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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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DOE OSTI2021

Multilevel Hierarchical Decomposition of Finite Element White Noise with Application to Multilevel Markov Chain Monte Carlo

In this work we develop a new hierarchical multilevel approach to generate Gaussian random field realizations in an algorithmically scalable manner that is well suited to incorporating into multilevel Markov chain Monte Carlo (MCMC) algorithms. This approach builds off of other partial differential equation (PDE) approaches for generating Gaussian random field realizations; in particular, a single field realization may be formed by solving a reaction-diffusion PDE with a spatial white noise source function as the right-hand side. While these approaches have been explored to accelerate forward uncertainty quantification tasks, e.g., multilevel Monte Carlo, the previous constructions are not directly applicable to multilevel MCMC frameworks which build fine-scale random fields in a hierarchical fashion from coarse-scale random fields. Our new hierarchical multilevel method relies on a hierarchical decomposition of the white noise source function in $L^2$ which allows us to form Gaussian random field realizations across multiple levels of discretization in a way that fits into multilevel MCMC algorithmic frameworks. After presenting our main theoretical results and numerical scaling results to showcase the utility of this new hierarchical PDE method for generating Gaussian random field realizations, this method is tested on a four-level MCMC algorithm to explore its feasibility.

algebraic multigrid↗
DOE OSTI2021

Modeling and Control of Cascaded Bridgeless Multilevel Rectifier Under Unbalanced Load Conditions

The goal of this project is to model and control a novel unidirectional cascaded multilevel bridgeless rectifier as an active front end in medium and high voltage applications. This topology has many advantages over a conventional cascaded H-bridge rectifier, such as lower implementation cost, higher reliability, and greater flexibility with similar power quality.The steady-state mathematical model is used to develop a method for the voltage balancing of dc cells. Power factor analysis is discussed to achieve unity power factor using fully controlled hbridge cells. Power loss, efficiency, and cost comparison studies between the traditional cascaded H-Bridge converter and the proposed bridgeless converter demonstrate the advantages. A novel control strategy is proposed to achieve dc voltage balancing, fast and robust grid synchronization and power factor correction under unbalanced load conditions. Simulation and experimental results validate the models and control method.

Cascaded Bridgeless Rectifier, Power factor analys↗
DOE OSTI2022

Internal Model-Based Active Damping Strategy for a Back-to-Back Modular Multilevel Converter System for Advanced Grid Support: Preprint

The proposed work focuses on the possibility of achieving the reduction in the size of the interfacing filter for the grid connection for a back-to-back modular multilevel converter system with the use of third order LCL filters. To achieve the same attenuation, it is possible to reduce the size of the interfacing filters by the usage of third order filters. However, this kind of filtering comes with the limitation of having sustained oscillations due to lack of damping especially during transient changes. Therefore, in this work, a methodology has been proposed based on the principle of internal model to cater for this unwanted oscillations. The third order system is modeled inside the microcontroller with the damping enabled. The error between the output from the model and the actual are compared and the error is utilized to accomplish the active damping strategy. The proposed architecture is verified via computer simulations based on MATLAB/Simulink domain and various case study results along with their discussion is presented in this paper.

dq control↗
DOE OSTI2024

Cyclable Variable Path Length Multilevel Structures for Lossless Ion Manipulations (SLIM) Platform for Enhanced Ion Mobility Separations

Ion mobility-mass spectrometry (IMS-MS) is increasingly used to analyze complex samples and provide structural information of unknown compounds. As the complexity of samples increases, there is a need to improve the resolution of IMS-MS instruments to increase the rate of molecular identification. In this work, we evaluated a cyclable and variable-pathlength multilevel Structures for Lossless Ion Manipulations (SLIM) platform to achieve a higher resolving power than previously possible. This new multilevel SLIM platform has eight separation levels connected by ion escalators and a path length of ~88 meters (~11 meters per level). Our new multilevel SLIM can also be operated in an ‘ion cycling’ mode where a set of return ion escalators transport ions from the eighth back to the first level, allowing even longer path lengths (and higher IMS resolution). The platform has been improved to enhance the ion transmission and IMS separation quality by reducing the spacing between SLIM boards as well as board thickness, reducing the ions’ escalator residence time. Compared to the previous generation, the new multilevel SLIM demonstrated a better transmission for a set of phosphazene ions, especially for the low-mobility ions. The new multilevel SLIM achieved better resolving powers than our previous 4-level SLIM. The collision cross-section-based resolving power of the SLIM platform was tested using a pair of singly-charged reverse sequence peptides (SDGRG 1+ , GRGDS 1+ ). We achieved 1100 resolving power using 88 meters of path length (i.e., 8 levels) and 1400 following an additional pass through the eight levels (i.e., 16 levels or 173.5 m). The multilevel SLIM was further evaluated to demonstrate the enhanced separation for a positively and negatively charged brain total lipid extract sample. Finally, the new multilevel SLIM enables much higher resolving powers for a wide range of ion mobilities, improved transmission for low-mobility ions, and the ability to perform even higher resolving power for ions of interest.

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

Accelerating multilevel Markov Chain Monte Carlo using machine learning models

Here, this work presents an efficient approach for accelerating multilevel Markov Chain Monte Carlo (MCMC) sampling for large-scale problems using low-fidelity machine learning models. While conventional techniques for large-scale Bayesian inference often substitute computationally expensive high-fidelity models with machine learning models, thereby introducing approximation errors, our approach offers a computationally efficient alternative by augmenting high-fidelity models with low-fidelity ones within a hierarchical framework. The multilevel approach utilizes the low-fidelity machine learning model (MLM) for inexpensive evaluation of proposed samples thereby improving the acceptance of samples by the high-fidelity model. The hierarchy in our multilevel algorithm is derived from geometric multigrid hierarchy. We utilize an MLM to accelerate the coarse level sampling. Training machine learning model for the coarsest level significantly reduces the computational cost associated with generating training data and training the model. We present an MCMC algorithm to accelerate the coarsest level sampling using MLM and account for the approximation error introduced. We provide theoretical proofs of detailed balance and demonstrate that our multilevel approach constitutes a consistent MCMC algorithm. Additionally, we derive the expression for cost reduction due to machine learning model to facilitate cost analysis of the hierarchical sampling algorithm. Our technique is demonstrated on a standard benchmark inference problem in groundwater flow, where we estimate the probability density of a quantity of interest using a four-level MCMC algorithm. Our proposed algorithm accelerates multilevel sampling by a factor of two while achieving similar accuracy compared to sampling using the standard multilevel algorithm.

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

Fast shared-memory streaming multilevel graph partitioning

In this report we show that a fast parallel graph partitioner can benefit many applications by reducing data transfers. The online methods for partitioning graphs have to be fast and they often rely on simple one-pass streaming algorithms, while the offline methods for partitioning graphs contain more involved algorithms and the most successful methods in this category belong to the multilevel approaches. In this work, we assess the feasibility of using streaming graph partitioning algorithms within the multilevel framework. Our end goal is to come up with a fast parallel offline multilevel partitioner that can produce competitive cutsize quality. We rely on a simple but fast and flexible streaming algorithm throughout the entire multilevel framework. This streaming algorithm serves multiple purposes in the partitioning process: a clustering algorithm in the coarsening, an effective algorithm for the initial partitioning, and a fast refinement algorithm in the uncoarsening. Its simple nature also lends itself easily for parallelization. The experiments on various graphs show that our approach is on the average up to 5.1x faster than the multi-threaded MeTiS, which comes at the expense of only 2x worse cutsize.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Multilevel-in-Space-and-Energy CMFD in VERA

For full-core modeling in the Virtual Environment for Reactor Analysis (VERA), the three-dimensional multigroup eigenvalue neutron transport problem is solved by MPACT. To improve the efficiency of MPACT, advancements have been made in the transport accelerator. Multilevel-in-energy and multilevel-in-space coarse mesh finite difference (CMFD) solvers were developed to improve the efficiency of the CMFD accelerator. In this paper a new multilevel-in-space-and-energy CMFD solver is developed with coarsening in both space and energy on every level. Several different strategies are investigated for coarsening groups in energy. Modified V-cycle and multiple-cycle algorithms are evaluated for solving the multilevel equations. The performance of these solvers is compared for typical full-core reactor physics problems.

42 ENGINEERING↗
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 OSTI2021

A Miniature Multilevel Structures for Lossless Ion Manipulations Ion Mobility Spectrometer with Wide Mobility Range Separation Capabilities

Here, ion mobility spectrometry employing structures for lossless ion manipulations (SLIM-IMS) is an attractive gas-phase separation technique due to its ability to achieve unprecedented effective ion path lengths (>1 km) and IMS resolving powers in a small footprint. The emergence of multilevel SLIM technology, where ions are transferred between vertically stacked SLIM electrode surfaces, has subsequently allowed for ultralong single pass path lengths (>40 m) to be achieved, enabling ultrahigh resolution IMS measurements to be performed over the entire mobility range in a single experiment. The implementation of multiple SLIM levels requires very little additional space for the SLIM system, and we developed a miniature SLIM module (miniSLIM) based on multilevel SLIM technology and report the performance here. The module is 11.1 cm x 6.7 cm x 1.4 cm (L x W x H) and consists of three SLIM levels totaling 1-meter path length. Ion trajectory simulations were used to optimize the SLIM board spacings and SLIM board thicknesses of the miniSLIM IMS system. Methods of efficiently transferring ions between SLIM levels were examined and a new approach using asymmetric traveling waves (TWs) was developed and implemented in the miniSLIM. We experimentally characterized the performance of the --meter multilevel miniSLIM IMS-MS relative to a drift tube IM--MS using an Agilent tuning mixture and tetraalkylammonium cations. The 1-meter miniSLIM achieved a resolving power of up to 131 (CCS/ΔCCS), ~1.5x higher than achievable with a 78 cm path length drift tube IMS, and successfully transmitted the entire ion mobility range in a single separation. We also demonstrated the miniSLIM’s performance as a standalone IMS system (i.e., without MS), showing baseline separation between Agilent tuning mixture cations with the full mobility range observed, and a standard peptide mixture with different charge states readily differentiated. Overall the miniSLIM provides a compact alternative to high performance IMS instruments possessing similar path lengths.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Multilevel Spectral Coarsening for Graph Laplacian Problems with Application to Reservoir Simulation

We extend previously developed two-level coarsening procedures for graph Laplacian problems written in a mixed saddle point form to the fully recursive multilevel case. The resulting hierarchy of discretizations gives rise to a hierarchy of upscaled models, in the sense that they provide approximation in the natural norms (in the mixed setting). This property enables us to utilize them in three applications: (i) as an accurate reduced model, (ii) as a tool in multilevel Monte Carlo simulations (in application to finite volume discretizations), and (iii) for providing a sequence of nonlinear operators in a full approximation scheme for solving nonlinear pressure equations discretized by the conservative two-point flux approximation. Finally, we illustrate the potential of the proposed multilevel technique in all three applications on a number of popular benchmark problems used in reservoir simulation.

multilevel Monte Carlo↗
DOE OSTI2021

Theoretical Analysis and Experimental Validation of Flying-Capacitor Multilevel Converters Under Short-Circuit Fault Conditions

Addressing the increasing demand for high- efficiency and high-power-density converters, the flying-capacitor multilevel converter has shown itself as a promising topology. A key advantage of this topology is the reduced voltage rating of the switches, though also makes it vulnerable to device failure during short-circuit conditions. Despite large interest in fault-tolerant operation of these converters, alongside detailed descriptions of flying capacitor balancing, little research has focused on the converter short-circuit fault analysis, which may cause a switch failure if not properly designed for. Therefore, this work presents a comprehensive model describing the large- signal short-circuit switching behavior of a general N -level flying- capacitor multilevel converter. Highly simplified models used to predict the evolution of the switch current and voltage stress during the fault are proposed, targeted at practicing engineers for conservative design guidelines. These models are used to determine the critical time for remedial action of the converter before reaching some predefined maximum conditions. A 2-to-10- level fully-configurable flying-capacitor multilevel converter and a fault circuit hardware prototype are used to experimentally perform different short-circuit tests that show a good match to the measured behavior.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Multilevel Training of Neural Networks

MTNN is a software library for applying multilevel algorithms on training neural networks. Based on PyTorch, it is designed to be an extensible framework to enable researchers to implement multilevel training algorithms on a variety of neural network models. This release includes a culmination of preliminary work in applying the multilevel Full Approximation Scheme technique on fully connected and convolutional neural networks to solve PDE problems (pending publication submission).

Li, Ruipeng↗
DOE OSTI2021

Understanding Multilevel Selection May Facilitate Management of Arbuscular Mycorrhizae in Sustainable Agroecosystems

Studies in natural ecosystems show that adaptation of arbuscular mycorrhizal (AM) fungi and other microbial plant symbionts to local environmental conditions can help ameliorate stress and optimize plant fitness. This local adaptation arises from the process of multilevel selection, which is the simultaneous selection of a hierarchy of groups. Studies of multilevel selection in natural ecosystems may inform the creation of sustainable agroecosystems through developing strategies to effectively manage crop microbiomes including AM symbioses. Field experiments show that the species composition of AM fungal communities varies across environmental gradients, and that the biomass of AM fungi and their benefits for plants generally diminish when fertilization and irrigation eliminate nutrient and water limitations. Furthermore, pathogen protection by mycorrhizas is only important in environments prone to plant damage due to pathogens. Consequently, certain agricultural practices may inadvertently select for less beneficial root symbioses because the conventional agricultural practices of fertilization, irrigation, and use of pesticides can make these symbioses superfluous for optimizing crop performance. The purpose of this paper is to examine how multilevel selection influences the flow of matter, energy, and genetic information through mycorrhizal microbiomes in natural and agricultural ecosystems, and propose testable hypotheses about how mycorrhizae may be actively managed to increase agricultural sustainability.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Scalable multilevel Monte Carlo methods exploiting parallel redistribution on coarse levels

Here, we study an element agglomeration coarsening strategy that requires data redistribution at coarse levels when the number of coarse elements becomes smaller than the number of MPI processes used on the finest level. The overall procedure generates coarse elements (general unstructured unions of fine grid elements) within the framework of element-based algebraic multigrid methods (or AMGe) studied previously. The AMGe-generated coarse spaces have the ability to exhibit approximation properties of the same order as the fine-level spaces since by construction they contain the piecewise polynomials of the same order as on the fine level. These approximation properties are key for the successful use of AMGe in multilevel solvers for nonlinear partial differential equations as well as for multilevel Monte Carlo (MLMC) simulations. The ability to coarsen without being constrained by the number of MPI processes, as described in the present paper, allows to improve the scalability of these solvers as well as the overall MLMC method. The paper illustrates this latter fact with detailed scalability study of MLMC simulations applied to model Darcy equations with a stochastic log-normal permeability field.

AMGe↗
DOE OSTI2023

Optimizing shift selection in multilevel Monte Carlo for disconnected diagrams in lattice QCD

The calculation of disconnected diagram contributions to physical signals is a computationally expensive task in Lattice QCD. To extract the physical signal, the trace of the inverse Lattice Dirac operator, a large sparse matrix, must be stochastically estimated. Because the variance of the stochastic estimator is typically large, variance reduction techniques must be employed. Multilevel Monte Carlo (MLMC) methods reduce the variance of the trace estimator by utilizing a telescoping sequence of estimators. Frequency Splitting is one such method that uses a sequence of inverses of shifted operators to estimate the trace of the inverse lattice Dirac operator, however there is no a priori way to select the shifts that minimize the cost of the multilevel trace estimation. Here we present a sampling and interpolation scheme that is able to predict the variances associated with Frequency Splitting under displacements of the underlying space time lattice. The interpolation scheme is able to predict the variances to high accuracy and therefore chooses shifts that correspond to an approximate minimum of the cost for the trace estimation. We show that Frequency Splitting with the chosen shifts displays significant speedups over multigrid deflation, and that these shifts can be used for multiple configurations within the same ensemble with no penalty to performance.

97 MATHEMATICS AND COMPUTING↗