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At least 145 records · Page 8

The Coupled Adjoint-State Equation in forward and inverse linear elasticity: Incompressible plane stress

A persistent challenge present in inverse or parameter estimation problems with interior data is how to deal with uncertainty in the boundary conditions employed in the forward or state model. In this work we focus on a linear plane stress inverse elasticity problem with measured displacement data where one component of the measured displacement field is known with considerably greater precision than the other. This situation is commonly encountered when the displacement field is measured using ultrasound or optical coherence tomography. We present a novel computational formulation in which no displacement or traction boundary conditions are assumed. The formulation results in coupling the state and adjoint equations, that are typically uncoupled when a well-posed state model is available. Two variants of residual-based stabilization are added. Our approach is applied to a simulated data set and experimental data from an ultrasound phantom.

42 ENGINEERING↗

Evaluating importance maps for TRIPOLI-4{sup R} using deterministic or on-line methods - 25446

Variance reduction is a key ingredient for solving radiation-protection problems with Monte-Carlo particle-transport codes. Many variance-reduction methods require the definition of an importance map and exhibit optimal performance if the importance map is given by the adjoint flux, the solution of the adjoint Boltzmann equation. This paper presents the implementation of the Consistent Adjoint-Driven Importance Sampling (CADIS) methodology via a coupling between the TRIPOLI-4 R Monte-Carlo particle-transport code and the IDT deterministic solver, Additionally, we describe the implementation of a new TRIPOLI-4 R score that makes it possible to estimate the adjoint flux during a direct Monte-Carlo calculation. These new features are expected to simplify the solution of difficult shielding problems. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗

Accelerating full waveform inversion via source stacking and cross-correlations

SUMMARY Accurate synthetic seismic wavefields can now be computed in 3-D earth models using the spectral element method (SEM), which helps improve resolution in full waveform global tomography. However, computational costs are still a challenge. These costs can be reduced by implementing a source stacking method, in which multiple earthquake sources are simultaneously triggered in only one teleseismic SEM simulation. One drawback of this approach is the perceived loss of resolution at depth, in particular because high-amplitude fundamental mode surface waves dominate the summed waveforms, without the possibility of windowing and weighting as in conventional waveform tomography. This can be addressed by redefining the cost-function and computing the cross-correlation wavefield between pairs of stations before each inversion iteration. While the Green’s function between the two stations is not reconstructed as well as in the case of ambient noise tomography, where sources are distributed more uniformly around the globe, this is not a drawback, since the same processing is applied to the 3-D synthetics and to the data, and the source parameters are known to a good approximation. By doing so, we can separate time windows with large energy arrivals corresponding to fundamental mode surface waves. This opens the possibility of designing a weighting scheme to bring out the contribution of overtones and body waves. It also makes it possible to balance the contributions of frequently sampled paths versus rarely sampled ones, as in more conventional tomography. Here we present the results of proof of concept testing of such an approach for a synthetic 3-component long period waveform data set (periods longer than 60 s), computed for 273 globally distributed events in a simple toy 3-D radially anisotropic upper mantle model which contains shear wave anomalies at different scales. We compare the results of inversion of 10 000 s long stacked time-series, starting from a 1-D model, using source stacked waveforms and station-pair cross-correlations of these stacked waveforms in the definition of the cost function. We compute the gradient and the Hessian using normal mode perturbation theory, which avoids the problem of cross-talk encountered when forming the gradient using an adjoint approach. We perform inversions with and without realistic noise added and show that the model can be recovered equally well using one or the other cost function. The proposed approach is computationally very efficient. While application to more realistic synthetic data sets is beyond the scope of this paper, as well as to real data, since that requires additional steps to account for such issues as missing data, we illustrate how this methodology can help inform first order questions such as model resolution in the presence of noise, and trade-offs between different physical parameters (anisotropy, attenuation, crustal structure, etc.) that would be computationally very costly to address adequately, when using conventional full waveform tomography based on single-event wavefield computations.

Romanowicz, Barbara↗

Linearization errors in discrete goal-oriented error estimation

This paper is concerned with goal-oriented a posteriori error estimation for nonlinear functionals in the context of nonlinear variational problems solved with continuous Galerkin finite element discretizations. A two-level, or discrete, adjoint-based approach for error estimation is considered. The traditional method to derive an error estimate in this context requires linearizing both the nonlinear variational form and the nonlinear functional of interest which introduces linearization errors into the error estimate. In this paper, we investigate these linearization errors. In particular, we develop a novel discrete goal-oriented error estimate that accounts for traditionally neglected nonlinear terms at the expense of greater computational cost. We demonstrate how this error estimate can be used to drive mesh adaptivity. Here, we show that accounting for linearization errors in the error estimate can improve its effectivity for several nonlinear model problems and quantities of interest. We also demonstrate that an adaptive strategy based on the newly proposed estimate can lead to more accurate approximations of the nonlinear functional with fewer degrees of freedom when compared to uniform refinement and traditional adjoint-based approaches.

42 ENGINEERING↗

Adjoint Klein-Nishina Sampling Methods: Efficiency, Speed and Applications

Three new rejection sampling methods for generating samples from the adjoint Klein-Nishina cross section are discussed: the two-branch rejection sampling procedure, the three-branch linear rejection sampling procedure and the three-branch inverse rejection sampling procedure. These methods have all been implemented in the Framework for REsearch in Nuclear ScIence and Engineering (FRENSIE). The efficiency and sample generation rate of each of these methods are evaluated to characterize the methods and to make recommendations regarding their use. The use of these methods in realistic transport simulations is also evaluated by incorporating a scattering function into the sampling process. Furthermore, the results of an infinite medium problem are presented to verify that the sampling procedure can be used in an adjoint Monte Carlo simulation to generate results that are in agreement with an equivalent forward simulation.

97 MATHEMATICS AND COMPUTING↗

The scattering problem for nonlocal potentials

We solve the direct and inverse scattering problems for integro-differential operators which are one-dimensional perturbations of the self-adjoint second derivative operator on the half-axis. We also describe the scattering data for this class of operators. Bibliography: 28 titles.

97 MATHEMATICS AND COMPUTING↗

Semi-analytical sensitivity analysis for nonlinear transient problems

Efficient analytical sensitivity computations are essential elements of gradient-based optimization schemes; however, they can be difficult to implement. This implementation issue is often resolved by adopting the semi-analytical method which exhibits the efficiency of the analytical methods and the ease of implementation of the finite difference method. However, care must be taken as semi-analytical sensitivities may exhibit errors due to truncation and round-off. Additional errors are introduced if the convergence tolerance of the primal analysis is not sufficiently small. This paper gives a general overview and some new developments of the analytical and semi-analytical sensitivity analyses for nonlinear steady-state, transient, and dynamic problems. We discuss the restrictive assumptions, accuracy, and consistency of these methods. Both adjoint and direct differentiation methods are studied. Numerical examples are provided.

42 ENGINEERING↗

Inverse design for waveguide dispersion with a differentiable mode solver

Inverse design of optical components based on adjoint sensitivity analysis has the potential to address the most challenging photonic engineering problems. However, existing inverse design tools based on finite-difference-time-domain (FDTD) models are poorly suited for optimizing waveguide modes for adiabatic transformation or perturbative coupling, which lies at the heart of many important photonic devices. Among these, dispersion engineering of optical waveguides is especially challenging in ultrafast and nonlinear optical applications involving broad optical bandwidths and frequency-dependent anisotropic dielectric material response. In this work, we develop gradient back-propagation through a general-purpose electromagnetic eigenmode solver and use it to demonstrate waveguide dispersion optimization for second harmonic generation with maximized phase-matching bandwidth. This optimization of three design parameters converges in eight steps, reducing the computational cost of optimization by ∼100x compared to exhaustive search and identifying new designs for broadband optical frequency doubling of laser sources in the 1.3–1.4 µm wavelength range. Furthermore, we demonstrate that the computational cost of gradient back-propagation is independent of the number of parameters, as required for optimization of complex geometries. This technique enables practical inverse design for a broad range of previously intractable photonic devices.

Gray, Dodd (ORCID:000000030469599X)↗

(U) Second Derivative of an (α,n) Neutron Source with Respect to Constituent Isotope Densities

We are deriving adjoint-based second-order sensitivities of a response in transport theory. Neutron problems need the second-order sensitivity of the inhomogeneous source with respect to the constituent isotope densities. We have previously derived and verified the first-order sensitivity of an (α,n) neutron source with respect to isotope densities and the subsequent first-order sensitivity of a leakage response. In this memo, we derive and verify the second-order sensitivity of an (α,n) neutron source with respect to constituent isotope densities. We show that the second-order sensitivity of a spontaneous-fission source with respect to constituent isotope densities is zero. The propagation of these second-order sensitivities to the second-order sensitivity of a response awaits the completion of the coding.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Stiffness optimization of non-linear elastic structures

Our paper revisits stiffness optimization of non-linear elastic structures. Due to the non-linearity, several possible stiffness measures can be identified and in this work conventional compliance, i.e. secant stiffness designs are compared to tangent stiffness designs. The optimization problem is solved by the method of moving asymptotes and the sensitivities are calculated using the adjoint method. And for the tangent cost function it is shown that although the objective involves the third derivative of the strain energy an efficient formulation for calculating the sensitivity can be obtained. Loss of convergence due to large deformations in void regions is addressed by using a fictitious strain energy such that small strain linear elasticity is approached in the void regions. We formulate a well-posed topology optimization problem by using restriction which is achieved via a Helmholtz type filter. The numerical examples provided show that for low load levels, the designs obtained from the different stiffness measures coincide whereas for large deformations significant differences are observed.

42 ENGINEERING↗

Comparison of ADVANTG Simulations to Simple Shielding Measurements - Paper 36

Monte Carlo (MC) radiation transport simulations, like those performed using Monte Carlo N-Particle (MCNP), can be highly accurate but require time to reduce the statistical uncertainties in the calculated detector response(s). Many different 'variance reduction' techniques devised over the years increase the efficiency of MC calculations, but these methods can be more art than science. Many of these methods are problem specific or require careful tuning of parameters for good performance. One of the best variance reduction methods, in terms of both reliable performance increases and ease of use, is the use of weight windows. Weight windows are derived from an importance map in space and energy that allows the transport code to focus more simulation time on particles that have a higher likelihood of being important to the final detector response. Less time is spent simulating particles that have little chance of making a contribution to the detector response. MCNP already includes the abilities to generate and use weight windows. Unfortunately, generating weight windows can take a very long time, perhaps longer than the original problem. Oak Ridge National Laboratory has led the development of hybrid methods using a discrete ordinates adjoint calculation to quickly develop an importance map (weight windows) for use in a Monte Carlo code. The Consistent Adjoint Driven Importance Sampling (CADIS) method uses an adjoint calculation to develop both an importance map and a biased source distribution that work together. This method is reasonably automatic, is easy to use, and has been implemented in the Automated Variance reduction Generator (ADVANTG) package that works with MCNP5. ADVANTG reads an MCNP input file and a small amount of extra user information and then runs an adjoint deterministic calculation using Denovo. The importance map and biased source distribution derived from the CADIS method can then be incorporated back into the original MCNP input file to enhance the figure-of-merit (FOM) of the calculation. The FOM is a measure of the efficiency of the calculation using the amount of run time and corresponding level of statistical uncertainty in the detector result. ADVANTG-enhanced MCNP input files have been shown to increase the FOM of many types of problems, obtaining the same level of statistical uncertainty in a shorter time compared to standard MCNP. ADVANTG can also generate variance reduction parameters (importance map and biased source) using the Forward-Weighted CADIS (FW-CADIS) method for optimizing mesh tallies. The CADIS method creates variance reduction parameters that optimize a tally's total quantity (flux, dose rate, interaction rate, etc.) and will not generally increase performance for all parts of a segmented tally. To optimize a segmented tally, the FW-CADIS method uses two discrete ordinates calculations to make variance reduction parameters that help compute a segmented tally with uniform relative uncertainties in each bin. This report will demonstrate that using ADVANTG for neutron and photon radiation shielding problems will (1) preserve the standard MCNP results and (2) obtain those results either with less statistical uncertainty or in shorter times than the standard MCNP calculation. The four demonstration problems in this report are based on simple neutron or photon transmission measurements through different materials. All of the problems here used the CADIS method and still saw improvement across the flux tallies segmented by particle energy. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗

Adjoint design sensitivity analysis of reduced atomic systems using generalized Langevin equation for lattice structures

An efficient adjoint design sensitivity analysis method is developed for reduced atomic systems. A reduced atomic system and the adjoint system are constructed in a locally confined region, utilizing generalized Langevin equation (GLE) for periodic lattice structures. Due to the translational symmetry of lattice structures, the size of time history kernel function that accounts for the boundary effects of the reduced atomic systems could be reduced to a single atom’s degrees of freedom. For the problems of highly nonlinear design variables, the finite difference method is impractical for its inefficiency and inaccuracy. However, the adjoint method is very efficient regardless of the number of design variables since one additional time integration is required for the adjoint GLE. Through numerical examples, the derived adjoint sensitivity turns out to be accurate and efficient through the comparison with finite difference sensitivity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

TH-E-17A-02: High-Pitch and Sparse-View Helical 4D CT Via Iterative Image Reconstruction Method Based On Tensor Framelet

Purpose: 4D CT is routinely performed during radiation therapy treatment planning of thoracic and abdominal cancers. Compared with the cine mode, the helical mode is advantageous in temporal resolution. However, a low pitch (∼0.1) for 4D CT imaging is often required instead of the standard pitch (∼1) for static imaging, since standard image reconstruction based on analytic method requires the low-pitch scanning in order to satisfy the data sufficient condition when reconstructing each temporal frame individually. In comparison, the flexible iterative method enables the reconstruction of all temporal frames simultaneously, so that the image similarity among frames can be utilized to possibly perform high-pitch and sparse-view helical 4D CT imaging. The purpose of this work is to investigate such an exciting possibility for faster imaging with lower dose. Methods: A key for highpitch and sparse-view helical 4D CT imaging is the simultaneous reconstruction of all temporal frames using the prior that temporal frames are continuous along the temporal direction. In this work, such a prior is regularized through the sparsity transform based on spatiotemporal tensor framelet (TF) as a multilevel and high-order extension of total variation transform. Moreover, GPU-based fast parallel computing of X-ray transform and its adjoint together with split Bregman method is utilized for solving the 4D image reconstruction problem efficiently and accurately. Results: The simulation studies based on 4D NCAT phantoms were performed with various pitches (i.e., 0.1, 0.2, 0.5, and 1) and sparse views (i.e., 400 views per rotation instead of standard >2000 views per rotation), using 3D iterative individual reconstruction method based on 3D TF and 4D iterative simultaneous reconstruction method based on 4D TF respectively. Conclusion: The proposed TF-based simultaneous 4D image reconstruction method enables high-pitch and sparse-view helical 4D CT with lower dose and faster speed.

60 APPLIED LIFE SCIENCES↗

Nonuniversal gaugino masses, the supersymmetric little hierarchy problem, and dark matter

We study a class of supersymmetric models with non-universal gaugino masses that could arise from F-terms in a general combination of the singlet and adjoint representations of SU(5). We explore models that satisfy present Large Hadron Collider and other bounds, showing how the allowed parameter space is divided into distinct "continents". Regions of parameter space that ameliorate the supersymmetric little hierarchy problem with a small mu parameter include the usual focus point scenario, but also natural areas with much lighter squarks and sleptons. These models are continuously connected in parameter space to regions in which stau co-annihilation or Higgs exchange is mostly responsible for dark matter annihilation, and to models in which the thermal relic abundance is achieved by slepton-mediated annihilation, reviving the bulk region that is severely restricted in mSUGRA models. In hybrid or confluence regions, several mechanisms combine to give the requisite dark matter annihilation rate. In each case we study the prospects for direct detection of dark matter. We also comment briefly on the impact of recent hints for M_h near 125 GeV from the LHC.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Optimal Control for Stochastic Delay Evolution Equations

In this paper, we investigate a class of infinite-dimensional optimal control problems, where the state equation is given by a stochastic delay evolution equation with random coefficients, and the corresponding adjoint equation is given by an anticipated backward stochastic evolution equation. We first prove the continuous dependence theorems for stochastic delay evolution equations and anticipated backward stochastic evolution equations, and show the existence and uniqueness of solutions to anticipated backward stochastic evolution equations. Then we establish necessary and sufficient conditions for optimality of the control problem in the form of Pontryagin’s maximum principles. To illustrate the theoretical results, we apply stochastic maximum principles to study two examples, an infinite-dimensional linear-quadratic control problem with delay and an optimal control of a Dirichlet problem for a stochastic partial differential equation with delay. Further applications of the two examples to a Cauchy problem for a controlled linear stochastic partial differential equation and an optimal harvesting problem are also considered.

97 MATHEMATICS AND COMPUTING↗

Upscaling of Mixed Finite Element Discretization Problems by the Spectral AMGe Method

Here, we propose two multilevel spectral techniques for constructing coarse discretization spaces for saddle-point problems corresponding to PDEs involving a divergence constraint, with a focus on mixed finite element discretizations of scalar self-adjoint second order elliptic equations on general unstructured grids. We use element agglomeration algebraic multigrid (AMGe), which employs coarse elements that can have nonstandard shape since they are agglomerates of fine-grid elements. The coarse basis associated with each agglomerated coarse element is constructed by solving local eigenvalue problems and local mixed finite element problems. This construction leads to stable upscaled coarse spaces and guarantees the inf-sup compatibility of the upscaled discretization. Also, the approximation properties of these upscaled spaces improve by adding more local eigenfunctions to the coarse spaces. The higher accuracy comes at the cost of additional computational effort, as the sparsity of the resulting upscaled coarse discretization (referred to as operator complexity) deteriorates when we introduce additional functions in the coarse space. We also provide an efficient solver for the coarse (upscaled) saddle-point system by employing hybridization, which leads to a symmetric positive definite (s.p.d.) reduced system for the Lagrange multipliers, and to solve the latter s.p.d. system, we use our previously developed spectral AMGe solver. Numerical experiments, in both two and three dimensions, are provided to illustrate the efficiency of the proposed upscaling technique.

97 MATHEMATICS AND COMPUTING↗

A modified Monte Carlo 'local importance function transform' method

The Local Importance Function Transform (LIFT) method uses an approximation of the contribution transport problem to bias a forward Monte-Carlo (MC) source-detector simulation [1-3]. Local (cell-based) biasing parameters are calculated from an inexpensive deterministic adjoint solution and used to modify the physics of the forward transport simulation. In this research, we have developed a new expression for the LIFT biasing parameter, which depends on a cell-average adjoint current to scalar flux (J{sup *}/{phi}{sup *}) ratio. This biasing parameter differs significantly from the original expression, which uses adjoint cell-edge scalar fluxes to construct a finite difference estimate of the flux derivative; the resulting biasing parameters exhibit spikes in magnitude at material discontinuities, causing the original LIFT method to lose efficiency in problems with high spatial heterogeneity. The new J{sup *}/{phi}{sup *} expression, while more expensive to obtain, generates biasing parameters that vary smoothly across the spatial domain. The result is an improvement in simulation efficiency. A representative test problem has been developed and analyzed to demonstrate the advantage of the updated biasing parameter expression with regards to solution figure of merit (FOM). For reference, the two variants of the LIFT method are compared to a similar variance reduction method developed by Depinay [4, 5], as well as MC with deterministic adjoint weight windows (WW). (authors)

97 MATHEMATICS AND COMPUTING↗