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DOE OSTI2024

MatRIS: Addressing the Challenges for Portability and Heterogeneity Using Tasking for Matrix Decomposition (Cholesky)

The ubiquitous in-node heterogeneity of HPC and cloud computing platforms makes software portability and performance optimization extremely challenging. Described here, the MatRIS multilevel math library abstraction framework employs tasking to alleviate these difficulties. MatRIS includes the IRIS task-based runtime on the bottom level and exposes different layers of abstraction to render algorithms architecturally agnostic. MatRIS ensures the decomposition and creation of tasks that represent the necessary encapsulation of the optimized kernels from both vendor and open-source math libraries. Once built, MatRIS can select different combinations of accelerators at runtime, making it portable even on diverse heterogeneous architectures. By leveraging the IRIS runtime’s features for managing heterogeneity, MatRIS deploys algorithms that remove the need to specify orchestration and data transfer. This study describes how the serial task abstraction of a tiled Cholesky factorization is made portable and scalable in the case of multi-device and multi-vendor heterogeneity on a node with NVIDIA and AMD GPUs by using MatRIS. First, we demonstrate that Cholesky in MatRIS provides multi-GPU scalability that offers competitive performance versus cuSolverMG. Then, we present the challenges and opportunities for heterogeneous execution.

Monil, M. A. H.↗

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 OSTI2016

Toward an optimal online checkpoint solution under a two-level HPC checkpoint model

The traditional single-level checkpointing method suffers from significant overhead on large-scale platforms. Hence, multilevel checkpointing protocols have been studied extensively in recent years. The multilevel checkpoint approach allows different levels of checkpoints to be set (each with different checkpoint overheads and recovery abilities), in order to further improve the fault tolerance performance of extreme-scale HPC applications. How to optimize the checkpoint intervals for each level, however, is an extremely difficult problem. In this paper, we construct an easy-to-use two-level checkpoint model. Checkpoint level 1 deals with errors with low checkpoint/recovery overheads such as transient memory errors, while checkpoint level 2 deals with hardware crashes such as node failures. Compared with previous optimization work, our new optimal checkpoint solution offers two improvements: (1) it is an online solution without requiring knowledge of the job length in advance, and (2) it shows that periodic patterns are optimal and determines the best pattern. We evaluate the proposed solution and compare it with the most up-to-date related approaches on an extreme-scale simulation testbed constructed based on a real HPC application execution. Simulation results show that our proposed solution outperforms other optimized solutions and can improve the performance significantly in some cases. Specifically, with the new solution the wall-clock time can be reduced by up to 25.3% over that of other state-of-the-art approaches. Lastly, a brute-force comparison with all possible patterns shows that our solution is always within 1% of the best pattern in the experiments.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Multi-output multilevel best linear unbiased estimators via semidefinite programming

Multifidelity forward uncertainty quantification (UQ) problems often involve multiple quantities of interest and heterogeneous models (e.g., different grids, equations, dimensions, physics, surrogate and reduced-order models). While computational efficiency is key in this context, multi-output strategies in multilevel/multifidelity methods are either sub-optimal or non-existent. In this paper we extend multilevel best linear unbiased estimators (MLBLUE) to multi-output forward UQ problems and we present new semidefinite programming formulations for their optimal setup. Not only do these formulations yield the optimal number of samples required, but also the optimal selection of low-fidelity models to use. While existing MLBLUE approaches are single-output only and require a non-trivial nonlinear optimization procedure, the new multi-output formulations can be solved reliably and efficiently. Here, we demonstrate the efficacy of the new methods and formulations in practical UQ problems with model heterogeneity.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

A Generic Two-Vector Model Predictive Control for Hybrid Multilevel Converters

In this article, a generic two-vector model predictive control (TV-MPC) strategy is proposed for the hybrid multilevel converters (HMCs). The proposed method selects two optimal voltage vectors among all the vector candidates using a geometric positioning approach to reduce the computational burden, which is a common issue in the existing MPC methods for HMC. Then duty cycles of the two selected vectors are optimized to minimize the current tracking error, such that the current tracking performance can be enhanced compared with the conventional MPC. In addition, the voltages of the floating dc capacitors can be balanced by evaluating all switching sequences that belong to the optimal voltage vectors with optimal duty cycles. Here, the concept of the proposed TV-MPC is generic and applicable for any HMCs. A typical HMC based on active neutral-point-clamped topology is adopted as a case study in this work. Comprehensive simulation and experimental studies are performed on an all silicon-carbide HMC prototype to validate the effectiveness of the proposed control scheme.

42 ENGINEERING↗

DOE OSTI2016

A resettable in-line particle concentrator using AC electrokinetics for distributed monitoring of microalgae in source waters

Green algae have been studied as an important and effective biomarker to indicate water quality due to their sensitivity to toxic agents in freshwater sources. But, conventional methods to monitor algal physiology use a chlorophyll fluorometer whose use is hampered by high-cost, large footprint, and limited sensitivity for practical samples containing low algal concentration. In order to overcome these constraints, we developed a multi-level electrode platform for resettable trapping of algae via AC electro-osmosis (ACEO) and negative dielectrophoresis. Preliminary experiments were performed in freshwater with conductivity of 0.02 S/m. Algal trapping was demonstrated at a low voltage of 2 V. The concentration effect was experimentally verified by measuring the fluorescence intensity of algae and using hemocytometer counting chambers at the inlet and outlet of the multilevel microchannel lab-on-a-chip. An optimal frequency was found for trapping, which agrees with the frequency dependence of ACEO flow velocity. Through-flow rate and electrode dimensions were optimized as well. Trapping efficiencies within the range of 26% - 65% have been obtained. A maximum trapping rate of 182 cells/s was obtained with a flow rate of 20 l/min. Our lab-on-a-chip shows high potential for improving the limit of detection in algal monitoring and enabling the development of a portable, integrated and automated system for monitoring the quality of source drinking waters.

30 DIRECT ENERGY CONVERSION↗

DOE OSTI2016

Using a derivative-free optimization method for multiple solutions of inverse transport problems

Identifying unknown components of an object that emits radiation is an important problem for national and global security. Radiation signatures measured from an object of interest can be used to infer object parameter values that are not known. This problem is called an inverse transport problem. An inverse transport problem may have multiple solutions and the most widely used approach for its solution is an iterative optimization method. This paper proposes a stochastic derivative-free global optimization algorithm to find multiple solutions of inverse transport problems. The algorithm is an extension of a multilevel single linkage (MLSL) method where a mesh adaptive direct search (MADS) algorithm is incorporated into the local phase. Furthermore, numerical test cases using uncollided fluxes of discrete gamma-ray lines are presented to show the performance of this new algorithm.

42 ENGINEERING↗

DOE OSTI2014

Multilevel Monte Carlo simulation of Coulomb collisions

We present a new, for plasma physics, highly efficient multilevel Monte Carlo numerical method for simulating Coulomb collisions. The method separates and optimally minimizes the finite-timestep and finite-sampling errors inherent in the Langevin representation of the Landau–Fokker–Planck equation. It does so by combining multiple solutions to the underlying equations with varying numbers of timesteps. For a desired level of accuracy ε, the computational cost of the method is O(ε{sup −2}) or O(ε{sup −2}(lnε){sup 2}), depending on the underlying discretization, Milstein or Euler–Maruyama respectively. This is to be contrasted with a cost of O(ε{sup −3}) for direct simulation Monte Carlo or binary collision methods. We successfully demonstrate the method with a classic beam diffusion test case in 2D, making use of the Lévy area approximation for the correlated Milstein cross terms, and generating a computational saving of a factor of 100 for ε=10{sup −5}. We discuss the importance of the method for problems in which collisions constitute the computational rate limiting step, and its limitations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

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 OSTI2017

Multilevel Particle Filters

In this paper the filtering of partially observed diffusions, with discrete-time observations, is considered. It is assumed that only biased approximations of the diffusion can be obtained for choice of an accuracy parameter indexed by l. A multilevel estimator is proposed consisting of a telescopic sum of increment estimators associated to the successive levels. Additionally, the work associated to $\mathcal{O}(\varepsilon^2)$ mean-squared error between the multilevel estimator and average with respect to the filtering distribution is shown to scale optimally, for example, as $\mathcal{O}(\varepsilon^{-2})$ for optimal rates of convergence of the underlying diffusion approximation. The method is illustrated with some toy examples as well as estimation of interest rate based on real S&P 500 stock price data.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Multilevel techniques for compression and reduction of scientific data—the univariate case

We present a multilevel technique for the compression and reduction of univariate data and give an optimal complexity algorithm for its implementation. A hierarchical scheme offers the flexibility to produce multiple levels of partial decompression of the data so that each user can work with a reduced representation that requires minimal storage whilst achieving the required level of tolerance. The algorithm is applied to the case of turbulence modelling in which the datasets are traditionally not only extremely large but inherently non-smooth and, as such, rather resistant to compression. Here, we decompress the data for a range of relative errors, carry out the usual analysis procedures for turbulent data, and compare the results of the analysis on the reduced datasets to the results that would be obtained on the full dataset. The results obtained demonstrate the promise of multilevel compression techniques for the reduction of data arising from large scale simulations of complex phenomena such as turbulence modelling.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Newmark local time stepping on high-performance computing architectures

In multi-scale complex media, finite element meshes often require areas of local refinement, creating small elements that can dramatically reduce the global time-step for wave-propagation problems due to the CFL condition. Local time stepping (LTS) algorithms allow an explicit time-stepping scheme to adapt the time-step to the element size, allowing near-optimal time-steps everywhere in the mesh. We develop an efficient multilevel LTS-Newmark scheme and implement it in a widely used continuous finite element seismic wave-propagation package. In particular, we extend the standard LTS formulation with adaptations to continuous finite element methods that can be implemented very efficiently with very strong element-size contrasts (more than 100x). Capable of running on large CPU and GPU clusters, we present both synthetic validation examples and large scale, realistic application examples to demonstrate the performance and applicability of the method and implementation on thousands of CPU cores and hundreds of GPUs.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

World’s First Vertical GaN based High Power (200 kW) Multi-level Traction Electric Drive Design

Vertical GaN (vGaN) technology leverages a fully conductive 3D semiconductor structure, enabling superior power density compared to GaN-on-Si and other wide bandgap devices. It offers a pathway to surpass cost and efficiency limitations of Si and SiC devices in traction applications. However, scaling for high-voltage, high-power systems remains challenging. This paper presents the design of an 800V, 200kW traction inverter utilizing vertical GaN devices. The inverter achieves ultra-high efficiency (> 99.5%) through advanced power module integration and employs multilevel neutral-point-less X-type (NPL.X) inverter topology to ensure optimal traction drive system performance. These innovations demonstrate the potential of vGaN for nextgeneration electric propulsion systems.

Alam, Khorshed [General Motors LLC, Detroit, MI (U↗

DOE OSTI2018

Smart Grid-Enabled CVR: An Advanced Application for Distribution Management Systems

A multilevel, multitasking smart grid-enabled conservation of voltage reduction (CVR) control and optimization methodology is proposed for advanced distribution management system (ADMS) platforms. The first level deals with the centralized optimization of volt/VAR optimization (VVO) devices; the second-level is for voltage control in the local domain or decentralized control; and the third level assesses the energy savings and CVR factor.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2020

Capacitor Voltage Ripple Estimation and Optimal Sizing of Modular Multi-Level Converters for Variable-Speed Drives

This article deals with the sizing of submodule capacitors for modular multilevel converters (MMCs) used for variable speed drives for medium voltage and high voltage electric machines. Variable speed drives are required to run over a wide frequency range from zero to a few hundred Hz or even over 1 kHz. Under low frequency operation (<30 Hz), a large current ripple flowing through the MMC submodule capacitors will cause significant capacitor voltage fluctuation. This article proposes an optimal submodule capacitor selection method based on the common-mode voltage injection. The proposed sizing model includes two functions: 1) accurately estimating the capacitor voltage ripple based on the drive system parameters; and 2) identifying the minimum capacitance of the submodule capacitors based on the allowed maximum capacitor voltage fluctuations. Simulation and experimental results show that the error between the actual and estimated values of the voltage fluctuation is within 3% using the proposed model.

42 ENGINEERING↗

DOE OSTI2019

Multifidelity Uncertainty Quantification with Applications in Wind Turbine Aerodynamics: Preprint

The propagation of input uncertainty through engineering models allows designers to better understand the range of possible outcomes resulting from design decisions. This could lead to greater trust between modelers and stakeholders in the wind energy industry. In this study, we apply multilevel-multifidelity Monte Carlo sampling to flow over an airfoil, assuming uncertainty in the inflow conditions, and characterize the associated computational savings compared to standard Monte Carlo approaches. The truth model is provided by an airfoil simulation with a very fine computational time step, and auxiliary lower-level models are provided by simulations with coarser time steps. Reynolds-averaged Navier Stokes and detached eddy simulations are used to obtain two different model fidelities. The primary quantity of interest for this analysis is the lift force, which is examined for a range of angles of attack. We launch an initial set of 'trial' samples to determine the optimal allocation of model evaluations, and these trial evaluations are used to inform a larger sampling effort. Using the multilevel-multifidelity approach, we achieve roughly an order of magnitude variance reduction in expected lift as compared to the standard Monte Carlo approach with an equivalent computational cost.

17 WIND ENERGY↗

DOE OSTI2023

Suppressing Structural Relaxation in Nanoscale Antimony to Enable Ultralow‐Drift Phase‐Change Memory Applications

Abstract Phase‐change random‐access memory (PCRAM) devices suffer from pronounced resistance drift originating from considerable structural relaxation of phase‐change materials (PCMs), which hinders current developments of high‐capacity memory and high‐parallelism computing that both need reliable multibit programming. This work realizes that compositional simplification and geometrical miniaturization of traditional GeSbTe‐like PCMs are feasible routes to suppress relaxation. While to date, the aging mechanisms of the simplest PCM, Sb, at nanoscale, have not yet been unveiled. Here, this work demonstrates that in an optimal thickness of only 4 nm, the thin Sb film can enable a precise multilevel programming with ultralow resistance drift coefficients, in a regime of ≈10 −4 –10 −3 . This advancement is mainly owed to the slightly changed Peierls distortion in Sb and the less‐distorted octahedral‐like atomic configurations across the Sb/SiO 2 interfaces. This work highlights a new indispensable approach, interfacial regulation of nanoscale PCMs, for pursuing ultimately reliable resistance control in aggressively‐miniaturized PCRAM devices, to boost the storage and computing efficiencies substantially.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Operation Optimization using Reinforcement Learning with Integrated Artificial Reasoning Framework

In large and complex systems, operational decision-making requires a systematic analysis with a vast amount of data from both process parameters and component status monitoring. In this paper, we present an integrated artificial reasoning approach for system state transition models that can help operational decision-making with explainable and traceable reasoning. The integrated artificial reasoning framework is a physics-based approach of defining the system structure in a Bayesian network, so we leveraged it in a Markov decision process (MDP) for finding optimal operational solutions. In our proposed framework, the MDP is implemented on a dynamic Bayesian network (DBN), which represents causalities in a system. The multilevel flow modeling was utilized in order to extract these causalities in a more efficient and objective manner. Since multilevel flow modeling is based on the fundamental energy and mass conservation laws, the target system is decomposed into several mass, energy, and information structures, which serve as the basis for a DBN. The MDP consists of the processes of finding a solution for the Bellman equation, which can be derived from the conditional probability equations of the constructed DBN. System operators can capture stochastic system dynamics as multiple subsystem state transitions based on their physical relations and uncertainties coming from the component degradation process or random failures. We analyzed a simplified example system to illustrate finding an optimal operational policy with this approach.

99 GENERAL AND MISCELLANEOUS↗