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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

A COUPLED DETERMINISTIC TRANSPORT CALCULATION IN COMSOL USING PROPER ORTHOGONAL DECOMPOSITION

A coupled physics problem consisting of radiation transport and heat transfer was modeled using COMSOL Multiphysics to simulate a criticality accident. Reduced order models (ROM) were created to accelerate the radiation transport calculation through Proper Orthogonal Decomposition (POD). Additionally, on-the-fly neutron cross sections were generated from a non-linear function through a feed forward neural network. The Livelink for MATLAB module allowed for data transfer between an otherwise independent solver and in-house modules. A data driven approach to POD was developed to act as a surrogate model to couple with heat transfer, with the POD module written in MATLAB coupled to an isolated heat transfer solve in COMSOL. A coupled transient solution resulted in a good approximation of the flux and temperature, with the maximum error being 3E-2 and 2.5E-3 respectively.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
NASA NTRS2004

DORIS satellite antenna maps derived from long-term residuals time series

Recent studies have shown that phase pattern models for the Jason-1 GPS antenna significantly benefit GPS-based precise orbit determination (POD) for the satellite. We have used a similar technique to derive DORIS receiver antenna maps, using all available DORIS tracking data over long time periods (from 1993.0 to 2004.0). We demonstrate that the derived correction models are satellite specific. For a given satellite, year-to-year estimations show clear systematic patterns. Some of these systematic patterns are attributable to the derivative of the multi-path effects in the direction of the satellite velocity. For early SPOT data, the patterns can be explained by an offset in the TAI time tagging (typically 8 (mu)s). In a second step, we have applied the SPOT2 antenna correction models in precise orbit determination and in the positioning of ground beacons. Preliminary results on DORIS/SPOT2 show that application of the DORIS antenna maps lead to a slight improvement of the derived POD and geodetic results (typically less than 5%).

precise orbit determination (POD)↗
DOE OSTI2022

Numerical investigation of the influence of shear and thermal stratification on the wind turbine tip‐vortex stability

Summary The interaction between wind turbine wakes and atmospheric turbulence is characterised by complex dynamics. In this study, two major components of the atmospheric boundary layer dynamics have been isolated, namely, the mean velocity profile shear and the thermal stratification, to examine their impact on the near‐wake development by undertaking a series of highly resolved large‐eddy simulations. Subsequently, instantaneous flow fields are extracted from the simulations and used to conduct Fourier analysis and proper orthogonal decomposition (POD) and compute the mean kinetic energy fluxes by different POD modes to better understand the tip‐vortex instability mechanisms. Our findings indicate that shear can significantly affect the breakup of the wind turbine tip‐vortices and the shape and stable length of the wake, whereas thermal stratification seems to only have limited contribution to the spatial development of the near‐wake field. Finally, our analysis shows that the applied perturbation frequency determines the tip‐vortex breakup location as it controls the onset of the mutual inductance instability.

17 WIND ENERGY↗
DOE OSTI2026

Local reduced-order modeling for electrostatic plasmas by physics-informed solution manifold decomposition

Despite advancements in high-performance computing and modern numerical algorithms, computational cost remains prohibitive for multi-query kinetic plasma simulations. Here, in this work, we develop data-driven reduced-order models (ROMs) for collisionless electrostatic plasma dynamics, based on the kinetic Vlasov-Poisson equation. Our ROM approach projects the equation onto a linear subspace defined by the proper orthogonal decomposition (POD) modes. We introduce an efficient tensorial method to update the nonlinear term using a precomputed third-order tensor. We capture multiscale behavior with a minimal number of POD modes by decomposing the solution manifold into multiple time windows and creating temporally local ROMs. We consider two strategies for decomposition: one based on the physical time and the other based on the electric field energy. Applied to the 1D1V Vlasov–Poisson simulations, that is, prescribed E-field, Landau damping, and two-stream instability, we demonstrate that our ROMs accurately capture the total energy of the system both for parametric and time extrapolation cases. The temporally local ROMs are more efficient and accurate than the single ROM. In addition, in the two-stream instability case, we show that the energy-windowing reduced-order model (EW-ROM) is more efficient and accurate than the time-windowing reduced-order model (TW-ROM). With the tensorial approach, EW-ROM solves the equation approximately 90 times faster than Eulerian simulations while maintaining a maximum relative error of 7.5% for the training data and 11% for the testing data.

Electrostatic plasmas↗
DOE OSTI2023

On the interaction of a wind turbine wake with a conventionally neutral atmospheric boundary layer

In this work, we investigate the dynamics of wind turbine tip-vortex breakdown in a conventionally neutral atmospheric boundary layer (ABL). To this end, high-resolution data are collected from large-eddy simulations of a wind turbine operating within a neutral ABL and studied by means of proper orthogonal decomposition (POD) and Fourier analysis. The high resolution of the generated data in both space and time allows us to gain insight into the tip-vortex breakdown mechanisms by (i) capturing the energy modes of the coherent structures, (ii) studying their contribution to the tip-vortex breakdown through their power spectra functions and mean kinetic energy (MKE) flux, and (iii) analysing the growth rate of each contributing perturbation frequency along tip vortices. Our analysis shows that under a fully turbulent scenario, the growth rate of perturbations along the tip vortices is largest for low wave numbers, i.e. long-wave perturbations. Additionally, the MKE flux reaches its highest value at two diameters downstream of the rotor plane, a behaviour that can be attributed to the coexistence of multiple interacting POD modes, with the streamwise vortex roller mode being the primary contributor to the total MKE flux budget, contributing approximately . Finally, comparisons with a laminar, uniform flow scenario subject to a single-frequency perturbation highlight the differences between the two ambient flow conditions. In the non-turbulent, uniform flow scenario, the growth rate attains its maximum value at a wave number corresponding to the out-of-phase mutual-inductance mechanism, whereas the MKE flux exhibits local minima and maxima along the wake and at different downstream locations depending on the perturbation frequency. Our analyses suggest that the breakdown of the wind turbine tip vortices under a fully turbulent neutral ABL inflow is due to complex interactions across a range of excitation frequencies, in which the mutual-inductance instability may not be the dominant one.

17 WIND ENERGY↗
DOE OSTI2022

Neural-network learning of SPOD latent dynamics

Here, we aim to reconstruct the latent space dynamics of high dimensional, quasi-stationary systems using model order reduction via the spectral proper orthogonal decomposition (SPOD). The proposed method is based on three fundamental steps: in the first, once that the mean flow field has been subtracted from the realizations (also referred to as snapshots), we compress the data from a high-dimensional representation to a lower dimensional one by constructing the SPOD latent space; in the second, we build the time-dependent coefficients by projecting the snapshots containing the fluctuations onto the SPOD basis and we learn their evolution in time with the aid of recurrent neural networks; in the third, we reconstruct the high-dimensional data from the learnt lower -dimensional representation. The proposed method is demonstrated on two different test cases, namely, a compressible jet flow, and a geophysical problem known as the Madden-Julian Oscillation. An extensive comparison between SPOD and the equivalent POD-based counterpart is provided and differences between the two approaches are highlighted. The numerical results suggest that the proposed model is able to provide low rank predictions of complex statistically stationary data and to provide insights into the evolution of phenomena characterized by specific range of frequencies. The comparison between POD and SPOD surrogate strategies highlights the need for further work on the characterization of the interplay of error between data reduction techniques and neural network forecasts.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

GeN-ROM—An OpenFOAM®-based multiphysics reduced-order modeling framework for the analysis of Molten Salt Reactors

This work presents a projection-based multiphysics Model Order Reduction (MOR) framework for the analysis of nuclear systems and its application to parametric simulations of Molten Salt Reactors (MSR). The framework, named GeN-ROM, is developed using OpenFOAM® and employs a Proper Orthogonal Decomposition aided Reduced-Basis technique (POD-RB). It can be used to reduce steady-state and transient multiphysics problems involving parametric fluid dynamics, heat exchange, and neutronics phenomena. For the treatment of structural elements in the hydraulic systems, a porous medium approach has been adopted. The reduction process is data-driven and snapshot information is extracted via POD to learn the solution manifold and to build global spatial basis functions. At the data collection phase, GeN-ROM makes use of the solvers available in GeN-Foam, a similarly OpenFOAM®-based multiphysics framework developed for the analysis of nuclear reactors. The global bases are used both to approximate the solution fields and to project the full-order equations onto lower-dimensional subspaces, thus considerably reducing the number of unknowns in a numerical system. This reduction leads to significant computational speedups, which is ideal for multi-query applications such as uncertainty quantification or design optimization. The developed tool has been tested using a 2D multiphysics model of the Molten Salt Fast Reactor (MSFR) with steady-state and transient scenarios, with speedups on the order of 10 – 10 5 .

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Equation‐Free Surrogate Modeling of Geophysical Flows at the Intersection of Machine Learning and Data Assimilation

Abstract There is a growing interest in developing data‐driven reduced‐order models for atmospheric and oceanic flows that are trained on data obtained either from high‐resolution simulations or satellite observations. The data‐driven models are non‐intrusive in nature and offer significant computational savings compared to large‐scale numerical models. These low‐dimensional models can be utilized to reduce the computational burden of generating forecasts and estimating model uncertainty without losing the key information needed for data assimilation (DA) to produce accurate state estimates. This paper aims at exploring an equation‐free surrogate modeling approach at the intersection of machine learning and DA in Earth system modeling. With this objective, we introduce an end‐to‐end non‐intrusive reduced‐order modeling (NIROM) framework equipped with contributions in modal decomposition, time series prediction, optimal sensor placement, and sequential DA. Specifically, we use proper orthogonal decomposition (POD) to identify the dominant structures of the flow, and a long short‐term memory network to model the dynamics of the POD modes. The NIROM is integrated within the deterministic ensemble Kalman filter (DEnKF) to incorporate sparse and noisy observations at optimal sensor locations obtained through QR pivoting. The feasibility and the benefit of the proposed framework are demonstrated for the NOAA Optimum Interpolation Sea Surface Temperature (SST) V2 data set. Our results indicate that the NIROM is stable for long‐term forecasting and can model dynamics of SST with a reasonable level of accuracy. Furthermore, the prediction accuracy of the NIROM gets improved by almost one order of magnitude by the DEnKF algorithm.

Pawar, Suraj↗
DOE OSTI2022

Reduced order modeling for flow and transport problems with Barlow Twins self-supervised learning

Abstract We propose a unified data-driven reduced order model (ROM) that bridges the performance gap between linear and nonlinear manifold approaches. Deep learning ROM (DL-ROM) using deep-convolutional autoencoders (DC–AE) has been shown to capture nonlinear solution manifolds but fails to perform adequately when linear subspace approaches such as proper orthogonal decomposition (POD) would be optimal. Besides, most DL-ROM models rely on convolutional layers, which might limit its application to only a structured mesh. The proposed framework in this study relies on the combination of an autoencoder (AE) and Barlow Twins (BT) self-supervised learning, where BT maximizes the information content of the embedding with the latent space through a joint embedding architecture. Through a series of benchmark problems of natural convection in porous media, BT–AE performs better than the previous DL-ROM framework by providing comparable results to POD-based approaches for problems where the solution lies within a linear subspace as well as DL-ROM autoencoder-based techniques where the solution lies on a nonlinear manifold; consequently, bridges the gap between linear and nonlinear reduced manifolds. We illustrate that a proficient construction of the latent space is key to achieving these results, enabling us to map these latent spaces using regression models. The proposed framework achieves a relative error of 2% on average and 12% in the worst-case scenario (i.e., the training data is small, but the parameter space is large.). We also show that our framework provides a speed-up of $$7 \times 10^{6}$$ 7 × 10 6 times, in the best case, and $$7 \times 10^{3}$$ 7 × 10 3 times on average compared to a finite element solver. Furthermore, this BT–AE framework can operate on unstructured meshes, which provides flexibility in its application to standard numerical solvers, on-site measurements, experimental data, or a combination of these sources.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Mechanically robust and superior conductive n-type polymer binders for high-performance micro-silicon anodes in lithium-ion batteries

Compared with nanostructured silicon (Si), the Si microparticle (SiMP) has more commercial prospects due to its low cost. However, SiMPs suffer from unavoidable fracture during electrochemical cycling owing to their significant volume change. Here we develop a series of novel n-type conductive polymer binders (CPBs) for SiMP anodes in lithium-ion batteries owing to their superior properties. Extraordinary electrochemical performance of cells with such unique binders could be achieved, which is because these designed polymers contain electron-withdrawing oxadiazole ring groups and easily ionizable sulfonate polar groups, exhibiting excellent ionic conductivity, outstanding wettability to the electrolyte, and improved electronic conductivity after doping. Moreover, the coexistence of rigid and flexible chains enables them to have exceptional strength and ductility. Besides, a unique electrochromic approach has been utilized to investigate the energy gap of the CPBs in n-doping states. The ionic and electronic conductivities of prepared CPBs in an eigenstate and n-doping state have been systematically studied by the electrochemical method, filling the current research gap in this field. Due to the high conductivity of b-POD, the capacity of SiMPs (4200 mA h g –1 ) can be almost entirely released during the first cycle of discharge, while the SiMP anodes prepared with the PAALi or CMC binder show a much lower initial capacity. Here, the high conductivity of b-POD also endows it with better cycling performance than non-conductive binders especially at high current densities, demonstrating its excellent fast-charging ability. More essentially, this work provides polymer binders without any intricate structural designs to obtain high-performance SiMP batteries, significantly enhancing their practical applications.

25 ENERGY STORAGE↗
DOE OSTI2021

Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders

A common strategy for the dimensionality reduction of nonlinear partial differential equations (PDEs) relies on the use of the proper orthogonal decomposition (POD) to identify a reduced subspace and the Galerkin projection for evolving dynamics in this reduced space. However, advection-dominated PDEs are represented poorly by this methodology since the process of truncation discards important interactions between higher-order modes during time evolution. In this study, we demonstrate that encoding using convolutional autoencoders (CAEs) followed by a reduced-space time evolution by recurrent neural networks overcomes this limitation effectively. We demonstrate that a truncated system of only two latent space dimensions can reproduce a sharp advecting shock profile for the viscous Burgers equation with very low viscosities, and a six-dimensional latent space can recreate the evolution of the inviscid shallow water equations. Additionally, the proposed framework is extended to a parametric reduced-order model by directly embedding parametric information into the latent space to detect trends in system evolution. Furthermore, our results show that these advection-dominated systems are more amenable to low-dimensional encoding and time evolution by a CAE and recurrent neural network combination than the POD-Galerkin technique.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

On closures for reduced order models - A spectrum of first-principle to machine-learned avenues

For over a century, reduced order models (ROMs) have been a fundamental discipline of theoretical fluid mechanics. Early examples include Galerkin models inspired by the Orr–Sommerfeld stability equation and numerous vortex models, of which the von Karman vortex street is one of the most prominent. Subsequent ROMs typically relied on first principles, like mathematical Galerkin models, weakly nonlinear stability theory, and two- and three-dimensional vortex models pioneered the data-driven proper orthogonal decomposition (POD) modeling. In early POD modeling, available data were used to build an optimal basis, which was then utilized in a classical Galerkin procedure to construct the ROM, but data have made a profound impact on ROMs beyond the Galerkin expansion. In this paper, we take a modest step and illustrate the impact of data-driven modeling on one significant ROM area. Specifically, we focus on ROM closures, which are correction terms that are added to the classical ROMs in order to model the effect of the discarded ROM modes in under-resolved simulations. Through simple examples, we illustrate the main modeling principles used to construct the classical ROMs, motivate and introduce modern ROM closures, and show how data-driven modeling, artificial intelligence, and machine learning have changed the standard ROM methodology over the last two decades. Finally, we outline our vision on how the state-of-the-art data-driven modeling can continue to reshape the field of reduced order modeling.

42 ENGINEERING↗
DOE OSTI2021

An LES study of secondary motion and wall shear stresses in a pipe bend

In this study, large-eddy simulations (LES) of a single-phase, turbulent flow in a 90 ° pipe bend are performed at three Reynolds numbers (5300, 27 000, and 45 000) to investigate the correlation between secondary flow motion and wall shear stresses, which is suspected to be a potential mechanism responsible for material erosion. The isothermal flows are validated against available experimental and numerical data first. The snapshot proper orthogonal decomposition (POD) is applied for the medium and high Reynolds number flows to identify the secondary flow motions and the oscillation of the Dean vortices that are found to cause swirl-switching. Distinguished frequencies of the POD time coefficients at Strouhal numbers of 0.25 and 0.28 are identified for Reynolds numbers at 27 000 and 45 000, respectively. Moreover, shear stress on the pipe wall and the associated power spectral density are obtained and shown to have the same oscillating frequency as the swirl-switching.

42 ENGINEERING↗
DOE OSTI2022

Machine-learning identification of the variability of mean velocity and turbulence intensity for wakes generated by onshore wind turbines: Cluster analysis of wind LiDAR measurements

Light detection and ranging (LiDAR) measurements of isolated wakes generated by wind turbines installed at an onshore wind farm are leveraged to characterize the variability of the wake mean velocity and turbulence intensity during typical operations, which encompass a breadth of atmospheric stability regimes and rotor thrust coefficients. The LiDAR measurements are clustered through the k-means algorithm, which enables identifying the most representative realizations of wind turbine wakes while avoiding the imposition of thresholds for the various wind and turbine parameters. Considering the large number of LiDAR samples collected to probe the wake velocity field, the dimensionality of the experimental dataset is reduced by projecting the LiDAR data on an intelligently truncated basis obtained with the proper orthogonal decomposition (POD). The coefficients of only five physics-informed POD modes are then injected in the k-means algorithm for clustering the LiDAR dataset. The analysis of the clustered LiDAR data and the associated supervisory control and data acquisition and meteorological data enables the study of the variability of the wake velocity deficit, wake extent, and wake-added turbulence intensity for different thrust coefficients of the turbine rotor and regimes of atmospheric stability. Furthermore, the cluster analysis of the LiDAR data allows for the identification of systematic off-design operations with a certain yaw misalignment of the turbine rotor with the mean wind direction.

17 WIND ENERGY↗
DOE OSTI2021

Nonlinear proper orthogonal decomposition for convection-dominated flows

Autoencoder techniques find increasingly common use in reduced order modeling as a means to create a latent space. This reduced order representation offers a modular data-driven modeling approach for nonlinear dynamical systems when integrated with a time series predictive model. In this Letter, we put forth a nonlinear proper orthogonal decomposition (POD) framework, which is an end-to-end Galerkin-free model combining autoencoders with long short-term memory networks for dynamics. By eliminating the projection error due to the truncation of Galerkin models, a key enabler of the proposed nonintrusive approach is the kinematic construction of a nonlinear mapping between the full-rank expansion of the POD coefficients and the latent space where the dynamics evolve. We test our framework for model reduction of a convection-dominated system, which is generally challenging for reduced order models. Our approach not only improves the accuracy, but also significantly reduces the computational cost of training and testing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Physics-constrained deep learning of nonlinear normal modes of spatiotemporal fluid flow dynamics

In this study, we present a physics-constrained deep learning method to discover and visualize from data the invariant nonlinear normal modes (NNMs) which contain the spatiotemporal dynamics of the fluid flow potentially containing strong nonlinearity. Specifically, we develop a NNM-physics-constrained convolutional autoencoder (NNM-CNN-AE) integrated with a multi-temporal-step dynamics prediction block to learn the nonlinear modal transformation, the NNMs containing the spatiotemporal dynamics of the flow, and reduced-order reconstruction and long-time future-state prediction of the flow fields, simultaneously. In test cases, we apply the developed method to analyze different flow regimes past a cylinder, including laminar flows with low Reynolds number in transient and steady states (RD = 100) and high Reynolds number flow (RD = 1000), respectively. The results indicate that the identified NNMs are able to reveal the nonlinear spatiotemporal dynamics of these flows, and the NNMs-based reduced-order modeling consistently achieves better accuracy with orders of magnitudes smaller errors in construction and prediction of the nonlinear velocity and vorticity fields, compared to the linear proper orthogonal decomposition (POD) method and the Koopman-constrained-CNN-AE using the same number or dimension of modes. We perform an analysis of the modal energy distribution of NNMs and find that compared to POD modes, the few fundamental NNMs capture a very high level of total energy of the flow, which is advantageous for reduced-order modeling and representation of the complex flows. Finally, we discuss the potentials and limitations of the presented method.

Mechanics↗
DOE OSTI2020

Characterization of turbulence under different stability conditions using lidar scanning data

The spatiotemporal scales of turbulence in the boundary layer flow vary with the static stability of the atmosphere. For example, turbulence structures in unstable conditions are often found to be large and coherent, whereas the turbulent structures in stable conditions are relatively small and sporadic. To better understand the behavior of such turbulent structures under different atmospheric stability conditions in the lower atmosphere, herein, we use scanning lidar data collected over several months during the US Department of Energy's second Wind Forecast Improvement Project (WFIP 2) in 2016. The radial velocity data from scanning lidar were gathered along the horizontal plane (PPI mode) and were analyzed using proper orthogonal decomposition (POD) and spectral energy methods. The results from these analyses show that the turbulent structures in daytime unstable conditions are different from those present during nighttime stable conditions in terms of amount of energy and coherent structures. The POD energy is distributed more evenly in all the higher spatial modes in the daytime unstable case compared to the nighttime stable case. Besides characterizing the turbulence in the flow, the lidar data were also used to compare the simulated flow field generated from the WRF-LES framework (Weather Research and Forecasting - large-eddy simulation) with the scanning lidar data. The results from both simulated and lidar scanned data show similar structures orienting the streak-like structure along the mean wind. This indicates that the streak-like structures can exist in the real atmosphere during unstable atmospheric condition cases.

Rai, Raj K.↗
DOE OSTI2024

S-OPT: A Points Selection Algorithm for Hyper-Reduction in Reduced Order Models

While projection-based reduced order models can reduce the dimension of full order solutions, the resulting reduced models may still contain terms that scale with the full order dimension. Hyper-reduction techniques are sampling-based methods that further reduce this computational complexity by approximating such terms with a much smaller dimension. The goal of this work is to introduce the points selection algorithm developed by Shin and Xiu as a hyper-reduction method. The selection algorithm was originally proposed as a stochastic collocation method for uncertainty quantification. Since the algorithm aims at maximizing a quantity $\mathcal{S}$ that measures both the column orthogonality and the determinant, we refer to the algorithm as S-OPT. Numerical examples are provided to demonstrate the performance of S-OPT and to compare its performance with a gappy proper orthogonal decomposition (POD) algorithm. Here, we found that using the S-OPT algorithm is shown to predict the full order solutions with higher accuracy than gappy POD especially when the number of sampling points is small, although we note that S-OPT shows slow asymptotic convergence with respect to the number of samples for some applications, e.g., Lagrangian hydrodynamics.

97 MATHEMATICS AND COMPUTING↗