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All sources NASA NTRS DOE OSTI

DOE OSTI2016

Multilevel sequential Monte Carlo samplers

Here, we study the approximation of expectations w.r.t. probability distributions associated to the solution of partial differential equations (PDEs); this scenario appears routinely in Bayesian inverse problems. In practice, one often has to solve the associated PDE numerically, using, for instance finite element methods and leading to a discretisation bias, with the step-size level h L . In addition, the expectation cannot be computed analytically and one often resorts to Monte Carlo methods. In the context of this problem, it is known that the introduction of the multilevel Monte Carlo (MLMC) method can reduce the amount of computational effort to estimate expectations, for a given level of error. This is achieved via a telescoping identity associated to a Monte Carlo approximation of a sequence of probability distributions with discretisation levels ${\infty}$ >h 0 >h 1 ...>h L . In many practical problems of interest, one cannot achieve an i.i.d. sampling of the associated sequence of probability distributions. A sequential Monte Carlo (SMC) version of the MLMC method is introduced to deal with this problem. In conclusion, it is shown that under appropriate assumptions, the attractive property of a reduction of the amount of computational effort to estimate expectations, for a given level of error, can be maintained within the SMC context.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

NASA NTRS1987

Experiments in encoding multilevel images as quadtrees

Image storage requirements for several encoding methods are investigated and the use of quadtrees with multigray level or multicolor images are explored. The results of encoding a variety of images having up to 256 gray levels using three schemes (full raster, runlength and quadtree) are presented. Although there is considerable literature on the use of quadtrees to store and manipulate binary images, their application to multilevel images is relatively undeveloped. The potential advantage of quadtree encoding is that an entire area with a uniform gray level may be encoded as a unit. A pointerless quadtree encoding scheme is described. Data are presented on the size of the quadtree required to encode selected images and on the relative storage requirements of the three encoding schemes. A segmentation scheme based on the statistical variation of gray levels within a quadtree quadrant is described. This parametric scheme may be used to control the storage required by an encoded image and to preprocess a scene for feature identification. Several sets of black and white and pseudocolor images obtained by varying the segmentation parameter are shown.

Lansing, Donald L.↗

DOE OSTI2013

Multilevel Monte Carlo for two phase flow and Buckley–Leverett transport in random heterogeneous porous media

Monte Carlo (MC) is a well known method for quantifying uncertainty arising for example in subsurface flow problems. Although robust and easy to implement, MC suffers from slow convergence. Extending MC by means of multigrid techniques yields the multilevel Monte Carlo (MLMC) method. MLMC has proven to greatly accelerate MC for several applications including stochastic ordinary differential equations in finance, elliptic stochastic partial differential equations and also hyperbolic problems. In this study, MLMC is combined with a streamline-based solver to assess uncertain two phase flow and Buckley–Leverett transport in random heterogeneous porous media. The performance of MLMC is compared to MC for a two dimensional reservoir with a multi-point Gaussian logarithmic permeability field. The influence of the variance and the correlation length of the logarithmic permeability on the MLMC performance is studied.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

A Multilevel in Space and Energy Solver for 3-D Multigroup Diffusion and Coarse-Mesh Finite Difference Eigenvalue Problems

The Multilevel in Space and Energy Diffusion (MSED) method accelerates the iterative convergence of multigroup diffusion eigenvalue problems by performing work on lower-order equations with only one group and/or coarser spatial grids. It consists of two primary components: (1) a grey (one-group) diffusion eigenvalue problem that is solved via Wielandt-shifted power iteration (PI) and (2) a multigrid-in-space linear solver. In previous work, the efficiency of MSED was verified using Fourier analysis and numerical results from a one-dimensional multigroup diffusion code. Since that work, MSED has been implemented as a solver for the coarse-mesh finite difference (CMFD) system in the three-dimensional Michigan Parallel Characteristics Transport (MPACT) code. In this paper, the results from the implementation of MSED in MPACT are introduced, and the changes needed to make MSED more suitable for MPACT are described. For problems without feedback, the conclusions in this paper show that MSED can reduce the CMFD run time by an order of magnitude and the overall run time by a factor of 2 to 3 compared to the default CMFD solver in MPACT [PI with the generalized minimal residual (GMRES) method]. For problems with feedback, the convergence of the outer Picard iteration scheme is worsened by the well-converged CMFD solutions produced by the standard MSED method. To overcome this unintuitive deficiency, MSED may be run with looser convergence criteria (a modified version of the MSED method called MSED-L) to circumvent the issue until the multiphysics iteration in MPACT is improved. Results show that MSED-L can reduce the CMFD run time in MPACT by an order of magnitude, without negatively impacting the outer Picard iteration scheme.

3-D↗

DOE OSTI2026

Two-Level System Spectroscopy from Correlated Multilevel Relaxation in Superconducting Qubits

Transmon qubits are a cornerstone of modern superconducting quantum computing platforms. Temporal fluctuations of energy relaxation in these qubits are widely attributed to microscopic two-level systems (TLSs) in device dielectrics and interfaces, yet isolating individual defects typically relies on tuning the qubit or the TLS into resonance. We demonstrate a novel spectroscopy method for fixed-frequency transmons based on multilevel relaxation: repeated preparation of the second excited state and simultaneous $T_1$ extraction of the first and second excited states reveals characteristic correlations in the decay rates of adjacent transitions. From these correlations we identify one or more dominant TLSs and reconstruct their frequency drift over time. Remarkably, we find that TLSs detuned by $\gtrsim 100\,\mathrm{MHz}$ from the qubit transition can still significantly influence relaxation. The proposed method provides a powerful tool for TLS spectroscopy without the need to tune the transmon frequency, either via a flux-tunable inductor or AC-Stark shifts.

Roy, Tanay [Fermilab] (ORCID:000000019442862X)↗

DOE OSTI2014

Dynamic implicit 3D adaptive mesh refinement for non-equilibrium radiation diffusion

The time dependent non-equilibrium radiation diffusion equations are important for solving the transport of energy through radiation in optically thick regimes and find applications in several fields including astrophysics and inertial confinement fusion. The associated initial boundary value problems that are encountered often exhibit a wide range of scales in space and time and are extremely challenging to solve. To efficiently and accurately simulate these systems we describe our research on combining techniques that will also find use more broadly for long term time integration of nonlinear multi-physics systems: implicit time integration for efficient long term time integration of stiff multi-physics systems, local control theory based step size control to minimize the required global number of time steps while controlling accuracy, dynamic 3D adaptive mesh refinement (AMR) to minimize memory and computational costs, Jacobian Free Newton–Krylov methods on AMR grids for efficient nonlinear solution, and optimal multilevel preconditioner components that provide level independent solver convergence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Evaluating Linear Ion Trap for MS3-Based Multiplexed Single-Cell Proteomics

There is a growing demand to develop high-throughput and high-sensitivity mass spectrometry methods for single-cell proteomics. The commonly used isobaric labeling-based multiplexed single-cell proteomics approach suffers from distorted protein quantification due to co-isolated interfering ions during MS/MS fragmentation, also known as ratio compression. We reasoned that the use of MS3-based quantification could mitigate ratio compression and provide better quantification. However, previous studies indicated reduced proteome coverages in the MS3 method, likely due to long duty cycle time and ion losses during multilevel ion selection and fragmentation. Here, in this paper, we described an improved MS acquisition method for MS3-based single-cell proteomics by employing a linear ion trap to measure reporter ions. We demonstrated that linear ion trap can increase the proteome coverages for single-cell-level peptides with even higher gain obtained via the MS3 method. The optimized real-time search MS3 method was further applied to study the immune activation of single macrophages. Among a total of 126 single cells studied, over 1200 and 1000 proteins were quantifiable when at least 50 and 75% nonmissing data were required, respectively. Our evaluation also revealed several limitations of the low-resolution ion trap detector for multiplexed single-cell proteomics and suggested experimental solutions to minimize their impacts on single-cell analysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1976

A lateral boundary formulation for multi-level prediction models

A method is proposed for treating the lateral boundaries of a limited-area weather prediction model. The method involves the relaxation of the interior flow in the vicinity of the boundary to the external fully prescribed flow. Analytical and numerical results obtained with a linearized multilevel model confirm the effectiveness of this computationally effective method. The method is shown to give an adequate representation of outgoing gravity waves with and without an ambient shear flow and to allow the substantially undistorted transmission of geostrophically balanced flow out of the interior of the limited domain.

Davies, H. C.↗

DOE OSTI2023

A Refinement-by-Superposition -Method for (curl)- and (div)-Conforming Discretizations

Here, we present refinement-by-superposition (RBS) hp-refinement infrastructure for computational electromagnetics (CEMs), which permits exponential rates of convergence. In contrast to dominant approaches to hp-refinement for continuous Galerkin methods, which rely on explicit constraint equations, the multilevel strategy presented drastically reduces the implementation complexity. Through the RBS methodology, enforcement of continuity occurs by construction, enabling arbitrary levels of refinement with ease, and without the practical (but not theoretical) limitations of constrained-node refinement. We outline the construction of the RBS hp-method for refinement with H (curl)- and H (div)-conforming finite cells. Numerical simulations for the 2-D finite element method (FEM) solution of the Maxwell eigenvalue problem demonstrate the effectiveness of RBS hp-refinement. As an additional goal of this work, we aim to promote the use of mixed-order (low- and high-order) elements in practical CEM applications.

42 ENGINEERING↗

NASA NTRS1976

Laser induced fluorescence applied to turbulent reacting flows

The saturated fluorescence method makes use of the great simplifications which occur when under conditions of intense radiation the excitation process becomes saturated. A description is presented of the saturated fluorescence method, taking into account rate equations and saturation, radiative transfer, the two-level system, a multilevel system, and measurements under saturation conditions. The detectability limits of the method are investigated. Fluorescence trapping is found to place an upper limit on the number density of the fluorescing species that can be measured without signal loss. Turbulence places time and spatial constraints on the measurements, but otherwise poses no difficulties. Saturated laser induced fluorescence spectroscopy appears to be a most promising method for measuring species concentrations in flames.

Daily, J. W.↗

NASA NTRS1974

Multilevel control optimization using subsystem relative performance index sensitivity

A method is presented for the design of optimal feedback controllers for large multivariable systems with subsystem sensitivity constraints. The weighted sum of subsystem and/or operational mode relative performance index sensitivities is defined as the overall performance index. The method is developed for linear systems with quadratic performance criteria and either full or partial state feedback. An example concerning the design of a stability augmentation system for a VTOL aircraft in the transition mode demonstrates the effectiveness of the design method.

Leininger, G. G.↗

DOE OSTI2022

Graph coarsening: from scientific computing to machine learning

Abstract The general method of graph coarsening or graph reduction has been a remarkably useful and ubiquitous tool in scientific computing and it is now just starting to have a similar impact in machine learning. The goal of this paper is to take a broad look into coarsening techniques that have been successfully deployed in scientific computing and see how similar principles are finding their way in more recent applications related to machine learning. In scientific computing, coarsening plays a central role in algebraic multigrid methods as well as the related class of multilevel incomplete LU factorizations. In machine learning, graph coarsening goes under various names, e.g., graph downsampling or graph reduction. Its goal in most cases is to replace some original graph by one which has fewer nodes, but whose structure and characteristics are similar to those of the original graph. As will be seen, a common strategy in these methods is to rely on spectral properties to define the coarse graph.

Chen, Jie↗

DOE OSTI2024

Performance of explicit and IMEX MRI multirate methods on complex reactive flow problems within modern parallel adaptive structured grid frameworks

Large-scale multiphysics simulations are computationally challenging due to the coupling of multiple processes with widely disparate time scales. The advent of exascale computing systems exacerbates these challenges since these systems enable ever-increasing size and complexity. In recent years, there has been renewed interest in developing multirate methods as a means to handle the large range of time scales, as these methods may afford greater accuracy and efficiency than more traditional approaches of using implicit-explicit (IMEX) and low-order operator splitting schemes. However, to date there have been few performance studies that compare different classes of multirate integrators on complex application problems. In this work, we study the performance of several newly developed multirate infinitesimal (MRI) methods, implemented in the SUNDIALS solver package, on two reacting flow model problems built on structured mesh frameworks. The first model revisits prior work on a compressible reacting flow problem with complex chemistry that is implemented using BoxLib but where we now include comparisons between a new explicit MRI scheme with the multirate spectral deferred correction (SDC) methods in the original paper. The second problem uses the same complex chemistry as the first problem, combined with a simplified flow model, but runs at a large spatial scale where explicit methods become infeasible due to stability constraints. Two recently developed IMEX MRI multirate methods are tested. These methods rely on advanced features of the AMReX framework on which the model is built, such as multilevel grids and multilevel preconditioners. The results from these two problems show that MRI multirate methods can offer significant performance benefits on complex multiphysics application problems and that these methods may be combined with advanced spatial discretization to compound the advantages of both.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1991

A parallel algorithm for multi-level logic synthesis using the transduction method

The Transduction Method has been shown to be a powerful tool in the optimization of multilevel networks. Many tools such as the SYLON synthesis system (X90), (CM89), (LM90) have been developed based on this method. A parallel implementation is presented of SYLON-XTRANS (XM89) on an eight processor Encore Multimax shared memory multiprocessor. It minimizes multilevel networks consisting of simple gates through parallel pruning, gate substitution, gate merging, generalized gate substitution, and gate input reduction. This implementation, called Parallel TRANSduction (PTRANS), also uses partitioning to break large circuits up and performs inter- and intra-partition dynamic load balancing. With this, good speedups and high processor efficiencies are achievable without sacrificing the resulting circuit quality.

Lim, Chieng-Fai↗

NASA NTRS1976

Decentralization, stabilization, and estimation of large-scale linear systems

In this short paper we consider three closely related aspects of large-scale systems: decentralization, stabilization, and estimation. A method is proposed to decompose a large linear system into a number of interconnected subsystems with decentralized (scalar) inputs or outputs. The procedure is preliminary to the hierarchic stabilization and estimation of linear systems and is performed on the subsystem level. A multilevel control scheme based upon the decomposition-aggregation method is developed for stabilization of input-decentralized linear systems Local linear feedback controllers are used to stabilize each decoupled subsystem, while global linear feedback controllers are utilized to minimize the coupling effect among the subsystems. Systems stabilized by the method have a tolerance to a wide class of nonlinearities in subsystem coupling and high reliability with respect to structural perturbations. The proposed output-decentralization and stabilization schemes can be used directly to construct asymptotic state estimators for large linear systems on the subsystem level. The problem of dimensionality is resolved by constructing a number of low-order estimators, thus avoiding a design of a single estimator for the overall system.

Siljak, D. D.↗

DOE OSTI2017

Efficient Scalable Parallel Higher Order Direct MoM-SIE Method With Hierarchically Semiseparable Structures for 3-D Scattering

A novel fast scalable parallel algorithm is proposed for the solution of large 3-D scattering problems based on: 1) the double (geometrical and current-approximation) higher order (DHO) method of moments (MoM) in the surface integral equation (SIE) formulation and 2) a direct solver for dense linear systems utilizing hierarchically semiseparable (HSS) structures. Namely, an HSS matrix representation is used for compression, factorization, and solution of the system matrix. In addition, a rank-revealing QR decomposition for memory compression is used, with a stopping criterion in terms of the relative rank tolerance value. One method for geometrical preprocessing of the scatterers based on the cobblestone distance sorting technique is employed in order to enhance the HSS algorithm accuracy and parallelization. Numerical examples show how the accuracy of the DHO HSS-MoM-SIE method is easily controllable by using the relative tolerance for the matrix compression. Furthermore, the examples demonstrate low memory consumption, as well as much faster simulation time, when compared to the direct LU decomposition. The method enables dramatically faster monostatic scattering computations than iterative solvers and reduced number of unknowns when compared to low-order discretizations. Finally, great scalability of the algorithm is demonstrated on more than one thousand processes.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Lifting MGARD: Construction of (pre)wavelets on the interval using polynomial predictors of arbitrary order

MGARD (MultiGrid Adaptive Reduction of Data) is an algorithm for compressing and refactoring scientific data, based on the theory of multigrid methods. The core algorithm is built around stable multilevel decompositions of conforming piecewise linear $C^0$ finite element spaces, enabling accurate error control in various norms and derived quantities of interest. In this work, we extend this construction to arbitrary order Lagrange finite elements $\mathbb{Q}_p$, $p \geq 0$, and propose a reformulation of the algorithm as a lifting scheme with polynomial predictors of arbitrary order. Additionally, a new formulation using a compactly supported wavelet basis is discussed, and an explicit construction of the proposed wavelet transform for uniform dyadic grids is described.

Reshniak, Viktor [Oak Ridge National Laboratory (O↗

NASA NTRS1977

The application of satellite data in monitoring strip mines

Strip mines in the New River Drainage Basin of Tennessee were studied through use of Landsat-1 imagery and aircraft photography. A multilevel analysis, involving conventional photo interpretation techniques, densitometric methods, multispectral analysis and statistical testing was applied to the data. The Landsat imagery proved adequate for monitoring large-scale change resulting from active mining and land-reclamation projects. However, the spatial resolution of the satellite imagery rendered it inadequate for assessment of many smaller strip mines, in the region which may be as small as a few hectares.

Sharber, L. A.↗