Search NASA⌕ Search

SEARCH · Search NASA

Results for “Adjoint methods”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

A spectral analysis of the domain decomposed Monte Carlo method for linear systems

The domain decomposed behavior of the adjoint Neumann-Ulam Monte Carlo method for solving linear systems is analyzed using the spectral properties of the linear oper- ator. Relationships for the average length of the adjoint random walks, a measure of convergence speed and serial performance, are made with respect to the eigenvalues of the linear operator. In addition, relationships for the effective optical thickness of a domain in the decomposition are presented based on the spectral analysis and diffusion theory. Using the effective optical thickness, the Wigner rational approxi- mation and the mean chord approximation are applied to estimate the leakage frac- tion of random walks from a domain in the decomposition as a measure of parallel performance and potential communication costs. The one-speed, two-dimensional neutron diffusion equation is used as a model problem in numerical experiments to test the models for symmetric operators with spectral qualities similar to light water reactor problems. We find, in general, the derived approximations show good agreement with random walk lengths and leakage fractions computed by the numerical experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Shutdown Dose Rate Analysis Using the Multi-Step CADIS Method

The Multi-Step Consistent Adjoint Driven Importance Sampling (MS-CADIS) hybrid Monte Carlo (MC)/deterministic radiation transport method was proposed to speed up the shutdown dose rate (SDDR) neutron MC calculation using an importance function that represents the neutron importance to the final SDDR. This work applied the MS-CADIS method to the ITER SDDR benchmark problem. The MS-CADIS method was also used to calculate the SDDR uncertainty resulting from uncertainties in the MC neutron calculation and to determine the degree of undersampling in SDDR calculations because of the limited ability of the MC method to tally detailed spatial and energy distributions. The analysis that used the ITER benchmark problem compared the efficiency of the MS-CADIS method to the traditional approach of using global MC variance reduction techniques for speeding up SDDR neutron MC calculation. Compared to the standard Forward-Weighted-CADIS (FW-CADIS) method, the MS-CADIS method increased the efficiency of the SDDR neutron MC calculation by 69%. The MS-CADIS method also increased the fraction of nonzero scoring mesh tally elements in the space-energy regions of high importance to the final SDDR.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2004

An Adjoint-Based Analysis of the Sampling Footprints of Tall Tower, Aircraft and Potential Future Lidar Observations of CO2

A detailed mechanistic understanding of the sources and sinks of CO2 will be required to reliably predict future CO2 levels and climate. A commonly used technique for deriving information about CO2 exchange with surface reservoirs is to solve an 'inverse problem', where CO2 observations are used with an atmospheric transport model to find the optimal distribution of sources and sinks. Synthesis inversion methods are powerful tools for addressing this question, but the results are disturbingly sensitive to the details of the calculation. Studies done using different atmospheric transport models and combinations of surface station data have produced substantially different distributions of surface fluxes. Adjoint methods are now being developed that will more effectively incorporate diverse datasets in estimates of surface fluxes of CO2. In an adjoint framework, it will be possible to combine CO2 concentration data from longterm surface and aircraft monitoring stations with data from intensive field campaigns and with proposed future satellite observations. We have recently developed an adjoint for the GSFC 3-D Parameterized Chemistry and Transport Model (PCTM). Here, we will present results from a PCTM Adjoint study comparing the sampling footprints of tall tower, aircraft and potential future lidar observations of CO2. The vertical resolution and extent of the profiles and the observation frequency will be considered for several sites in North America.

Andrews, Arlyn↗
DOE OSTI2020

A scalable matrix-free spectral element approach for unsteady PDE constrained optimization using PETSc/TAO

In this work, we provide a new approach for the efficient matrix-free application of the transpose of the Jacobian for the spectral element method for the adjoint-based solution of partial differential equation (PDE) constrained optimization. This results in optimizations of nonlinear PDEs using explicit integrators where the integration of the adjoint problem is not more expensive than the forward simulation. Solving PDE constrained optimization problems entails combining expertise from multiple areas, including simulation, computation of derivatives, and optimization. The Portable, Extensible Toolkit for Scientific computation (PETSc) together with its companion package, the Toolkit for Advanced Optimization (TAO), is an integrated numerical software library that contains an algorithmic/software stack for solving linear systems, nonlinear systems, ordinary differential equations, differential algebraic equations, and large-scale optimization problems and, as such, is an ideal tool for performing PDE-constrained optimization. This paper describes an efficient approach in which the software stack provided by PETSc/TAO can be used for large-scale nonlinear time-dependent problems. Time integration can involve a range of high-order methods, both implicit and explicit. The PDE-constrained optimization algorithm used is gradient-based and seamlessly integrated with the simulation of the physical problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Automated divertor target design by adjoint shape sensitivity analysis and a one-shot method

As magnetic confinement fusion progresses towards the development of first reactor-scale devices, computational tokamak divertor design is a topic of high priority. Presently, edge plasma codes are used in a forward approach, where magnetic field and divertor geometry are manually adjusted to meet design requirements. Due to the complex edge plasma flows and large number of design variables, this method is computationally very demanding. On the other hand, efficient optimization-based design strategies have been developed in computational aerodynamics and fluid mechanics. Such an optimization approach to divertor target shape design is elaborated in the present paper. A general formulation of the design problems is given, and conditions characterizing the optimal designs are formulated. Using a continuous adjoint framework, design sensitivities can be computed at a cost of only two edge plasma simulations, independent of the number of design variables. Furthermore, by using a one-shot method the entire optimization problem can be solved at an equivalent cost of only a few forward simulations. The methodology is applied to target shape design for uniform power load, in simplified edge plasma geometry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Fission Matrix Convergence Diagnostic of the Iterated Fission Probability Method

Monte Carlo methods have been applied to reactor problems in order to solve for adjoint-weighted quantities. The Iterated Fission Probability (IFP) method allows adjoint-weighted tallies to be recorded during a forward Monte-Carlo simulation. A key parameter in the IFP method is the number of generations that must pass before the progeny neutrons of a progenitor neutron are tallied. A convergence diagnostic for the IFP is developed using a deterministic code. In particular, a discrete ordinates code is used as a surrogate to demonstrate the theoretical properties of the proposed Monte Carlo convergence diagnostic. The diagnostic is applied to 1-D slab problems and quantifies the error associated with tallying the neutron progeny before an asymptotic distribution is achieved. The results show that the default value of 10 for the number of generations used in MCNP is acceptable for most classes of problems. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRSDate not supplied

Multi-Impulse to Time Optimal Finite Burn Trajectory Conversion

A novel algorithm is presented that provides an improvement over a traditional parameter optimization method when solving time-optimal, finite-burn pseudo-rendezvous spacecraft trajectory problems. A hybrid optimization procedure is described that converts a set of multiple-impulses, representing high- or low-thrust maneuvers, to an exact time-optimal finite-burn trajectory for a thrust limited, constant exhaust velocity spacecraft. The Hybrid Method applies a control law derived from the Euler-Lagrange system of equations within the classical Indirect Method to a modern Direct Method. An iterative adjoint-control transformation and an evolving constraint vector are introduced to solve the optimal control two-point boundary value problem. This method requires no prior knowledge of the solution, which adds simplicity to the trajectory design process and aids automation. Examples are shown for low-thrust apogee raise maneuvers, non-coplanar Earth orbit transfers, and a modified Deep Space 1 low-thrust trajectory. A numerically significant improvement to objective cost is shown across all application problems compared to a traditional solution method, as well as a significant improvement to convergence speed for a select class of problems.

Joshua A Fogel↗
DOE OSTI2019

Adjoint approach to calculating shape gradients for three-dimensional magnetic confinement equilibria

The shape gradient quantifies the change in some figure of merit resulting from differential perturbations to a shape. Shape gradients can be applied to gradient-based optimization, sensitivity analysis and tolerance calculation. An efficient technique for computing the shape gradient for toroidal three-dimensional magnetohydrodynamic (MHD) equilibria is introduced. The method is based on the self-adjoint property of the equations for driven perturbations of MHD equilibria and is similar to the Onsager symmetry of transport coefficients. Two versions of the shape gradient are considered. One describes the change in a figure of merit due to an arbitrary displacement of the outer flux surface; the other describes the change in the figure of merit due to the displacement of a coil. The method is implemented for several example figures of merit and compared with direct calculation of the shape gradient. In these examples the adjoint method reduces the number of equilibrium computations by factors of $O(N)$ , where $N$ is the number of parameters used to describe the outer flux surface or coil shapes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Deterministic-Monte Carlo Hybrid Methods for Eigenvalue Sensitivity Coefficient Calculations [Slides]

Hybrid method was developed based on a need to generate accurate sensitivities for specified systems with CLUTCH. This new method provides improved sensitivities with HMF-028-001, specifically with 238 U in the large reflector region. With the importance of each voxel predetermined with the adjoint flux, the hybrid method is able to generate more accurate sensitivities. More testing is needed for other types of systems and materials (i.e., thermal and intermediate energy ranges and different moderators and reflectors). Initial results are very promising and continual development of the new hybrid method is currently in progress.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1975

Numerical methods for evaluating the derivatives of eigenvalues and eigenvectors

Two numerical methods are presented for computing the derivatives of eigenvalues and eigenvectors which do not require complete solution of the eigenvalue problem if only a few derivatives are sought. The 'iterative' method may be used to find the first derivative of one or all of the eigenvectors together with the second derivative of their eigenvalues in a self-adjoint system. If the left- and right-hand eigenvectors are known, the first derivative of the eigenvector corresponding to the largest eigenvalue and the second derivative of the largest eigenvalue may be obtained for a nonself-adjoint system. The 'algebraic' method may be used to find all orders of the derivatives, provided they exist, without requiring the left-hand eigenvectors.

Rudisill, C. S.↗
DOE OSTI2020

Bayesian Poroelastic Aquifer Characterization From InSAR Surface Deformation Data. Part I: Maximum A Posteriori Estimate

Characterizing the properties of groundwater aquifers is essential for predicting aquifer response and managing groundwater resources. In this work, we develop a high-dimensional scalable Bayesian inversion framework governed by a three-dimensional quasi-static linear poroelastic model to characterize lateral permeability variations in groundwater aquifers. In this work, we determine the maximum a posteriori (MAP) point of the posterior permeability distribution from centimeter-level surface deformation measurements obtained from Interferometric Synthetic Aperture Radar (InSAR). The scalability of our method to high parameter dimension is achieved through the use of adjoint-based derivatives, inexact Newton methods to determine the MAP point, and a Mat´ern class sparse prior precision operator. Together, these guarantee that the MAP point is found at a cost, measured in number of forward/adjoint poroelasticity solves, that is independent of the parameter dimension. We apply our methodology to a test case for a municipal well in Mesquite, Nevada, in which InSAR and GPS surface deformation data are available. We solve problems with up to 320,824 state variable degrees of freedom (DOFs) and 16,896 parameter DOFs. A consistent treatment of noise level is employed so that the aquifer characterization result does not depend on the pixel spacing of surface deformation data. Our results show that the use of InSAR data significantly improves characterization of lateral aquifer heterogeneity, and the InSAR-based aquifer characterization recovers complex lateral displacement trends observed by independent daily GPS measurements.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

Assessment of Activation on Level L3 of the Tokamak Building due to the ITER Tokamak Cooling Water System

The ITER fusion reactor is being built to demonstrate the feasibility of fusion power and will be the largest tokamak in the world. The tokamak cooling water system (TCWS) will extract the heat generated during operations and includes large amounts of piping and equipment such as pumps and heat exchangers (HXs) that are located in a large shielded region on level L3 of the tokamak building. During operation, water in the TCWS will be activated by plasma neutrons and then flow into this shielded region. The activated coolant will in turn activate the steel in the TCWS during operation and result in an activation gamma source and radiation responses that must be assessed to inform equipment selection and maintenance schedules.The activation of materials in the shielded region of level L3 was assessed at several decay times and for different equipment options using the Oak Ridge National Laboratory (ORNL) shutdown dose rate (SDDR) code suite. The ORNL SDDR code suite implements the rigorous two-step method using the Multi-Step Consistent Adjoint-Driven Importance Sampling (MS-CADIS) method to create effective neutron variance reduction parameters for the photon response of interest. In conclusion, two different HX designs, shell and tube and shell and plate, were considered, as well as the impact of cobalt impurities in steel equipment.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2015

Introduction to Adjoint Models

In this lecture, some fundamentals of adjoint models will be described. This includes a basic derivation of tangent linear and corresponding adjoint models from a parent nonlinear model, the interpretation of adjoint-derived sensitivity fields, a description of methods of automatic differentiation, and the use of adjoint models to solve various optimization problems, including singular vectors. Concluding remarks will attempt to correct common misconceptions about adjoint models and their utilization.

EnKF↗
NASA NTRS2005

Adjoint Sensitivity Analysis of Orbital Mechanics: Application to Computations of Observables' Partials with Respect to Harmonics of the Planetary Gravity Fields

An approach is presented to the inversion of gravity fields based on evaluation of partials of observables with respect to gravity harmonics using the solution of adjoint problem of orbital dynamics of the spacecraft. Corresponding adjoint operator is derived directly from the linear operator of the linearized forward problem of orbital dynamics. The resulting adjoint problem is similar to the forward problem and can be solved by the same methods. For given highest degree N of gravity harmonics desired, this method involves integration of N adjoint solutions as compared to integration of N2 partials of the forward solution with respect to gravity harmonics in the conventional approach. Thus, for higher resolution gravity models, this approach becomes increasingly more effective in terms of computer resources as compared to the approach based on the solution of the forward problem of orbital dynamics.

gravity fields↗
DOE OSTI2022

Dynamic Learning of Correlation Potentials for a Time-Dependent Kohn-Sham System

We develop methods to learn the correlation potential for a time-dependent Kohn-Sham (TDKS) system in one spatial dimension. We start from a low-dimensional two-electron system for which we can numerically solve the time-dependent Schr¨odinger equation; this yields electron densities suitable for training models of the correlation potential. We frame the learning problem as one of optimizing a least-squares objective subject to the constraint that the dynamics obey the TDKS equation. Applying adjoints, we develop efficient methods to compute gradients and thereby learn models of the correlation potential. Our results show that it is possible to learn values of the correlation potential such that the resulting electron densities match ground truth densities. We also show how to learn correlation potential functionals with memory, demonstrating one such model that yields reasonable results for trajectories outside the training set.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Analysis of Shutdown Dose Rate in Fusion Energy Systems Using Hybrid Monte Carlo/Deterministic Techniques - Paper 138

Accurate assessments of shutdown dose rate (SDDR) are critical to support operation, maintenance, and waste disposal planning and to guide possible design changes of critical components in fusion energy systems. An SDDR calculation involves three steps: 1. a neutron transport calculation to determine the space and energy neutron flux distributions, 2. an activation calculation for computing the photon source distribution, and 3. a photon transport calculation for the estimation of the final SDDR. A companion paper describes the challenges of SDDR computations in fusion energy systems and the status of the techniques that are currently being used in SDDR analysis. Of these techniques, the rigorous 2-step (R2S) computational system entails Monte Carlo (MC) neutron and photon transport calculations coupled with a comprehensive activation step using a dedicated inventory code and library. The use of global MC variance reduction techniques was suggested for accelerating the SDDR MC neutron transport calculation. These techniques, which attempt to calculate MC tallies with nearly uniform relative uncertainties in both the low-flux space-energy regions and the high-flux space-energy regions, do not preferentially focus the MC computational efforts toward space-energy regions of high importance to the final decay dose. The ability of these approaches to accurately predict SDDR is inhibited by their prohibitive computational costs, which will be on the order of thousands of processor-years for full-scale modeling of an entire fusion plant. The companion paper describes the theoretical background of the Multi-Step Consistent Adjoint Driven Importance Sampling (MS-CADIS) method, which has been proposed to speed up SDDR MC neutron calculations. The MS-CADIS method uses the CADIS method, which has been successfully used for more than a decade in shielding calculations, but focuses on multistep shielding calculations such as SDDR analyses. The companion paper also describes a new method for calculating the uncertainties in SDDR due to uncertainties in the MC neutron calculation. This new method of uncertainty propagation uses the MS-CADIS neutron adjoint source to propagate the uncertainties in the neutron fluxes to the SDDR. This paper describes the application of the MS-CADIS method for speeding up the SDDR MC calculations and for calculating the SDDR uncertainty due to the neutron flux uncertainties. A new metric for assessing the reliability of SDDR calculations was also suggested and used in this analysis. The ITER benchmark problem was used in this analysis. The problem resembles the configuration and geometrical arrangement of an upper port plug in ITER. The analysis compared the efficiency of the MS-CADIS method to the traditional approach of using global MC variance reduction techniques for speeding up SDDR MC neutron calculation. The application of the MS-CADIS method to SDDR calculations in fusion energy systems was tested using the ITER benchmark problem. Compared to the standard FW-CADIS method, the increase in the efficiency of the SDDR neutron MC calculation due to the use of the MS-CADIS method was between 18% and 69%. The MS-CADIS method also increases the fraction of non-zero-scoring mesh tally elements in the space-energy regions of high importance to the final SDDR. Implementation of the MS-CADIS method in the SCALE and the ADVANTG code systems is currently under way. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗