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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

High-order accurate solutions of the point kinetics equations with the spectral deferred correction method

Solving initial value problems with higher-order methods can improve the accuracy of the simulation results or the efficiency of the calculation. In this paper, we apply the spectral deferred correction (SDC) method to solve the initial value problem of the point kinetics equations (PKE). SDC is a stable, robust, and efficient high-order time-integration method capable of an arbitrary order of accuracy. For our implementation we show that it is A-stable for orders up to 8 and the order of accuracy is verified for PKE problems with a range of different reactivities. A 5.-order SDC method was then implemented to solve the exact PKE (EPKE) in the Transient Multilevel (TML) method of MPACT. The error from solutions of the EPKE is shown to be negligible. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Multilevel Monte Carlo Predictions of First Passage Times in Three-Dimensional Discrete Fracture Networks: A Graph-Based Approach

In this paper, we present a method combining multilevel Monte Carlo (MLMC) and a graph-based primary subnetwork identification algorithm to provide estimates of the mean and variance of the distribution of first passage times in fracture media at significantly lower computational cost than standard Monte Carlo (MC) methods. Simulations of solute transport are performed using a discrete fracture network (DFN), and instead of using various grid resolutions for levels in the MLMC, which is standard practice in MLMC, we identify a hierarchy of subnetworks in the DFN based on the shortest topological paths through the network using a graph-based method. While the mean of these ensembles is of critical importance, the variance is also essential in fractured media where uncertainty is an overarching theme, and understanding variability across an ensemble is a requirement for safety assessments. The method provides good estimates of the mean and variance at two orders of magnitude lower computational cost than MC.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

System and method for optimizing fundamental frequency modulation for a cascaded multilevel inverter

A system and a method for optimizing fundamental frequency modulation in a cascaded multilevel inverter (CMI) are provided. The CMI includes at least a first H-bridge module and a second H-bridge module connected in series with the first H-bridge module. The first H-bridge module is operated according to a first duty cycle and the second H-bridge module is operated according to a second duty cycle. The first duty cycle is greater than the second duty cycle. The first and second H-bridge modules are controlled utilizing fundamental frequency modulation. A portion of the first duty cycle is transferred to the second duty cycle thereby optimizing fundamental frequency modulation by at least improving power sharing between the first and second H-bridge modules and improving equalization of DC capacitor currents and voltage ripples while maintaining the same fundamental modulation to the output voltage waveform.

42 ENGINEERING↗
DOE OSTI2025

A two-level GPU-accelerated incomplete LU preconditioner for general sparse linear systems

This paper presents a parallel preconditioning approach based on incomplete LU (ILU) factorizations in the framework of Domain Decomposition (DD) for general sparse linear systems. We focus on distributed memory parallel architectures, specifically, those that are equipped with graphic processing units (GPUs). In addition to block-Jacobi, we present general purpose two-level ILU Schur complement-based approaches, where different strategies are presented to solve the coarse-level reduced system. These strategies are combined with modified ILU methods in the construction of the coarse-level operator, in order to effectively remove smooth errors by targeting an algebraically smooth vector. We leverage available GPU-based sparse matrix kernels to accelerate the setup and the solve phases of the proposed ILU preconditioner. We evaluate the efficiency of the proposed methods as a smoother for algebraic multigrid (AMG) and as a preconditioner for Krylov subspace methods on challenging anisotropic diffusion problems and a collection of general sparse matrices.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Biomechanical Analysis of Multilevel Posterior Cervical Spinal Fusion Constructs

Study Design: Controlled Laboratory Study Objective: To compare multilevel posterior cervical fusion (PCF) constructs stopping at C7, T1, and T2 under cyclic load to determine the range of motion (ROM) between the lowest instrumented level and lowest instrumented-adjacent level (LIV-1). Summary of Background Data: PCF is a mainstay of treatment for various cervical spine conditions. The transition between the flexible cervical spine and rigid thoracic spine can lead to construct failure at the cervicothoracic junction. There is little evidence to determine the most appropriate level at which to stop a multilevel PCF. Methods: Fifteen human cadaveric cervicothoracic spines were randomly assigned to 1 of 3 treatment groups: PCF stopping at C7, T1, or T2. Specimens were tested in their native state, following a simulated PCF, and after cyclic loading. Specimens were loaded in flexion-extension), lateral bending, and axial rotation. Three-dimensional kinematics were recorded to evaluate ROM. Results: The C7 group had greater flexion-extension motion than the T1 and T2 groups following instrumentation (10.17±0.83 degree vs. 2.77±1.66 degree and 1.06±0.55 degree, P <0.001), and after cyclic loading (10.42±2.30 degree vs. 2.47±0.64 degree and 1.99±1.23 degree, P <0.001). There was no significant difference between the T1 and T2 groups. The C7 group had greater lateral bending ROM than both thoracic groups after instrumentation (8.81±3.44 degree vs. 3.51±2.52 degree, P =0.013 and 1.99±1.99 degree, P =0.003) and after cyclic loading. The C7 group had greater axial rotation motion than the thoracic groups (4.46±2.27 degree vs. 1.26±0.69 degree, P =0.010; and 0.73±0.74 degree, P =0.003) following cyclic loading. Conclusion: Motion at the cervicothoracic junction is significantly greater when a multilevel PCF stops at C7 rather than T1 or T2. This is likely attributable to the transition from a flexible cervical spine to a rigid thoracic spine. Although this does not account for in vivo fusion, surgeons should consider extending multilevel PCF constructs to T1 when feasible. Level of Evidence: Not applicable.

Neurosciences & Neurology↗
DOE OSTI2020

Estimating posterior quantity of interest expectations in a multilevel scalable framework

Scalable approaches for uncertainty quantification are necessary for characterizing prediction confidence in large-scale subsurface flow simulations with uncertain permeability. To this end we explore a multilevel Monte Carlo approach for estimating posterior moments of a particular quantity of interest, where we employ an element-agglomerated algebraic multigrid (AMG) technique to generate the hierarchy of coarse spaces with guaranteed approximation properties for both the generation of spatially correlated random fields and the forward simulation of Darcy's law to model subsurface flow. In both these components (sampling and forward solves), we exploit solvers that rely on state-of-the-art scalable AMG. To illustrate the applicability of this approach, numerical tests are performed on two 3D examples-a unit cube and an egg-shaped domain with an irregular boundary-where the scalability of each simulation as well as the scalability of the overall algorithm are demonstrated.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Multilevel-in-width training for deep neural network regression

A common challenge in regression is that for many problems, the degrees of freedom required for a high-quality solution also allows for overfitting. Regularization is a class of strategies that seek to restrict the range of possible solutions so as to discourage overfitting while still enabling good solutions, and different regularization strategies impose different types of restrictions. In this paper, we present a multilevel regularization strategy that constructs and trains a hierarchy of neural networks, each of which has layers that are wider versions of the previous network's layers. Here, we draw intuition and techniques from the field of Algebraic Multigrid (AMG), traditionally used for solving linear and nonlinear systems of equations, and specifically adapt the Full Approximation Scheme (FAS) for nonlinear systems of equations to the problem of deep learning. Training through V-cycles then encourage the neural networks to build a hierarchical understanding of the problem. We refer to this approach as multilevel-in-width to distinguish from prior multilevel works which hierarchically alter the depth of neural networks. The resulting approach is a highly flexible framework that can be applied to a variety of layer types, which we demonstrate with both fully connected and convolutional layers. We experimentally show with PDE regression problems that our multilevel training approach is an effective regularizer, improving the generalize performance of the neural networks studied.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A New Configuration of Paralleled Modular ANPC Multilevel Converter Controlled by an Improved Modulation Method for 1 MHz, 1 MW EV Charger

In this work, a new configuration of the modular multilevel converter (MLC) based on the parallel connection of three-level active-neutral-point-clamped (3L-ANPC) cells as well as its improved modulation method is proposed for 1 MHz, 1 MW electric vehicle (EV) megacharger. In the proposed paralleled modular ANPC-MLC, only six high-frequency silicon carbide (SiC) power switches operating at 333 kHz are required to generate 1 MHz switching frequency spectrum. Moreover, the operating voltage of all power devices is halved, the magnitude of the first switching frequency harmonic cluster is decreased by the factor of five, and the load current is equally distributed between the 3L-ANPC legs by employing the proposed improved modulation method. Hence, the modularity, efficiency, and power density of the proposed converter are notably increased, whereas the value of passive components and the overall switching loss are remarkably decreased. In addition, an optimized design of the one 3L-ANPC cell of the proposed paralleled modular ANPC-MLC for 1 MHz, 1MW EV megacharger using Ansys SIwave, Icepak, and Q3D finite element method platforms is presented and analyzed in detail. The provided experimental results of the down-scaled setup verify the feasibility and viability of the proposed configuration as well as its improved switching pattern.

42 ENGINEERING↗
DOE OSTI2023

Urban Flood Modeling: Uncertainty Quantification and Physics‐Informed Gaussian Processes Regression Forecasting

Abstract Estimating uncertainty in flood model predictions is important for many applications, including risk assessment and flood forecasting. We focus on uncertainty in physics‐based urban flooding models. We consider the effects of the model's complexity and uncertainty in key input parameters. The effect of rainfall intensity on the uncertainty in water depth predictions is also studied. As a test study, we choose the Interconnected Channel and Pond Routing (ICPR) model of a part of the city of Minneapolis. The uncertainty in the ICPR model's predictions of the floodwater depth is quantified in terms of the ensemble variance using the multilevel Monte Carlo (MC) simulation method. Our results show that uncertainties in the studied domain are highly localized. Model simplifications, such as disregarding the groundwater flow, lead to overly confident predictions, that is, predictions that are both less accurate and uncertain than those of the more complex model. We find that for the same number of uncertain parameters, increasing the model resolution reduces uncertainty in the model predictions (and increases the MC method's computational cost). We employ the multilevel MC method to reduce the cost of estimating uncertainty in a high‐resolution ICPR model. Finally, we use the ensemble estimates of the mean and covariance of the flood depth for real‐time flood depth forecasting using the physics‐informed Gaussian process regression method. We show that even with few measurements, the proposed framework results in a more accurate forecast than that provided by the mean prediction of the ICPR model.

Kohanpur, Amir H.↗
DOE OSTI2018

Circulating Current Resonant Oscillation in Modular Multilevel Converters for Variable Frequency Operation and Its Suppression Method

This paper studies the phenomenon of resonant oscillation in Modular Multilevel Converters (MMCs) for variable frequency operation. Without proper control, it may easily induce huge MMC inner circulating currents and damage major power devices. A Laplace model is established to clarify the mechanism of resonant oscillation in MMCs, and Bode diagrams are used to study the frequency response over a wide frequency range. Meanwhile, a straightforward resonant suppression method based on circulating current control is used to damp out the resonant condition, and a cross comparison is conducted in terms of system losses, capacitor voltage ripples, and load voltage harmonics with and without the resonant oscillation. Both simulation and experimental results are provided to validate the MMC resonant oscillation theory and its suppression control method.

Modular multilevel converter, resonant oscillation↗
DOE OSTI2024

Multilevel Parareal Algorithm with Averaging for Oscillatory Problems

The present study is an extension of the work done by Peddle, Haut, and Wingate and Haut and Wingate, where a two-level Parareal method with mapping and averaging is examined. The method proposed in this paper is a multilevel Parareal method with arbitrarily many levels, which is not restricted to the two-level case. We give an asymptotic error estimate which reduces to the two-level estimate for the case when only two levels are considered. Introducing more than two levels has important consequences for the averaging procedure, as we choose separate averaging windows for each of the different levels, which is an additional new feature of the present study. The different averaging windows make the proposed method especially appropriate for nonlinear multiscale problems, because we can introduce a level for each intrinsic scale of the problem and adapt the averaging procedure such that we reproduce the behavior of the model on the particular scale resolved by the level. The method is applied to nonlinear differential equations. The nonlinearities can generate a range of frequencies in the problem. The computational cost of the new method is investigated and studied on several examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Scalable hierarchical PDE sampler for generating spatially correlated random fields using nonmatching meshes: Scalable hierarchical PDE sampler using nonmatching meshes

This work describes a domain embedding technique between two nonmatching meshes used for generating realizations of spatially correlated random fields with applications to large-scale sampling-based uncertainty quantification. The goal is to apply the multilevel Monte Carlo (MLMC) method for the quantification of output uncertainties of PDEs with random input coefficients on general and unstructured computational domains. We propose a highly scalable, hierarchical sampling method to generate realizations of a Gaussian random field on a given unstructured mesh by solving a reaction–diffusion PDE with a stochastic right-hand side. The stochastic PDE is discretized using the mixed finite element method on an embedded domain with a structured mesh, and then, the solution is projected onto the unstructured mesh. This work describes implementation details on how to efficiently transfer data from the structured and unstructured meshes at coarse levels, assuming that this can be done efficiently on the finest level. We investigate the efficiency and parallel scalability of the technique for the scalable generation of Gaussian random fields in three dimensions. An application of the MLMC method is presented for quantifying uncertainties of subsurface flow problems. Here, we demonstrate the scalability of the sampling method with nonmatching mesh embedding, coupled with a parallel forward model problem solver, for large-scale 3D MLMC simulations with up to 1.9·109 unknowns.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Scalable Multilevel Uncertainty Quantification Concepts for Extreme-Scale Multiscale Problems

Our work in this project is aimed at making fundamental advances in multilevel and multiscale methods for problems with uncertainties related to flows in porous media. The main thrust of this research is to develop a systematic multiscale, multilevel parallel approaches for problems with uncertainties and use them in the uncertainty quantification. A key emphasis is on problems without an apparent scale separation in space, time, and uncertainty spaces. Multiscale solution methods are currently under active investigation. However, the develop- ment of multiscale methods for problems with uncertainties where the scales and uncertainties are tightly coupled is a research area that is less explored. During this project, we have made some significant contributions to the developments of multiscale methods, the uncertainty quantification for multiscale methods, multiscale model learning, uncertainty quantification in inverse problems, and applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Method of Green’s Potentials for Elliptic PDEs in Domains with Random Apertures

Problems with topological uncertainties appear in many fields ranging from nano-device engineering to the design of bridges. In many of such problems, a part of the domains boundaries is subjected to random perturbations making inefficient conventional schemes that rely on discretization of the whole domain. Here, we study elliptic PDEs in domains with boundaries comprised of a deterministic part and random apertures, and apply the method of modified potentials with Green’s kernels defined on the deterministic part of the domain. This approach allows to reduce the dimension of the original differential problem by reformulating it as a boundary integral equation posed on the random apertures only. The multilevel Monte Carlo method is then applied to this modified integral equation and its optimal ϵ -2 asymptotical complexity is shown. Finally, we provide the qualitative analysis of the proposed technique and support it with numerical results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Using Machine Learning to Discern Eruption in Noisy Environments: A Case Study Using CO2-Driven Cold-Water Geyser in Chimayó, New Mexico

In this paper, we present an approach based on machine learning (ML) to distinguish eruption and precursory signals of Chimayó geyser (New Mexico, U.S.A.) under noisy environmental conditions. This geyser can be considered a natural analog of CO 2 intrusion into shallow water aquifers. By studying this geyser, we can understand upwelling of CO 2 -rich fluids from depth, which has relevance to leak monitoring in a CO 2 sequestration project. ML methods such as random forests (RFs) are known to be robust multiclass classifiers and perform well under unfavorable, noisy conditions. However, the extent of the RF method’s accuracy is poorly understood for this CO 2 -driven geysering application. The current study aims to quantify the performance of RF classifiers to discern the geyser state. Toward this goal, we first present the data collected from the seismometer that is installed near the Chimayó geyser. The seismic signals collected at this site contain different types of noises such as daily temperature variations, animal movement near the geyser, and human activity. First, we filter the signals from these noises by combining the Butterworth high-pass (BH) filter and an autoregressive (AR) method in a multilevel fashion. We show that by combining these filtering techniques in a hierarchical fashion leads to a reduction in noise in the seismic data without removing the precursors and eruption event signals. We then use RF on the filtered data to classify the state of geyser into three classes: remnant noise, precursor, and eruption states. RF classifier is constructed based on the comprehensive features extracted using the Tsfresh Python package. We show that the classification accuracy using RF on the filtered data is greater than 90%. We also evaluate the accuracy of other classical time-series methods such as dynamic time warping (DTW) on filtered data along with RF on partially filtered data in which we remove the daily trends. Classification accuracy shows that DTW performs poorly (44%) and RF on partially filtered data performs decently (87%). Denoising seismic signals from both daily trends and human activity enhances RF classifier performance by 7%. Finally, these aspects make the proposed ML framework attractive for event discrimination and signal enhancement under noisy conditions, with strong potential for application to monitor leaks in CO 2 sequestration.

58 GEOSCIENCES↗