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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.

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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Optimal Multistage Algorithm for Adjoint Computation

We reexamine the work of Stumm and Walther on multistage algorithms for adjoint computation. We provide an optimal algorithm for this problem when there are two levels of checkpoints, in memory and on disk. Previously, optimal algorithms for adjoint computations were known only for a single level of checkpoints with no writing and reading costs; a well-known example is the binomial checkpointing algorithm of Griewank and Walther. Stumm and Walther extended that binomial checkpointing algorithm to the case of two levels of checkpoints, but they did not provide any optimality results. We bridge the gap by designing the first optimal algorithm in this context. We experimentally compare our optimal algorithm with that of Stumm and Walther to assess the difference in performance.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2006

Model Predictive Optimal Control of a Time-Delay Distributed-Parameter Systems

This paper presents an optimal control method for a class of distributed-parameter systems governed by first order, quasilinear hyperbolic partial differential equations that arise in many physical systems. Such systems are characterized by time delays since information is transported from one state to another by wave propagation. A general closed-loop hyperbolic transport model is controlled by a boundary control embedded in a periodic boundary condition. The boundary control is subject to a nonlinear differential equation constraint that models actuator dynamics of the system. The hyperbolic equation is thus coupled with the ordinary differential equation via the boundary condition. Optimality of this coupled system is investigated using variational principles to seek an adjoint formulation of the optimal control problem. The results are then applied to implement a model predictive control design for a wind tunnel to eliminate a transport delay effect that causes a poor Mach number regulation.

Nguyen, Nhan↗
DOE OSTI2017

Adjoint-Based Constant-Mass Partial Derivatives

It is well known that the adjoint equation in transport theory provides an economical means of computing derivatives of a system response to system parameters. It is also well known, though not often remarked on, that adjoint-based partial derivatives with respect to mass density are constant-volume derivatives. Likewise, adjoint-based partial derivatives with respect to dimensions (i.e., internal interface locations and the outer system boundary) are constant-density derivatives. In this paper, we derive a formula for the constant-mass partial derivative of a response with respect to internal interface locations and the outer system boundary. The formula uses the partial derivatives for density and dimensions, which may be adjoint-based. This paper includes numerical comparisons for a two-dimensional (r-z) cylinder that also demonstrate the correctness of the regular adjoint-based derivatives for surface locations. Adjoint-based derivatives for the neutron problems were computed using the new SENSMG code at Los Alamos National Laboratory.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Adjoint DSMC for nonlinear Boltzmann equation constrained optimization

Applications for kinetic equations such as optimal design and inverse problems often involve finding unknown parameters through gradient-based optimization algorithms. Based on the adjoint-state method, we derive two different frameworks for approximating the gradient of an objective functional constrained by the nonlinear Boltzmann equation. While the forward problem can be solved by the DSMC method, it is difficult to efficiently solve the high-dimensional continuous adjoint equation obtained by the “optimize-then-discretize” approach. This challenge motivates us to propose an adjoint DSMC method following the “discretize-then-optimize” approach for Boltzmann-constrained optimization. We also analyze the properties of the two frameworks and their connections. Here, several numerical examples are presented to demonstrate their accuracy and efficiency.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2006

Adjoint Sensitivity Computations for an Embedded-Boundary Cartesian Mesh Method and CAD Geometry

Cartesian-mesh methods are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric Computer-Aided Design (CAD) tools. Our goal is to combine the automation capabilities of Cartesian methods with an eficient computation of design sensitivities. We address this issue using the adjoint method, where the computational cost of the design sensitivities, or objective function gradients, is esseutially indepeudent of the number of design variables. In previous work, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm included the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Central to this development is the computation of volume-mesh sensitivities to obtain a reliable approximation of the objective finction gradient. Motivated by the success of mesh-perturbation schemes commonly used in body-fitted unstructured formulations, we propose an approach based on a local linearization of a mesh-perturbation scheme similar to the spring analogy. This approach circumvents most of the difficulties that arise due to non-smooth changes in the cut-cell layer as the boundary shape evolves and provides a consistent approximation tot he exact gradient of the discretized abjective function. A detailed gradient accurace study is presented to verify our approach. Thereafter, we focus on a shape optimization problem for an Apollo-like reentry capsule. The optimization seeks to enhance the lift-to-drag ratio of the capsule by modifyjing the shape of its heat-shield in conjunction with a center-of-gravity (c.g.) offset. This multipoint and multi-objective optimization problem is used to demonstrate the overall effectiveness of the Cartesian adjoint method for addressing the issues of complex aerodynamic design. This abstract presents only a brief outline of the numerical method and results; full details will be given in the final paper.

Nemec, Marian↗
NASA NTRS1993

Receptivity in parallel flows: An adjoint approach

Linear receptivity studies in parallel flows are aimed at understanding how external forcing couples to the natural unstable motions which a flow can support. The vibrating ribbon problem models the original Schubauer and Skramstad boundary layer experiment and represents the classic boundary layer receptivity problem. The process by which disturbances are initiated in convectively-unstable jets and shear layers has also received attention. Gaster was the first to handle the boundary layer analysis with the recognition that spatial modes, rather than temporal modes, were relevant when studying convectively-unstable flows that are driven by a time-harmonic source. The amplitude of the least stable spatial mode, far downstream of the source, is related to the source strength by a coupling coefficient. The determination of this coefficient is at the heart of this type of linear receptivity study. The first objective of the present study was to determine whether the various wave number derivative factors, appearing in the coupling coefficients for linear receptivity problems, could be reexpressed in a simpler form involving adjoint eigensolutions. Secondly, it was hoped that the general nature of this simplification could be shown; indeed, a rather elegant characterization of the receptivity properties of spatial instabilities does emerge. The analysis is quite distinct from the usual Fourier-inversion procedures, although a detailed knowledge of the spectrum of the Orr-Sommerfeld equation is still required. Since the cylinder wake analysis proved very useful in addressing control considerations, the final objective was to provide a foundation upon which boundary layer control theory may be developed.

Hill, D. Christopher↗
NASA NTRS1992

Canonical transformations for space trajectory optimization

Canonical transformations are developed between the Cartesian coordinates, equinoctial elements, trajectory variables, and orbital elements for coplanar space trajectory optimization problems. The canonical transformations permit the state and adjoint or their solution, transversality conditions, the optimal control, and integrals of the motion, to be transformed between any of the common sets of coordinates for planar space trajectory optimization problems. Variations on the canonical transformations shown are straightforward to develop given the group properties of the canonical transformations.

Haissig, Christine M.↗
NASA NTRS1993

Adjoint methods for aerodynamic wing design

A model inverse design problem is used to investigate the effect of flow discontinuities on the optimization process. The optimization involves finding the cross-sectional area distribution of a duct that produces velocities that closely match a targeted velocity distribution. Quasi-one-dimensional flow theory is used, and the target is chosen to have a shock wave in its distribution. The objective function which quantifies the difference between the targeted and calculated velocity distributions may become non-smooth due to the interaction between the shock and the discretization of the flowfield. This paper offers two techniques to resolve the resulting problems for the optimization algorithms. The first, shock-fitting, involves careful integration of the objective function through the shock wave. The second, coordinate straining with shock penalty, uses a coordinate transformation to align the calculated shock with the target and then adds a penalty proportional to the square of the distance between the shocks. The techniques are tested using several popular sensitivity and optimization methods, including finite-differences, and direct and adjoint discrete sensitivity methods. Two optimization strategies, Gauss-Newton and sequential quadratic programming (SQP), are used to drive the objective function to a minimum.

Grossman, Bernard↗
NASA NTRS1981

Static shape determination and control for a large space antenna

An integral operator approach is used to derive solutions to static shape determination and control problems associated with large space structures. Problem assumptions include a linear self-adjoint system model, observations and control forces at discrete points, and quadratic performance criteria for the comparison of estimates or control forces. Results are illustrated by simulations with a finite element model of a large space antenna. Modal expansions for terms in the solution algorithms are presented, using modes from the static or associated dynamic model. These expansions provide approximate solutions in the event that a closed form analytical solution to the system boundary value problem is not available.

Weeks, C.↗
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↗
DOE OSTI2017

Monte Carlo Perturbation Theory Estimates of Sensitivities to System Dimensions

Here, Monte Carlo methods are developed using adjoint-based perturbation theory and the differential operator method to compute the sensitivities of the k-eigenvalue, linear functions of the flux (reaction rates), and bilinear functions of the forward and adjoint flux (kinetics parameters) to system dimensions for uniform expansions or contractions. The calculation of sensitivities to system dimensions requires computing scattering and fission sources at material interfaces using collisions occurring at the interface—which is a set of events with infinitesimal probability. Kernel density estimators are used to estimate the source at interfaces using collisions occurring near the interface. The methods for computing sensitivities of linear and bilinear ratios are derived using the differential operator method and adjoint-based perturbation theory and are shown to be equivalent to methods previously developed using a collision history–based approach. The methods for determining sensitivities to system dimensions are tested on a series of fast, intermediate, and thermal critical benchmarks as well as a pressurized water reactor benchmark problem with iterated fission probability used for adjoint-weighting. The estimators are shown to agree within 5% and 3σ of reference solutions obtained using direct perturbations with central differences for the majority of test problems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1981

Shape determination and control for large space structures

An integral operator approach is used to derive solutions to static shape determination and control problems associated with large space structures. Problem assumptions include a linear self-adjoint system model, observations and control forces at discrete points, and performance criteria for the comparison of estimates or control forms. Results are illustrated by simulations in the one dimensional case with a flexible beam model, and in the multidimensional case with a finite model of a large space antenna. Modal expansions for terms in the solution algorithms are presented, using modes from the static or associated dynamic mode. These expansions provide approximated solutions in the event that a used form analytical solution to the system boundary value problem is not available.

Weeks, C. J.↗
DOE OSTI2019

Low-Rank Solution Methods for Stochastic Eigenvalue Problems

In this report, we study efficient solution methods for stochastic eigenvalue problems arising from discretization of self-adjoint partial differential equations with random data, where the underlying operators depend linearly on the random parameters. With the stochastic Galerkin approach, the solutions are represented as generalized polynomial chaos expansions. When these solutions can be approximated well by low-rank objects, we introduce a low-rank variant of the inverse subspace iteration algorithm for computing one or several minimal eigenvalues and corresponding eigenvectors of parameter-dependent matrices. In the algorithm, the iterates are approximated by low-rank matrices, which leads to significant cost savings. Furthermore, the algorithm is tested on two benchmark problems, a stochastic diffusion problem with some poorly separated eigenvalues, and an operator derived from a discrete stochastic Stokes problem whose minimal eigenvalue is related to the inf-sup stability constant. Numerical experiments show that the low-rank algorithm produces accurate solutions compared to the Monte Carlo method, and it uses much less computational time than the original algorithm without low-rank approximation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Reduction by symmetries in singular quantum-mechanical problems: General scheme and application to Aharonov-Bohm model

We develop a general technique for finding self-adjoint extensions of a symmetric operator that respects a given set of its symmetries. Problems of this type naturally arise when considering two- and three-dimensional Schrödinger operators with singular potentials. The approach is based on constructing a unitary transformation diagonalizing the symmetries and reducing the initial operator to the direct integral of a suitable family of partial operators. We prove that symmetry preserving self-adjoint extensions of the initial operator are in a one-to-one correspondence with measurable families of self-adjoint extensions of partial operators obtained by reduction. The general scheme is applied to the three-dimensional Aharonov-Bohm Hamiltonian describing the electron in the magnetic field of an infinitely thin solenoid. We construct all self-adjoint extensions of this Hamiltonian, invariant under translations along the solenoid and rotations around it, and explicitly find their eigenfunction expansions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1990

Application of adjoint operators to neural learning

A technique for the efficient analytical computation of such parameters of the neural architecture as synaptic weights and neural gain is presented as a single solution of a set of adjoint equations. The learning model discussed concentrates on the adiabatic approximation only. A problem of interest is represented by a system of N coupled equations, and then adjoint operators are introduced. A neural network is formalized as an adaptive dynamical system whose temporal evolution is governed by a set of coupled nonlinear differential equations. An approach based on the minimization of a constrained neuromorphic energylike function is applied, and the complete learning dynamics are obtained as a result of the calculations.

Barhen, J.↗
DOE OSTI2015

Improved Sensitivity Relations in State Constrained Optimal Control

Sensitivity relations in optimal control provide an interpretation of the costate trajectory and the Hamiltonian, evaluated along an optimal trajectory, in terms of gradients of the value function. While sensitivity relations are a straightforward consequence of standard transversality conditions for state constraint free optimal control problems formulated in terms of control-dependent differential equations with smooth data, their verification for problems with either pathwise state constraints, nonsmooth data, or for problems where the dynamic constraint takes the form of a differential inclusion, requires careful analysis. In this paper we establish validity of both ‘full’ and ‘partial’ sensitivity relations for an adjoint state of the maximum principle, for optimal control problems with pathwise state constraints, where the underlying control system is described by a differential inclusion. The partial sensitivity relation interprets the costate in terms of partial Clarke subgradients of the value function with respect to the state variable, while the full sensitivity relation interprets the couple, comprising the costate and Hamiltonian, as the Clarke subgradient of the value function with respect to both time and state variables. These relations are distinct because, for nonsmooth data, the partial Clarke subdifferential does not coincide with the projection of the (full) Clarke subdifferential on the relevant coordinate space. We show for the first time (even for problems without state constraints) that a costate trajectory can be chosen to satisfy the partial and full sensitivity relations simultaneously. The partial sensitivity relation in this paper is new for state constraint problems, while the full sensitivity relation improves on earlier results in the literature (for optimal control problems formulated in terms of Lipschitz continuous multifunctions), because a less restrictive inward pointing hypothesis is invoked in the proof, and because it is validated for a stronger set of necessary conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Release of MCNP6.2 and WHISPER-1.1 - Guidance for NCS users

In 2017, a new version of the MCNP6 Monte Carlo code package was released: MCNP6.2. This is the first version of MCNP to include the WHISPER package to support sensitivity-uncertainty based nuclear criticality safety validation. The coding changes to MCNP6.2 physics are relatively insignificant. Corrections to the S(α,β) thermal scattering numerics are generally negligible relative to problem statistics (or, in rare cases, prevent aborts). Similarly, the changes to adjoint-weighting for computing kinetics parameters may result in small differences, generally negligible compared to problem statistics. The change to the MCNP6.2 geometry treatment to correctly handle coincident surfaces in problems with universe/fill features will produce different round-off in the geometry tracking. This will produce differences in results relative to previous versions, but those differences should be small relative to problem statistics, and are not a concern. An immediate benefit of using MCNP6.2 (rather than MCNP6.1) is that the new version is typically 1.5-2 times faster.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2018

Data-Driven Machine Learning for Wind Plant Flow Modeling

In this study, we introduce a data-driven machine learning framework for improving the accuracy of wind plant flow models by learning turbulence model corrections based on data from higher-fidelity simulations. First, a high-dimensional PDE-constrained optimization problem is solved using gradient-based optimization with adjoints to determine optimal eddy viscosity fields that improve the agreement of a medium-fidelity Reynolds-Averaged Navier Stokes (RANS) model with large eddy simulations (LES). A supervised learning problem is then constructed to find general, predictive representations of the optimal turbulence closure. A machine learning technique using Gaussian process regression is trained to predict the eddy viscosity field based on local RANS flow field information like velocities, pressures, and their gradients. The Gaussian process is trained on LES simulations of a single turbine and implemented in a wind plant simulation with 36 turbines. We show improvement over the baseline RANS model with the machine learning correction, and demonstrate the ability to provide accurate confidence levels for the corrections that enable future uncertainty quantification studies.

17 WIND ENERGY↗