Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “stochastic approximation”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 307 records · Page 17

Producing High-fidelity Synthetic Population Ensembles at Scale

Used within social simulations, synthetic population ensembles enable uncertainty quantification (UQ) methods for obtaining more robust model inference and prediction. A synthetic population ensemble is a series of plausible virtual reconstructions of an area’s population at the granularity of people and residences, generated stochastically to preserve privacy of the source population survey’s respondents. In this paper, we demonstrate the production of large synthetic population ensembles for the US via Oak Ridge National Laboratory’s UrbanPop framework to support modeling of high spatial resolution energy affordability metrics from nationwide social surveys in collaboration with the fusionACS project. Our initial task involves creating ensembles for 17 US metropolitan areas, each consisting of 41 population instances (a base realization and 40 replicates). To accomplish this task at scale, we configured an integrated system comprised of a research cloud, virtual containerization, GPU-enhanced functionality, and a dual API/CLI to interact with UrbanPop’s maturing Likeness Python ecosystem. We observe a reduction in theoretical execution time while maintaining high-fidelity approximations of residential totals by metropolitan area and the demographic characteristics of neighborhoods. We discuss expansion of our approach to produce synthetic population ensembles for the entire US, particularly plans to establish automated workflows for job orchestration to increase computational efficiency, as well as provide outlook for broadening applications of the ensembles.

Gaboardi, James [ORNL] (ORCID:0000000247766826)↗

A data-driven sensor placement approach for detecting voltage violations in distribution systems

Stochastic fluctuations in power injections from distributed energy resources (DERs) combined with load variability can cause constraint violations (e.g., exceeded voltage limits) in electric distribution systems. To monitor grid operations, sensors are placed to measure important quantities such as the voltage magnitudes. Here, in this paper, we consider a sensor placement problem which seeks to identify locations for installing sensors that can capture all possible violations of voltage magnitude limits. We formulate a bilevel optimization problem that minimizes the number of sensors and avoids false sensor alarms in the upper level while ensuring detection of any voltage violations in the lower level. This problem is challenging due to the nonlinearity of the power flow equations and the presence of binary variables. Accordingly, we employ recently developed conservative linear approximations of the power flow equations that overestimate or underestimate the voltage magnitudes. By replacing the nonlinear power flow equations with conservative linear approximations, we can ensure that the resulting sensor locations and thresholds are sufficient to identify any constraint violations. Additionally, we apply various problem reformulations to significantly improve computational tractability while simultaneously ensuring an appropriate placement of sensors. Lastly, we improve the quality of the results via an approximate gradient descent method that adjusts the sensor thresholds. We demonstrate the effectiveness of our proposed method for several test cases, including a system with multiple switching configurations.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Quasilinear theory of general electromagnetic fluctuations including discrete particle effects for magnetized plasmas: General analysis

The general quasilinear Fokker–Planck kinetic equation for the gyrophase-averaged plasma particle distribution functions in magnetized plasmas is derived, making no restrictions on the energy of the particles and on the frequency of the electromagnetic fluctuations and avoiding the often made Coulomb approximation of the electromagnetic interactions. Here, the inclusion of discrete particle effects breaks the dichotomy of nonlinear kinetic plasma theory divided into the test particle and the test fluctuation approximation because it provides expression of both the non-collective and collective electromagnetic fluctuation spectra in terms of the plasma particle distribution functions. Within the validity of the quasilinear approach, the resulting full quasilinear transport equation can be regarded as a determining nonlinear equation for the time evolution of the plasma particle distribution functions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Scalable Generation of High-fidelity Synthetic Population Ensembles

Used within social simulations, synthetic population ensembles enable uncertainty quantification (UQ) methods for obtaining more robust model inference and prediction. A synthetic population ensemble is a series of plausible virtual reconstructions of an area’s population at the granularity of people and residences, generated stochastically to preserve privacy of the source population survey’s respondents. In this paper, we demonstrate the production of large synthetic population ensembles for the U.S. via Oak Ridge National Laboratory’s UrbanPop framework to support modeling of high spatial resolution energy affordability metrics from nationwide social surveys in collaboration with the fusionACS project. The study involves two scenarios: creating ensembles for (1) 17 U.S. metropolitan areas in 2019 and (2) full U.S. Census Divisions in 2023, with each scenario consisting of 41 population instances (a base realization and 40 replicates). To accomplish this task at scale, we configured an integrated system within a research cloud, comprised of virtual containerizations, GPU-enhanced functionality, and orchestrated deployments of UrbanPop’s maturing Likeness Python ecosystem. Results demonstrate we maintained high-fidelity approximations of residential totals by areas of interest and the demographic characteristics of neighborhoods while reducing manual workflow burdens. Finally, we discuss plans to fine-tune and further develop our automated workflows for truly distributed job orchestration to increase computational efficiency, as well as provide an outlook for broadening applications of the ensembles.

Cluster computing↗

Low‐dimensional manifold learning for uncertainty quantification in complex multi‐scale stochastic systems

Broadly speaking, the goals of the project are to develop techniques to use manifold learning to develop reduced‐order and surrogate models for "hyper‐reduction" of very high‐dimensional complex multi‐scale systems. This is being achieved by employing a newly proposed form of manifold projection and learning that leverages recent advancements in computational geometry and data‐driven modeling. In particular, we are applying a manifold projection technique to project the solutions of very high‐dimensional systems onto the so‐called Grassmannmanifold, a Reimannian manifold comprised of orthonormal matrices. We then apply data‐driven machine learning techniques to classify the solutions on the manifold (e.g. clustering techniques) according to their proximity on the manifold and leverage a further nonlinear dimension reduction to organize the structured data on the manifold. Finally, we are developing novel techniques that enable us to directly interpolate the hyper‐reduced data such that we can predict the solution of the complex, high‐ dimensional system without need to call the full expensive computational model. Given their adherence to the underlying structure of the solution of the physical system, it is expected that these approximate solutions will be sufficiently constrained so as to (approximately) adhere to physical principles.

97 MATHEMATICS AND COMPUTING↗

Dynamic Probabilistic Safety Assessment Studies for Advanced Reactor Using RAVEN

Probabilistic Safety Assessment (PSA) is used extensively to evaluate the risks associated with complex engineering systems like Nuclear Power Plants (NPPs). Current PSA models are based on the Event-Tree/Fault-Tree (ET/FT) methodology. ET and FT models are static and are based on Boolean logic approaches. In the past, concerns have been raised in the literature regarding the capability of the traditional static modelling approaches to adequately account for the impact of process, hardware, software, firmware and human interactions on the stochastic system behaviour. To overcome the limitations of the traditional approach to PSA, several dynamic PSA methodologies have been proposed. One of the dynamic PSA methodologies used for dynamic evaluations is Dynamic Event Tree (DET) framework which can be used to assess the impact of the parameter variability and scenario dynamics on the PSA model for the initiating event. The DET framework couples the stochastic model (number of component/trains that start on demand, operator action timing, etc.) with a Thermal-Hydraulic (TH) model of the plant. This paper explores the use of DET along with a case study on advanced reactor. The initiating event selected for the study was Class IV power supply failure event. The TH analysis considering uncertainty in various parameters was performed using RELAP5 and Reactor Analysis and Virtual control ENvironment (RAVEN) tool. Based on the uncertainty analysis, it is concluded that the peak clad temperatures (PCT) are within the limits in all the code runs implying a high-degree of safety margin. However, variation in time to reach the PCT was observed among the code runs and the mean time to reach the PCT was found to be around 8590sec (approximately 2.4 hours). Hence, sufficient time margin is available for human intervention and the operator might have a relatively stress-free state during such an accident scenario. Due to the static nature of the traditional PSA models, the safety margin available was lesser, whereas, with the help of dynamic PSA models, one can demonstrate that the actual available safety margin is more in the present case study and is valuable input from the design point of view.

99 GENERAL AND MISCELLANEOUS↗

Acoustic Tomography of the Atmosphere: A Large-Eddy Simulation Sensitivity Study

Accurate measurement of atmospheric turbulent fluctuations is critical for understanding environmental dynamics and improving models in applications such as wind energy. Advanced remote sensing technologies are essential for capturing instantaneous velocity and temperature fluctuations. Acoustic tomography (AT) offers a promising approach that utilizes sound travel times between an array of transducers to reconstruct turbulence fields. This study presents a systematic evaluation of the time-dependent stochastic inversion (TDSI) algorithm for AT using synthetic travel-time measurements derived from large-eddy simulation (LES) fields under both neutral and convective atmospheric boundary-layer conditions. Unlike prior work that relied on field observations or idealized fields, the LES framework provides a ground-truth atmospheric state, enabling quantitative assessment of TDSI retrieval reliability, sensitivity to travel-time measurement noise, and dependence on covariance model parameters and temporal data integration. A detailed sensitivity analysis was conducted to determine the best-fit model parameters, identify the tolerance thresholds for parameter mismatch, and establish a maximum spatial resolution. The TDSI algorithm successfully reconstructed large-scale velocity and temperature fluctuations with root mean square errors ( RMSE s) below 0.35 m/s and 0.12 K, respectively. Spectral analysis established a maximum spatial resolution of approximately 1.4 m, and reconstructions remained robust for travel-time measurement uncertainties up to 0.002 s. These findings provide critical insights into the operational limits of TDSI and inform future applications of AT for atmospheric turbulence characterization and system design.

17 WIND ENERGY↗

Stability of Kuramoto networks subject to large and small fluctuations from heterogeneous and spatially correlated noise

Oscillatory networks subjected to noise are broadly used to model physical and technological systems. Due to their nonlinear coupling, such networks typically have multiple stable and unstable states that a network might visit due to noise. In this article, we focus on the assessment of fluctuations resulting from heterogeneous and spatially correlated noise inputs on Kuramoto model networks. We evaluate the typical, small fluctuations near synchronized states and connect the network variance to the overlap between stable modes of synchronization and the input noise covariance. Going beyond small to large fluctuations, we introduce the indicator mode approximation that projects the dynamics onto a single amplitude dimension. Such an approximation allows for estimating rates of fluctuations to saddle instabilities, resulting in phase slips between connected oscillators. Statistics for both regimes are quantified in terms of effective noise amplitudes that are compared and contrasted for several noise models. In conclusion, bridging the gap between small and large fluctuations, we show that a larger network variance does not necessarily lead to higher rates of large fluctuations.

42 ENGINEERING↗

Stage-local partitioned two-step runge-kutta methods for large systems of ordinary differential equations

We introduce stage-local partitioned two-step Runge-Kutta methods are an extension of standard two-step Runge-Kutta methods, which are an alternative to the standard additive two-step Runge-Kutta methods currently existing in the literature. Furthermore, these new schemes are designed with an eye towards truly N-partitioned systems and leverage local stage approximations to make several computationally interesting approximations viable. Specifically, the focus on local stage approximations makes possible the construction of truly asynchronous schemes, in the parallel sense, possible. In addition, we show that an implicit-explicit approach to these schemes can lead to methods that require the inversion of only local nonlinear systems.

Applied Dynamical Systems↗

Train Like a (Var)Pro: Efficient Training of Neural Networks with Variable Projection

Deep neural networks (DNNs) have achieved state-of-the-art performance across a variety of traditional machine learning tasks, e.g., speech recognition, image classification, and segmentation. The ability of DNNs to efficiently approximate high-dimensional functions has also motivated their use in scientific applications, e.g., to solve partial differential equations and to generate surrogate models. In this paper, we consider the supervised training of DNNs, which arises in many of the above applications. We focus on the central problem of optimizing the weights of the given DNN such that it accurately approximates the relation between observed input and target data. Devising effective solvers for this optimization problem is notoriously challenging due to the large number of weights, nonconvexity, data sparsity, and nontrivial choice of hyperparameters. To solve the optimization problem more efficiently, we propose the use of variable projection (VarPro), a method originally designed for separable nonlinear least-squares problems. Our main contribution is the Gauss--Newton VarPro method (GNvpro) that extends the reach of the VarPro idea to nonquadratic objective functions, most notably cross-entropy loss functions arising in classification. These extensions make GNvpro applicable to all training problems that involve a DNN whose last layer is an affine mapping, which is common in many state-of-the-art architectures. In our four numerical experiments from surrogate modeling, segmentation, and classification, GNvpro solves the optimization problem more efficiently than commonly used stochastic gradient descent (SGD) schemes. Finally, GNvpro finds solutions that generalize well, and in all but one example better than well-tuned SGD methods, to unseen data points.

97 MATHEMATICS AND COMPUTING↗

An efficient surrogate model of secondary electron formation and evolution

This work extends the adjoint-deep learning framework for runaway electron (RE) evolution, developed by McDevitt et al. [Phys. Plasmas 32, 042503 (2025)], to account for large-angle collisions. By incorporating large-angle collisions, the framework allows the avalanche of REs to be captured, an essential component of RE dynamics. This extension is accomplished by using a Rosenbluth–Putvinski approximation to estimate the distribution of secondary electrons generated by large-angle collisions. By evolving both the primary and multiple generations of secondary electrons, the present formulation can capture both the detailed temporal evolution of a RE population beginning from an arbitrary initial momentum space distribution, along with providing approximations to the saturated growth and decay rates of the RE population. Predictions of the adjoint-deep learning framework are verified against a traditional RE solver, with good agreement present across a broad range of parameters.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Improving Estimation of the Koopman Operator with Kolmogorov–Smirnov Indicator Functions

It has become common to perform kinetic analysis using approximate Koopman operators that transform high-dimensional timeseries of observables into ranked dynamical modes. The key to the practical success of the approach is the identification of a set of observables that form a good basis on which to expand the slow relaxation modes. Good observables are, however, difficult to identify a priori and suboptimal choices can lead to significant underestimations of characteristic time scales. Leveraging the representation of slow dynamics in terms of Hidden Markov Models (HMM), we propose a simple and computationally efficient clustering procedure to infer surrogate observables that form a good basis for slow modes. Here, we apply the approach to an analytically solvable model system as well as on three protein systems of different complexities. We consistently demonstrate that the inferred indicator functions can significantly improve the estimation of the leading eigenvalues of Koopman operators and correctly identify key states and transition time scales of stochastic systems, even when good observables are not known a priori.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Manifold Learning-Based Polynomial Chaos Expansions for High-Dimensional Surrogate Models

In this work we introduce a manifold learning-based method for uncertainty quantification (UQ) in systems describing complex spatiotemporal processes. Our first objective is to identify the embedding of a set of high-dimensional data representing quantities of interest of the computational or analytical model. For this purpose, we employ Grassmannian diffusion maps, a two-step nonlinear dimension reduction technique which allows us to reduce the dimensionality of the data and identify meaningful geometric descriptions in a parsimonious and inexpensive manner. Polynomial chaos expansion is then used to construct a mapping between the stochastic input parameters and the diffusion coordinates of the reduced space. An adaptive clustering technique is proposed to identify an optimal number of clusters of points in the latent space. The similarity of points allows us to construct a number of geometric harmonic emulators which are finally utilized as a set of inexpensive pretrained models to perform an inverse map of realizations of latent features to the ambient space and thus perform accurate out-of-sample predictions. Thus, the proposed method acts as an encoder-decoder system which is able to automatically handle very high-dimensional data while simultaneously operating successfully in the small-data regime. The method is demonstrated on two benchmark problems and on a system of advection-diffusion-reaction equations which model a first-order chemical reaction between two species. In all test cases, the proposed method is able to achieve highly accurate approximations which ultimately lead to the significant acceleration of UQ tasks.

42 ENGINEERING↗

An experiment-informed discrete element modelling study of knife milling for flexural biomass feedstocks

A discrete element method (DEM) based approach is used to study the relationships between material attributes (MAs), processing parameters (PPs), and quality attributes (QAs) for the knife milling of maize stalks. An approximate DEM shape model was conceptualized based on real maize stalks and calibrated based on experimental bending test data for flexural properties (elastic bending stiffness, elastic bending angle limit, elastoplastic ratio, etc.). DEM simulations of maize stalk comminution in a Jordan Reduction Solutions (“JRS”) knife mill were performed to investigate the relationships between the MAs (maize stalk size and breakage stress limit), PPs (impeller rotational speed), and QAs (mass throughput and output particle size distribution (PSD)). The DEM results suggest that stalk length has little influence on mass throughput and PSD, whilst stalks with larger cross sections tend to generate larger sizes of milled particles given the same breakage stress limit. Both the DEM and experimental results show that faster impeller rotation (or higher power) does not necessarily generate higher throughput or smaller output PSD, especially for maize stalks of higher breakage stress limit. The correlations between these MAs, PPs and QAs are found highly stochastic, though breakage stress limit dictates mass throughput, regardless of stalk size. The DEM-predicted output particle size tended to match the experimental data with coarse PSDs based on sieve size but showed weakened fidelity with finer material, indicating the potential for further model improvement.

09 BIOMASS FUELS↗

Development of a framework for sequential Bayesian design of experiments: Application to a pilot-scale solvent-based CO 2 capture process

In this paper, a methodology is developed for sequential design of experiments (SDoE) for process systems and applied to a solvent-based CO 2 capture system. In this approach, the prior knowledge of the system is used to prioritize process data collection at specific operating conditions. These data are then incorporated into a Bayesian inference methodology for updating a stochastic model by refining estimations of its underlying parameters, and the updated model is then used to generate the next set of test runs. Thus, the new knowledge obtained from the data is used to guide subsequent iterations of the experimental runs, ensuring that the overall data collection is maximally informative given that most experimental campaigns, especially at pilot or higher-scale plants, are costly, time-consuming, and resource-limited. The test run objective for this work was to minimize the maximum model prediction uncertainty for key output variables, but the methodology is generic and can be readily applied to other test run objectives. This methodology is applied to an aqueous monoethanolamine (MEA) pilot plant campaign at the National Carbon Capture Center (NCCC) in Wilsonville, Alabama, USA. The SDoE framework was utilized for two iterations, while collecting 18 sets of data representing different process conditions, and this resulted in an overall average reduction in uncertainty of approximately 50% in the prediction of CO 2 capture percentage. Moreover, 11 additional data sets were obtained with variation of absorber packing height for further model validation. This work shows the capability of the SDoE framework to maximize learning given limited resources, allowing for the reduction of model uncertainty, which is of great importance for many applications including reduction of technical risk associated with scale-up and economic analysis.

20 FOSSIL-FUELED POWER PLANTS↗

Effect of particle size on the capture of uranium oxide colloidal particles from aqueous suspensions via high-gradient magnetic filtration

The effectiveness of High Gradient Magnetic Filtration (HGMF) in capturing uranium oxide particles from suspensions was investigated in this study. Two sets of experiments were performed to evaluate the importance of size on the capture of uranium oxide particles. The first considered two batches sieved into size bins of< 5, 5–10, 10–15, and 15–20 µm, while the second was performed using two suspensions with diameters smaller than 1.0 µm and between 1.0 and 1.5 µm. Iron oxide experiments, with particles between 0.3 and 0.8 µm, were performed for calibration purposes. In all experiments, a surfactant (Triton-X100 or sodium dodecyl sulfate) was used to prevent particle aggregation and limit the influence of non-magnetic capture mechanisms. A magnetic field of approximately 1.1 Tesla was generated using a water cooled electromagnet. HGMF was performed using tubular filters packed with ferromagnetic stainless-steel wool. Of the initial four uranium oxide particle sizes, magnetic capture was only observed for particles with a diameter of less than 5 µm, while larger particles experienced no magnetic and minimal total capture. For particles with diameters smaller than 1.0 µm and between 1.0 and 1.5 µm, capture efficiencies increased by 39 ± 9% and 34 ± 6% respectively, solely due to the magnetic field. Although the magnetic force is proportional to particle diameter, the capture efficiency decreased as diameter increased. So these results suggest that Brownian diffusion, which is influential for micron sized particles and increases with decreasing particle size, is acting in conjunction with the magnetic force to influence the efficacy of HGMF for uranium oxide. This important finding underscores the effectiveness of Brownian diffusion in increasing the rate of collision between particles and collector fibers. A stochastic trajectory model was developed to incorporate the influence of Brownian motion on particle behavior and filter removal efficiency. Modeling results are discussed and compared for uranium and iron oxide particles.

42 ENGINEERING↗

DPM: A deep learning PDE augmentation method with application to large-eddy simulation

A framework is introduced that leverages known physics to reduce overfitting in machine learning for scientific applications. The partial differential equation (PDE) that expresses the physics is augmented with a neural network that uses available data to learn a description of the corresponding unknown or unrepresented physics. Training within this combined system corrects for missing, unknown, or erroneously represented physics, including discretization errors associated with the PDE's numerical solution. For optimization of the network within the PDE, an adjoint PDE is solved to provide high-dimensional gradients, and a stochastic adjoint method (SAM) further accelerates training. Additionally, the approach is demonstrated for large-eddy simulation (LES) of turbulence. High-fidelity direct numerical simulations (DNS) of decaying isotropic turbulence provide the training data used to learn sub-filter-scale closures for the filtered Navier–Stokes equations. Out-of-sample comparisons show that the deep learning PDE method outperforms widely-used models, even for filter sizes so large that they become qualitatively incorrect. It also significantly outperforms the same neural network when a priori trained based on simple data mismatch, not accounting for the full PDE. Measures of discretization errors, which are well-known to be consequential in LES, point to the importance of the unified training formulation's design, which without modification corrects for them. For comparable accuracy, simulation runtime is significantly reduced. A relaxation of the typical discrete enforcement of the divergence-free constraint in the solver is also successful, instead allowing the DPM to approximately enforce incompressibility physics. Since the training loss function is not restricted to correspond directly to the closure to be learned, training can incorporate diverse data, including experimental data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NO PLIF flow visualization and time-resolved temperature distributions in laser induced breakdown plumes

NO planar laser induced fluorescence (PLIF) is used to obtain images of laser-induced breakdown plasma plumes in NO-seeded nitrogen and dry air at near atmospheric pressure. Single-shot PLIF-images show that the plume development 5–50 μs after the breakdown pulse is fairly reproducible shot-to-shot, although the plume becomes increasingly stochastic on longer timescales, 100–500 μs. The stochastic behavior of the plume is quantified using probability distributions of the loci of the plume boundary. Analysis of the single-shot images indicates that the mixing of the plume with ambient gas on sub-ms time scale is insignificant. The induced flow velocity in the plume is fairly low, up to 30 m s –1 , suggesting that laser breakdowns are ineffective for mixing enhancement in high speed flows. The ensemble-averaged PLIF images indicate the evolution of the plume from an initially elongated shape to near-spherical to toroidal shape, with a subsequent radial expansion and formation of an axial jet in the center. Temperature distributions in the plume in air are obtained from the NO PLIF images, using two rotational transitions in the NO(X, v' = 0 → A, v'' = 0) band, J'' = 6.5 and 12.5 of the Q R 12 + Q 2 branch. The results indicate that the temperature in the plume remains high, above 1000 K, for approximately 100 μs, after which it decays gradually, to below 500 K at 500 μs. The residual NO fraction in the plume is ~0.1%, indicating that repetitive laser-assisted ignition may result in significant NO-generation. Furthermore, these measured temperature and velocity distributions can be used for detailed validation of kinetic models of laser-induced breakdown and assessment of their predictive capability.

42 ENGINEERING↗