in terms of shot-by-shot performances, by simulating alarms on each discharge as in the PCS framework. Due to the optimised performance metric chosen to evaluate DPRF, we find that almost all disruptive discharges are detected in average with few hundred of milliseconds of warning time, but this comes at a high cost of false alarms produced. Performances are not satisfying ITER requirements, where the success rate has to be higher than 95%, but this is not completely unexpected. DPRF is trained on many years of major disruptions occurring during the flattop phase of the plasma current on DIII-D, but without any differentiation by cause. Furthermore, we find that DPRF is affected by a relatively high fraction of false alarms occurring during the first 500 milliseconds from the flattop onset. This subtle effect, more evident on the discharges where DPRF ran in real-time, can be marginalized by taking specific precautions on the validity range of the predictions, and performances do improve. Even if presently burdened by some limitations, DPRF provides an incredible and novel advantage. Thanks to the feature contribution analysis (e.g., the identification of which signals contributed to triggering an alarm), it is possible to interpret and explain DPRF predictions. It is the first time that such interpretability features is exploited by a disruption predictor: by uncovering the disruption events' causes, a better understanding of disruption dynamics is achieved, and a clear path toward the design of disruption avoidance strategies can be provided.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Super Resolving Unrolled Neural Networks for Remote Sensing

In remote sensing systems, the capabilities of the system are constrained by the complex interactions between size, weight, and power (SWAP) of potential designs. In electro-optical (EO) systems, examples of these critical parameters include the system’s sensitivity and resolution. Those parameters can be increased by ever larger optical apertures and focal planes but at the cost of more SWAP. Multi-image super resolution (MISR) techniques allow resolution to be enhanced via computation rather than more sophisticated optical hardware. These algorithms combine multiple images together into a single, higher resolution image, trading temporal resolution and computation for spatial resolution. Fielded MISR techniques, such as Drizzle, can require several hundred images to create a single super resolved image, implying reduced temporal resolution, increased data acquisition load, and limiting mission applications. Iterative techniques, such as model-based image reconstruction and compressive sensing, have been shown to create super resolved images using fewer images than Drizzle. They do this by posing an optimization problem that balances accuracy between a highly accurate physical model and an image model. In the case of super resolution, the physical model is defined by the relation between low resolution input images and the desired high resolution output image. The image model encodes some assumptions about the super resolved image. These assumptions are meant to suppress reconstruction artifacts that arise due to deterministic physical model error, stochastic measurement noise, and potential undersampling. In practice, the performance of iterative methods are limited by imaging models compatible with optimization. Deep learning-based methods can effectively learn image models of arbitrary complexity, but lack the theoretical explainability and robustness of iterative techniques. Consensus equilibrium (CE) generalizes the iterative techniques beyond optimization, enabling blackbox algorithms such as traditional and neural image denoisers to be used as the image model. CE-based approaches retain much of the explainability and robustness of iterative techniques while allowing the expressiveness of machine learning image models to be used. Additionally, by unrolling iterations of CE with an embedded image denoiser, the image denoiser can be further trained and specialized to the specific application with potentially higher quality reconstructions. Under this project, we demonstrated the feasibility of training an unrolled neural network based upon CE. While we didn’t train one, we showed that the CE process is differentiable and its gradient can be tractably computed. We also explored the usage of a variants of CE akin to generative neural works. Most importantly, we applied the CE framework to a number of problems including non-blind deconvolution, upsampling, single-image super resolution, MISR, event-based sensing, and saturated deconvolution. Our MISR prototype creates high quality reconstructions with an order of magnitude fewer images than previous approaches and, critically, produces these reconstructions fast enough for practical usage.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

Discovering Hidden Geothermal Signatures using Unsupervised Machine Learning

Discovering hidden geothermal resources is a very challenging task. It requires the mining of large datasets, including various diverse data attributes representing subsurface hydrogeological and geothermal conditions. The commonly used Play Fairway Analysis (PFA) typically relies on subject-matter expertise to analyze site or regional data to estimate geothermal conditions and prospectivity. Here, we demonstrate an alternative approach based on machine learning (ML) to process a geothermal dataset of Southwest New Mexico (SWNM). The study region includes low- and medium-temperature hydrothermal systems. However, most of these systems are poorly characterized because of insufficient existing data and limited past explorative studies. This study aims to discover hidden patterns and relationships in the SWNM geothermal dataset to better understand regional hydrothermal conditions. This is achieved by applying an unsupervised machine learning algorithm based on non-negative matrix factorization coupled with customized k-means clustering (NMFk). NMFk can automatically identify (1) hidden (latent) signatures characterizing datasets, (2) the optimal number of these signatures, (3) dominant data attributes associated with each signature, and (4) spatial distribution of the extracted signatures. Here, NMFk is applied to analyze 18 geological, geophysical, hydrogeological, geothermal attributes at 44 locations in SWNM. NMFk successfully finds data patterns and identifies the spatial associations of hydrothermal signatures with the four physiographic provinces in SWNM (Colorado Plateau, Volcanic Field, Basin and Range, and the Rio Grande rift). The algorithm identified up to 5 hydrothermal signatures in the SWNM datasets that differentiate between low- and medium-temperature hydrothermal systems in different provinces. Also, the algorithm identifies two medium-temperature hydrothermal systems in SWNM that require further exploration for geothermal resource development. Based on our analyses, 12 of the attributes are important to identify medium-temperature hydrothermal systems, and the remaining six attributes are critical to characterize low-temperature hydrothermal systems. Based on the obtained results, we identify potential physiographic provinces for further exploration to characterize them as geothermal resources. The resulting NMFk model can be applied to predict geothermal conditions and their uncertainties at new SWNM locations based on limited data from unexplored areas.

58 GEOSCIENCES↗
DOE OSTI2025

Machine-Learning-Based Multiscale Methods for 3D Modelling of Granular Materials by Incorporating History-Dependent State Variables

Over the past decades, the prevalence of machine learning (ML) methods has made the development of ML-based constitutive models for granular materials undoubtedly a popular subject. Numerous studies have been made to feature the loading path or history-dependent stress-strain response of granular media using neural networks. In this work, a novel finite element method (FEM)–ML multiscale approach was developed by incorporating internal variables to improve the simulation accuracy of 3D history-dependent granular materials for the first time. To this end, a surrogate constitutive model based on the single-step-based multi-layer perceptron (MLP) neural network was used to replace representative volume element (RVE) simulations conducted by the discrete element method (DEM) in the multiscale FEM–DEM approach. Although the prediction principle of the MLP aligns with the FEM algorithm, artificially added internal variables are required to differentiate the loading history. To address this issue, history variables associated with the Frobenius norm are proposed to be fed into the MLP coupled with the strain tensor to extract the history-dependent behaviour of granular assemblies. The developed FEM–ML approach was demonstrated in 3D conventional triaxial compression (CTC) simulations. Compared to the multiscale FEM–DEM approach, the proposed FEM–ML method exhibits a significantly improved computational efficiency.

granular materials↗
DOE OSTI2024

Differentiable Multiphysics Codes: A Breakthrough Technology for Simulation and Computing

This document summarizes the findings of a strategic planning exercise commissioned by the Weapons Simulation and Computing, Computational Physics (WSC/CP) program at the Lawrence Livermore National Laboratory (LLNL) in FY24. During the year, the committee met with multiple stakeholder communities to gather input, opinions, suggestions and concerns which have been incorporated throughout this document. The key findings from this exercise are summarized: • The development of multiphysics modelling and simulation (mod/sim) codes and software technologies, their deployment on exascale compute platforms, and their broad adoption across the NNSA is a major success of the Advanced Simulation and Computing (ASC) program and the Exascale Computing Project (ECP). Sustained investment in these core technologies is essential. • Today’s state of the art involves running ensembles of O(100K) simulations to perform uncertainty quantification (UQ) and design studies using multiple statistical methods such as Bayesian optimization to understand sensitivities of our models and explore parameterized design spaces. Even with exascale computing, we are practically limited to O(10) parameters in these studies since the number of simulations required to sample the space scales exponentially with the number of design parameters. • The data from these simulation ensembles is increasingly being used to train machine learned (ML) surrogates (or reduced order models, ROMs) which can then be used for optimization or real time design exploration. However, the trained surrogates are still limited in the number of parameters they can represent due to the sampling limitations previously noted. • Augmenting our suite of integrated multiphysics simulation codes, both current and emerging, with the ability to compute gradients (solution derivatives) of arbitrary simulation outputs with respect to (some or all) simulation inputs would be a breakthrough technology, opening the door to a new era of efficient and automated inverse design based on verified and validated mod/sim capabilities. • This capability, which we refer to as differentiable multiphysics codes (DMCs), would revolutionize both UQ and optimization studies by breaking the curse of dimensionality that presently limits our “gradient-free” ensemble based computing approach. A similar breakthrough occurred in the AI/ML community once the ability to compute gradients of arbitrary loss functions using back-propagation became commonplace. Gradient information from the multiphysics codes can also be used to dramatically improve the efficiency and scale of training of ML/ROM surrogates for rapid assessments. • Achieving this in our suite of codes will be a grand challenge, similar to the amount of effort that was required to transition from CPU to GPU computing. It will require buy-in from the entire WSC/CP program and beyond, including all integrated codes, physics and engineering models, third-party library dependencies and performance portability abstractions. It will also require investment in research and development of numerical methods for computing adjoints of coupled physics across multiple adaptively refined moving meshes and of stochastic (Monte Carlo) and mesh free (SPH) methods. • New software and numerical techniques, largely pioneered by the AI/ML community, make this feasible. Chief among these is automatic differentiation (AD), the ability to employ AD at point-wise locations in a physics calculation (instead of traditional black-box approaches) and the ability to perform “back-propagation in time” (or reverse mode AD) for non-linear partial differential equations (PDEs). Fundamentally, the conclusion of this strategic planning exercise is that the time is right to undertake a large scale effort in WSC, centered on the existing integrated codes, to continue the natural evolution of mod/sim in the age of AI/ML. Instead of attempting to replace mod/sim with purely data driven AI/ML models, we believe the key to success is to integrate AI/ML by building on top of the decades of hard-won knowledge and the verified/validated multiphysics modelling capability that is the hallmark of the ASC program.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Dynamic Parameter Estimation with Physics-based Neural Ordinary Differential Equations

Accurate estimation of dynamic parameters of gen-erators is crucial to building a reliable model for dynamical studies and reliable operation of the power system. This paper develops a physics-based neural ordinary differential equations (ODE) approach to learn the parameters of generator dynamic model using phasor measurement units (PMU) data. We design a physics-based neural network to represent the swing equations of the power system dynamics. A loss function is defined as the difference between dynamic simulation results from the physics-based neural networks and pseudo PMU measurements. The parameters of generator dynamic model are iteratively updated using the neural ODEs and the adjoint method. By exploiting the mini-batch scheme in neural ODE training, the parameter estimation performance is significantly improved. Numerical study results on a 3-machine 9-bus system show that the proposed algorithm outperforms state-of-the-art baseline method in both computation time and dynamic parameter estimation accuracy.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Machine-learned closure of URANS for stably stratified turbulence: connecting physical timescales & data hyperparameters of deep time-series models

Stably stratified turbulence (SST), a model that is representative of the turbulence found in the oceans and atmosphere, is strongly affected by fine balances between forces and becomes more anisotropic in time for decaying scenarios. Moreover, there is a limited understanding of the physical phenomena described by some of the terms in the Unsteady Reynolds-Averaged Navier–Stokes (URANS) equations—used to numerically simulate approximate solutions for such turbulent flows. Rather than attempting to model each term in URANS separately, it is attractive to explore the capability of machine learning (ML) to model groups of terms, i.e. to directly model the force balances. We develop deep time-series ML for closure modeling of the URANS equations applied to SST. We consider decaying SST which are homogeneous and stably stratified by a uniform density gradient, enabling dimensionality reduction. We consider two time-series ML models: long short-term memory and neural ordinary differential equation. Both models perform accurately and are numerically stable in a posteriori (online) tests. Furthermore, we explore the data requirements of the time-series ML models by extracting physically relevant timescales of the complex system. We find that the ratio of the timescales of the minimum information required by the ML models to accurately capture the dynamics of the SST corresponds to the Reynolds number of the flow. The current framework provides the backbone to explore the capability of such models to capture the dynamics of high-dimensional complex dynamical system like SST flows.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Stochastic Learning Approach for Binary Optimization: Application to Bayesian Optimal Design of Experiments

Here, we present a novel stochastic approach to binary optimization suited for optimal experimental design (OED) for Bayesian inverse problems governed by mathematical models such as partial differential equations. The OED utility function, namely, the regularized optimality criterion, is cast into a stochastic objective function in the form of an expectation over a multivariate Bernoulli distribution. The probabilistic objective is then solved by using a stochastic optimization routine to find an optimal observational policy. This formulation (a) is generally applicable to binary optimization problems with soft constraints and is ideal for OED and sensor placement problems; (b) does not require differentiability of the original objective function (e.g., a utility function in OED applications) with respect to the design variable, and thus it enables direct employment of sparsity-enforcing penalty functions such as $\ell_0$, without needing to utilize a continuation procedure or apply a rounding technique; (c) exhibits much lower computational cost than traditional gradient-based relaxation approaches; and (d) can be applied to both linear and nonlinear OED problems with proper choice of the utility function. The proposed approach is analyzed from an optimization perspective with detailed convergence analysis of the optimization approach and is also analyzed from a machine learning perspective with correspondence to policy gradient reinforcement learning. The approach is demonstrated numerically by using an idealized two-dimensional Bayesian linear inverse problem and validated by extensive numerical experiments carried out for sensor placement in a parameter identification setup.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Symplectic machine learning model for fast simulation of space-charge effects

Symplectic simulation of space-charge effects is crucial for the design and operation of high-intensity particle accelerators. Traditional methods for simulating these effects are often computationally expensive, resulting in significant overhead. In this work, we introduce a generative model based on a U-Net architecture within a generative adversarial network framework to efficiently simulate space-charge effects. The model is trained to predict the transverse multiparticle space-charge Hamiltonian, which can be physically computed using a gridless spectral method. The one-step symplectic transverse transfer map for the particles is then obtained by differentiating the predicted Hamiltonian. Benchmarking results demonstrate that this generative model achieves an order of magnitude higher computational efficiency compared to the spectral method, providing a highly efficient alternative for simulating space-charge effects with a large number of particles. By maintaining symplecticity, the model effectively preserves the phase-space structure and mitigates nonphysical errors in long-term simulations. This model has been integrated into jutrack, a novel autodifferentiable accelerator modeling code developed in the julia programming language.

Beam code development & simulation techniques↗
NASA NTRS2014

Analysis and Prediction of Weather Impacted Ground Stop Operations

When the air traffic demand is expected to exceed the available airport's capacity for a short period of time, Ground Stop (GS) operations are implemented by Federal Aviation Administration (FAA) Traffic Flow Management (TFM). The GS requires departing aircraft meeting specific criteria to remain on the ground to achieve reduced demands at the constrained destination airport until the end of the GS. This paper provides a high-level overview of the statistical distributions as well as causal factors for the GSs at the major airports in the United States. The GS's character, the weather impact on GSs, GS variations with delays, and the interaction between GSs and Ground Delay Programs (GDPs) at Newark Liberty International Airport (EWR) are investigated. The machine learning methods are used to generate classification models that map the historical airport weather forecast, schedule traffic, and other airport conditions to implemented GS/GDP operations and the models are evaluated using the cross-validations. This modeling approach produced promising results as it yielded an 85% overall classification accuracy to distinguish the implemented GS days from the normal days without GS and GDP operations and a 71% accuracy to differentiate the GS and GDP implemented days from the GDP only days.

Analysis↗
DOE OSTI2019

Equation Discovery Using Fast Function Extraction: a Deterministic Symbolic Regression Approach

Advances in machine learning (ML) coupled with increased computational power have enabled identification of patterns in data extracted from complex systems. ML algorithms are actively being sought in recovering physical models or mathematical equations from data. This is a highly valuable technique where models cannot be built using physical reasoning alone. In this paper, we investigate the application of fast function extraction (FFX), a fast, scalable, deterministic symbolic regression algorithm to recover partial differential equations (PDEs). FFX identifies active bases among a huge set of candidate basis functions and their corresponding coefficients from recorded snapshot data. This approach uses a sparsity-promoting technique from compressive sensing and sparse optimization called pathwise regularized learning to perform feature selection and parameter estimation. Furthermore, it recovers several models of varying complexity (number of basis terms). FFX finally filters out many identified models using non-dominated sorting and forms a Pareto front consisting of optimal models with respect to minimizing complexity and test accuracy. Numerical experiments are carried out to recover several ubiquitous PDEs such as wave and heat equations among linear PDEs and Burgers, Korteweg–de Vries (KdV), and Kawahara equations among higher-order nonlinear PDEs. Additional simulations are conducted on the same PDEs under noisy conditions to test the robustness of the proposed approach.

42 ENGINEERING↗
DOE OSTI2022

Privacy policy robustness to reverse engineering

Differential privacy policies allow one to preserve data privacy while sharing and analyzing data. However, these policies are susceptible to an array of attacks. In particular, often a portion of the data desired to be privacy protected is exposed online. Access to these pre-privacy protected data samples can then be used to reverse engineer the privacy policy. With knowledge of the generating privacy policy, an attacker can use machine learning to approximate the full set of originating data. Bayesian inference is one method for reverse engineering both model and model parameters. We present a methodology for evaluating and ranking privacy policy robustness to Bayesian inference-based reverse engineering, and demonstrated this method across data with a variety of temporal trends.

Kusne, Aaron Gilad↗
DOE OSTI2019

Design optimization of a scramjet under uncertainty using probabilistic learning on manifolds

Here, we demonstrate, on a scramjet combustion problem, a constrained probabilistic learning approach that augments physics-based datasets with realizations that adhere to underlying constraints and scatter. The constraints are captured and delineated through diffusion maps, while the scatter is captured and sampled through a projected stochastic differential equation. The objective function and constraints of the optimization problem are then efficiently framed as non-parametric conditional expectations. Different spatial resolutions of a large-eddy simulation filter are used to explore the robustness of the model to the training dataset and to gain insight into the significance of spatial resolution on optimal design.

42 ENGINEERING↗