Complex imaging of phase domains by deep neural networks
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Wu, Longlong↗
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Results for “Iterative methods”
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MO-A-BRD-02: Noise Suppression for Dual-Energy CT Through Entropy Minimization
Purpose: In dual energy CT (DECT), noise amplification during signal decomposition significantly limits the utility of basis material images. Since clinically relevant objects contain a limited number of materials, we propose to suppress noise in decomposed images through entropy minimization within a 2D transformation space. Distinct from other noise suppression techniques, the entropy minimization method does not estimate and suppress noise based on spatial variations of signals and thus maximally preserves image spatial resolution. Methods: From decomposed images, we first generate a 2D plot of scattered data points, using basis material densities as coordinates. Data points representing the same material generate a cluster with a highly asymmetric shape. We orient an axis by minimizing the entropy in a 1D histogram of these points projected onto the axis. To suppress noise, we replace the pixel values of decomposed images with center-of-mass values in the direction perpendicular to the optimized axis. The proposed method's performance is assessed using a Catphan 600 phantom and an anthropomorphic head phantom. Electron density calculations are used to quantify its accuracy. Our results are compared to those without noise suppression, with a filtering method, and with a recently developed iterative method. Results: On both phantoms, the proposed method reduces noise standard deviations of the decomposed images by at least on order of magnitude. In the Catphan study, this method retains the spatial resolution of the CT images and increases the accuracy of electron density calculations. In the head phantom study, the proposed method outperforms the others in retaining fine, intricate structures. Conclusion: This work shows that the proposed method of noise suppression through entropy minimization for DECT suppresses noise without loss of spatial resolution while increasing electron density calculation accuracy. Future investigations will analyze possible bias and incorporate spatial information into the technique for further noise reduction. The work is partially supported by the NIH under the grant number R21EB012700.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Airy function approach and Numerov method to study the anharmonic oscillator potentials V(x) = Ax{sup 2α} + Bx{sup 2}
The numerical solutions of the time independent Schrödinger equation of different one-dimensional potentials forms are sometime achieved by the asymptotic iteration method. Its importance appears, for example, on its efficiency to describe vibrational system in quantum mechanics. In this paper, the Airy function approach and the Numerov method have been used and presented to study the oscillator anharmonic potential V(x) = Ax{sup 2α} + Bx{sup 2}, (A>0, B<0), with (α = 2) for quadratic, (α =3) for sextic and (α =4) for octic anharmonic oscillators. The Airy function approach is based on the replacement of the real potential V(x) by a piecewise-linear potential v(x), while, the Numerov method is based on the discretization of the wave function on the x-axis. The first energies levels have been calculated and the wave functions for the sextic system have been evaluated. These specific values are unlimited by the magnitude of A, B and α. It’s found that the obtained results are in good agreement with the previous results obtained by the asymptotic iteration method for α =3.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Performance of asynchronous optimized Schwarz with one-sided communication
In asynchronous iterative methods on distributed-memory computers, processes update their local solutions using data from other processes without an implicit or explicit global synchronization that corresponds to advancing the global iteration counter. Here in this work, we test the asynchronous optimized Schwarz domain-decomposition iterative method using various one-sided (remote direct memory access) communication schemes with passive target completion. The results show that when one-sided communication is well-supported, the asynchronous version of optimized Schwarz can outperform the synchronous version even for perfectly balanced partitionings of the problem on a supercomputer with uniform nodes.
97 MATHEMATICS AND COMPUTING↗
Enhancement of flow measurements using fluid-dynamic constraints
Novel experimental modalities acquire spatially resolved velocity measurements for steady state and transient flows which are of interest for engineering and biological applications. One of the drawbacks of such high resolution velocity data is their susceptibility to measurement errors. In this paper, we propose a novel filtering strategy that allows enhancement of the noisy measurements to obtain reconstruction of smooth divergence free velocity and corresponding pressure fields which together approximately comply to a prescribed flow model. The main step in our approach consists of the appropriate use of the velocity measurements in the design of a linearized flow model which can be shown to be well-posed and consistent with the true velocity and pressure fields up to measurement and modeling errors. The reconstruction procedure is then formulated as an optimal control problem for this linearized flow model. The resulting filter has analyzable smoothing and approximation properties. We briefly discuss the discretization of the approach by finite element methods and comment on the efficient solution by iterative methods. The capability of the proposed filter to significantly reduce data noise is demonstrated by numerical tests including the application to experimental data. In addition, we compare with other methods like smoothing and solenoidal filtering.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Robust parallel iterative solvers for linear and least-squares problems (Final Technical Report)
The primary goal of this project is to study and develop robust iterative methods for solving linear systems of equations and least squares systems. The focus of the Minnesota team is on algorithms development, robustness issues, and on tests and validation of the methods on realistic problems. 1. The project begun with an investigation on how to practically update a preconditioner obtained from an ILU-type factorization, when the coefficient matrix changes. 2. We investigated strategies to improve robustness in parallel preconditioners in a specific case of a PDE with discontinuous coefficients. 3. We explored ways to adapt standard preconditioners for solving linear systems arising from the Helmholtz equation. These are often difficult linear systems to solve by iterative methods. 4. We have also worked on purely theoretical issues related to the analysis of Krylov subspace methods for linear systems. 5. We developed an effective strategy for performing ILU factorizations for the case when the matrix is highly indefinite. The strategy uses shifting in some optimal way. The method was extended to the solution of Helmholtz equations by using complex shifts, yielding very good results in many cases. 6. We addressed the difficult problem of preconditioning sparse systems of equations on GPUs. 7. A by-product of the above work is a software package consisting of an iterative solver library for GPUs based on CUDA. This was made publicly available. It was the first such library that offers complete iterative solvers for GPUs. 8. We considered another form of ILU which blends coarsening techniques from Multigrid with algebraic multilevel methods. 9. We have released a new version on our parallel solver - called pARMS [new version is version 3]. As part of this we have tested the code in complex settings - including the solution of Maxwell and Helmholtz equations and for a problem of crystal growth.10. As an application of polynomial preconditioning we considered the problem of evaluating f(A)v which arises in statistical sampling. 11. As an application to the methods we developed, we tackled the problem of computing the diagonal of the inverse of a matrix. This arises in statistical applications as well as in many applications in physics. We explored probing methods as well as domain-decomposition type methods. 12. A collaboration with researchers from Toulouse, France, considered the important problem of computing the Schur complement in a domain-decomposition approach. 13. We explored new ways of preconditioning linear systems, based on low-rank approximations.
97 MATHEMATICS AND COMPUTING↗
Relativistic solutions for the spin-1 particles in the two-dimensional Smorodinsky–Winternitz potential
In this study, we investigate relativistic spin-1 particles in the V(x,y)=(ω{sub 0}{sup 2}/2)(x{sup 2}+y{sup 2})+k{sub 1}/x{sup 2}+k{sub 2}/y{sup 2} type of Smorodinsky–Winternitz potentials. In the first case, since this Smorodinsky–Winternitz potential has two dimensions, the system was transformed into polar coordinates from Cartesian coordinates. By using Duffin–Kemmer–Petiau formalism with the non-central Smorodinsky–Winternitz potential in two dimensions, the exact bound state energy eigenvalues and corresponding eigenfunctions were determined within the framework of the asymptotic iteration method. Bound state eigenfunctions were obtained in terms of confluent hypergeometric functions. -- Highlights: •We introduce formalism of the DKP equation in two dimensions. •The DKP equation with S–W potential is considered for spin-1 particles. •In order to solve the DKP equation, we explain the asymptotic iteration method (AIM). •Bound state energy eigenvalues and eigenfunctions are obtained by using AIM.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Comparison of a 2D nonlocal transport model to ECRH experiments in LHD
In this work, a recently developed model of nonlocal transport in two dimensions (2D), the “iterative method”, is applied to the published results of ECRH experiments performed in the Large Helical Device. It is found from the temperature profiles obtained from the 2D model that the sharply peaked electron temperature profiles observed in such experiments, and previously associated with local transport and “internal transport barriers” or Core Electron-Root Confinement, are also consistent with nonlocal transport. It is shown that the iterative method is suited to handling both scenarios
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
An iterative reconstruction of cosmological initial density fields
We present an iterative method to reconstruct the linear-theory initial conditions from the late-time cosmological matter density field, with the intent of improving the recovery of the cosmic distance scale from the baryon acoustic oscillations. We present tests using the dark matter density field in both real and redshift space generated from an N-body simulation. In redshift space at z = 0.5, we find that the reconstructed displacement field using our iterative method are more than 80 percent correlated with the true displacement field of the dark matter particles on scales k < 0.10 h Mpc -1 . Furthermore, we show that the two-point correlation function of our reconstructed density field matches that of the initial density field substantially better, especially on small scales (<40 h -1 Mpc). Our redshift-space results are improved if we use an anisotropic smoothing so as to account for the reduced small-scale information along the line of sight in redshift space.
79 ASTRONOMY AND ASTROPHYSICS↗
The Wave Energy Converter Design Process: Methods Applied in Industry and Shortcomings of Current Practices
Wave energy is among the many renewable energy technologies being researched and developed to address the increasing demand for low-emissions energy. The unique design challenges for wave energy converter design—integrating complex and uncertain technological, economic, and ecological systems, overcoming the structural challenges of ocean deployment, and dealing with complex system dynamics—have lead to a disjointed progression of research and development. There is no common design practice across the wave energy industry and there is no published synthesis of the practices that are used by developers. In this paper, we summarize the methods being employed in WEC design as well as promising methods that have yet to be applied. We contextualize these methods within an overarching design process. We present results from a survey of WEC developers to identify methods that are common in industry. From the review and survey results, we conclude that the most common methods of WEC design are iterative methods in which design parameters are defined, evaluated, and then changed based on evaluation results. This leaves a significant space for improvement of methods that help designers make better-informed decisions prior to sophisticated evaluation, and methods of using the evaluation results to make better design decisions during iteration. Despite the popularity of optimization methods in academic research, they are less common in industry development. We end this paper with a summary of the areas of WEC design in which the testing and development of new methods is necessary, and where more research is required to fully understand the influence of design decisions on WEC performance.
16 TIDAL AND WAVE POWER↗
Hybrid eigensolvers for nuclear configuration interaction calculations
We examine and compare several iterative methods for solving large-scale eigenvalue problems arising from nuclear structure calculations. In particular, we discuss the possibility of using block Lanczos method, a Chebyshev filtering based subspace iterations and the residual minimization method accelerated by direct inversion of iterative subspace (RMM-DIIS) and describe how these algorithms compare with the standard Lanczos algorithm and the locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm. Although the RMM-DIIS method does not exhibit rapid convergence when the initial approximations to the desired eigenvectors are not sufficiently accurate, it can be effectively combined with either the block Lanczos or the LOBPCG method to yield a hybrid eigensolver that has several desirable properties. We will describe a few practical issues that need to be addressed to make the hybrid solver efficient and robust.
97 MATHEMATICS AND COMPUTING↗
Stabilization of the 81-channel coherent beam combination using machine learning
We develop a rapidly converging algorithm for stabilizing a large channel-count diffractive optical coherent beam combination. An 81-beam combiner is controlled by a novel, machine-learning based, iterative method to correct the optical phases, operating on an experimentally calibrated numerical model. A neural-network is trained to detect phase errors based on interference pattern recognition of uncombined beams adjacent to the combined one. Due to the non-uniqueness of solutions in the full space of possible phases, the network is trained within a limited phase perturbation/error range. This also reduces the number of samples needed for training. Simulations have proven that the network can converge in one step for small phase perturbations. When the trained neural-network is applied to a realistic case of 360 degree full range, an iterative scheme exploits random walking at the beginning, with the accuracy of prediction on phase feedback direction, to allow the neural-network to step into the training range for fast convergence. This neural-network-based iterative method of phase detection works tens of times faster than the commonly used stochastic parallel gradient descent approach (SPGD) using a single-detector and random dither when both are tested with random phase perturbations.
Wang, Dan↗
Application of the inverse fast multipole method as a preconditioner in a 3D Helmholtz boundary element method
Here we investigate an efficient preconditioning of iterative methods (such as GMRES) for solving dense linear systems Ax = b that follow from a boundary element method (BEM) for the 3D Helmholtz equation, focusing on the low-frequency regime. While matrix–vector products in GMRES can be accelerated through the low-frequency fast multipole method (LFFMM), the BEM often remains computationally expensive due to the large number of GMRES iterations. We propose the application of the inverse fast multipole method (IFMM) as a preconditioner to accelerate the convergence of GMRES. The IFMM is in essence an approximate direct solver that uses a multilevel hierarchical decomposition and low-rank approximations. The proposed IFMM-based preconditioning has a tunable parameter ε that balances the cost to construct a preconditioner M, which is an approximation of A -1 , and the cost to perform the iterative process by means of M. Namely, using a small (respectively, large) value of ε takes a long (respectively, short) time to construct M, while the number of iterations can be small (respectively, large). A comprehensive set of numerical examples involving various boundary value problems with complicated geometries and mixed boundary conditions is presented to validate the efficiency of the proposed method. We show that the IFMM preconditioner (with a nearly optimal ε of 10 -2 ) clearly outperforms some common preconditioners for the BEM, achieving 1.2–10.8 times speed-up of the computations, in particular when the scale of the underlying scatterer is about five wavelengths or more. In addition, the IFMM preconditioner is capable of solving complicated problems (in a reasonable amount of time) that BD preconditioner can not.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
An asymptotic-preserving Lagrangian algorithm for the time-dependent anisotropic heat transport equation
We propose a Lagrangian numerical algorithm for a time-dependent, anisotropic temperature transport equation in magnetized plasmas in the large guide field regime. The approach is based on an analytical integral formal solution of the parallel (i.e., along the magnetic field) transport equation with sources, and it is able to accommodate both local and non-local parallel heat flux closures. The numerical implementation is based on an operator-split formulation, with two straightforward steps: a perpendicular transport step (including sources), and a Lagrangian (field-line integral) parallel transport step. Algorithmically, the first step is amenable to the use of modern iterative methods, while the second step has a fixed cost per degree of freedom (and is therefore scalable). Accuracy-wise, the approach is free from the numerical pollution introduced by the discrete parallel transport term when the perpendicular to parallel transport coefficient ratio X ⊥ /X ∥ becomes arbitrarily small, and is shown to capture the correct limiting solution when ε = X⊥L 2 ∥ /X1L 2 ⊥ → 0 (with L∥∙ L⊥ , the parallel and perpendicular diffusion length scales, respectively). Therefore, the approach is asymptotic-preserving. We demonstrate the capabilities of the scheme with several numerical experiments with varying magnetic field complexity in two dimensions, including the case of transport across a magnetic island.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Reducing the small-heart effect in pediatric gated myocardial perfusion single-photon emission computed tomography
Background: We compared two reconstruction algorisms and two cardiac functional evaluation software programs in terms of their accuracy for estimating ejection fraction (EF) of small hearts (SH). Methods: The study group consisted of 66 pediatric patients. Data were reconstructed using a filtered back projection (FBP) method without the resolution correction (RC) and an iterative method based on an ordered subset expectation maximization (OSEM) algorithm with the RC. EF was evaluated using two software programs of quantitative gated single-photon emission computed tomography (SPECT) (QGS) and cardioREPO. We compared the EF of gated myocardial perfusion SPECT to echocardiographic measurement (Echo). Results: Forty-eight of 66 patients had an end-systolic volume < 20 mL which was used as the criterion for being included in the SH group, and the SH effect led to an overestimation of EF. While significant differences were observed between Echo (66.9 ± 5.0%) and QGS-FBP without RC (76.9 ± 8.4%, P < .0001), QGS-OSEM with RC (76.6 ± 8.6%, P < .0001), and cardioREPO-FBP without RC (72.1 ± 10.0%, P = .0011), no significant difference was observed between Echo and cardioREPO-OSEM with RC (67.4 ± 6.1%) in SH group. Conclusions: In pediatric gated myocardial perfusion SPECT, the SH effect can be significantly reduced when an OSEM algorithm is used with RC in combination with the specific cardioREPO algorithm.
62 RADIOLOGY AND NUCLEAR MEDICINE↗
Exploring Iterative Optimization Methods to Develop a MIMO Control Input.
Abstract not provided.
Wilbanks, James Justin↗
The NILO-CMFD Method for Iteratively Solving Coupled Neutron Transport–Thermal Hydraulics Problems
Not provided.
Nuclear Science & Technology↗