Adjoint system integrals for optimal spaceN-impulse transfer

2000 ◽  
Vol 21 (4) ◽  
pp. 433-436
Author(s):  
Wu Yuliang
Keyword(s):  
Adjoint System

scholarly journals Adjoint-based exact Hessian computation

2021 ◽  
Author(s):  
Shin-ichi Ito ◽  
Takeru Matsuda ◽  
Yuto Miyatake
Keyword(s):  
Krylov Subspace ◽  
Hessian Matrix ◽  
Adjoint System ◽  
Coefficient Matrix ◽  
Scalar Function ◽  
Second Order ◽  
Subspace Method ◽  
Initial Value ◽  
Research Fields ◽  
Memory Efficiency

AbstractWe consider a scalar function depending on a numerical solution of an initial value problem, and its second-derivative (Hessian) matrix for the initial value. The need to extract the information of the Hessian or to solve a linear system having the Hessian as a coefficient matrix arises in many research fields such as optimization, Bayesian estimation, and uncertainty quantification. From the perspective of memory efficiency, these tasks often employ a Krylov subspace method that does not need to hold the Hessian matrix explicitly and only requires computing the multiplication of the Hessian and a given vector. One of the ways to obtain an approximation of such Hessian-vector multiplication is to integrate the so-called second-order adjoint system numerically. However, the error in the approximation could be significant even if the numerical integration to the second-order adjoint system is sufficiently accurate. This paper presents a novel algorithm that computes the intended Hessian-vector multiplication exactly and efficiently. For this aim, we give a new concise derivation of the second-order adjoint system and show that the intended multiplication can be computed exactly by applying a particular numerical method to the second-order adjoint system. In the discussion, symplectic partitioned Runge–Kutta methods play an essential role.

scholarly journals Optimal control of stochastic phase-field models related to tumor growth

2020 ◽  
Vol 26 ◽  
pp. 104
Author(s):  
Carlo Orrieri ◽  
Elisabetta Rocca ◽  
Luca Scarpa
Keyword(s):  
Optimal Control ◽  
Tumor Growth ◽  
Phase Field ◽  
Phase Field Model ◽  
Growth Dynamics ◽  
Necessary Optimality Conditions ◽  
Reaction Diffusion ◽  
Adjoint System ◽  
Reaction Diffusion Equation ◽  
Cahn Hilliard Equation

We study a stochastic phase-field model for tumor growth dynamics coupling a stochastic Cahn-Hilliard equation for the tumor phase parameter with a stochastic reaction-diffusion equation governing the nutrient proportion. We prove strong well-posedness of the system in a general framework through monotonicity and stochastic compactness arguments. We introduce then suitable controls representing the concentration of cytotoxic drugs administered in medical treatment and we analyze a related optimal control problem. We derive existence of an optimal strategy and deduce first-order necessary optimality conditions by studying the corresponding linearized system and the backward adjoint system.

scholarly journals Optimized lattice-based metamaterials for elastostatic cloaking

2021 ◽  
Vol 477 (2253) ◽  
pp. 20210418
Author(s):  
E. D. Sanders ◽  
M. A. Aguiló ◽  
G. H. Paulino
Keyword(s):  
Objective Function ◽  
Uniaxial Tension ◽  
Weighted Least Squares ◽  
Elliptical Hole ◽  
Adjoint System ◽  
System Optimization ◽  
Small Region ◽  
Shear Loading ◽  
Stiffness Properties ◽  
Stiffness Characteristics

An optimization-based approach is proposed to design elastostatic cloaking devices in two-dimensional (2D) lattices. Given an elastic lattice with a defect, i.e. a circular or elliptical hole, a small region (cloak) around the hole is designed to hide the effect of the hole on the elastostatic response of the lattice. Inspired by the direct lattice transformation approach to elastostatic cloaking in 2D lattices, the lattice nodal positions in the design region are obtained using a coordinate transformation of the reference (undisturbed) lattice nodes. Subsequently, additional connectivity (i.e. a ground structure) is defined in the design region and the stiffness properties of these elements are optimized to mimic the global stiffness characteristics of the reference lattice. A weighted least-squares objective function is proposed, where the weights have a physical interpretation—they are the design-dependent coefficients of the design lattice stiffness matrix. The formulation leads to a convex objective function that does not require a solution to an additional adjoint system. Optimization-based cloaks are designed considering uniaxial tension in multiple directions and are shown to exhibit approximate elastostatic cloaking, not only when subjected to the boundary conditions they were designed for but also for uniaxial tension in directions not used in design and for shear loading.

Naval Research Laboratory Multiscale Targeting Guidance for T-PARC and TCS-08

2010 ◽  
Vol 25 (2) ◽  
pp. 526-544 ◽  
Author(s):  
Carolyn A. Reynolds ◽  
James D. Doyle ◽  
Richard M. Hodur ◽  
Hao Jin
Keyword(s):  
Tropical Cyclone ◽  
Research Laboratory ◽  
Large Scale ◽  
Adjoint System ◽  
Horizontal Resolution ◽  
Naval Research Laboratory ◽  
Naval Research ◽  
Prediction System ◽  
Initial State ◽  
The North

Abstract As part of The Observing System Research and Predictability Experiment (THORPEX) Pacific Asian Regional Campaign (T-PARC) and the Office of Naval Research’s (ONR’s) Tropical Cyclone Structure-08 (TCS-08) experiments, a variety of real-time products were produced at the Naval Research Laboratory during the field campaign that took place from August through early October 2008. In support of the targeted observing objective, large-scale targeting guidance was produced twice daily using singular vectors (SVs) from the Navy Operational Global Atmospheric Prediction System (NOGAPS). These SVs were optimized for fixed regions centered over Guam, Taiwan, Japan, and two regions over the North Pacific east of Japan. During high-interest periods, flow-dependent SVs were also produced. In addition, global ensemble forecasts were produced and were useful for examining the potential downstream impacts of extratropical transitions. For mesoscale models, TC forecasts were produced using a new version of the Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS) developed specifically for tropical cyclone prediction (COAMPS-TC). In addition to the COAMPS-TC forecasts, mesoscale targeted observing products were produced using the COAMPS forecast and adjoint system twice daily, centered on storms of interest, at a 40-km horizontal resolution. These products were produced with 24-, 36-, and 48-h lead times. The nonhydrostatic adjoint system used during T-PARC/TCS-08 contains an exact adjoint to the explicit microphysics. An adaptive response function region was used to target favorable areas for tropical cyclone formation and development. Results indicate that forecasts of tropical cyclones in the western Pacific are very sensitive to the initial state.

CVODES: The Sensitivity-Enabled ODE Solver in SUNDIALS

2005 ◽  
Author(s):  
Radu Serban ◽  
Alan C. Hindmarsh
Keyword(s):  
System Integration ◽  
Adjoint System ◽  
Problem Solver ◽  
Variable Order ◽  
Initial Value ◽  
Adjoint Sensitivity ◽  
Forward Solution ◽  
Independent Manner ◽  
Differentiation Formula ◽  
Variable Step

CVODES, which is part of the SUNDIALS software suite, is a stiff and nonstiff ordinary differential equation initial value problem solver with sensitivity analysis capabilities. CVODES is written in a data-independent manner, with a highly modular structure to allow incorporation of different preconditioning and/or linear solver methods. It shares with the other SUNDIALS solvers several common modules, most notably the generic kernel of vector operations and a set of generic linear solvers and preconditioners. CVODES solves the IVP by one of two methods — backward differentiation formula or Adams-Moulton — both implemented in a variable-step, variable-order form. The forward sensitivity module in CVODES implements the simultaneous corrector method, as well as two flavors of staggered corrector methods. Its adjoint sensitivity module provides a combination of checkpointing and cubic Hermite interpolation for the efficient generation of the forward solution during the adjoint system integration. We describe the current capabilities of CVODES, its design principles, and its user interface, and provide an example problem to illustrate the performance of CVODES.

A Hybrid Adjoint Network Model for Thermoacoustic Optimization

2021 ◽  
Author(s):  
Fellcitas Schäfer ◽  
Luca Magri ◽  
Wolfgang Polifke
Keyword(s):  
Network Model ◽  
Hybrid Approach ◽  
Adjoint System ◽  
Scattering Matrix ◽  
Adjoint Equations ◽  
Jump Conditions ◽  
Discrete Adjoint ◽  
Direct Scattering ◽  
Annular Combustor ◽  
Continuous Adjoint

Abstract A method is proposed that allows the computation of the continuous adjoint of a thermoacoustic network model based on the discretized direct equations. This hybrid approach exploits the self-adjoint character of the duct element, which allows all jump conditions to be derived from the direct scattering matrix. In this way, the need to derive the adjoint equations for every element of the network model is eliminated. This methodology combines the advantages of the discrete and continuous adjoint, as the accuracy of the continuous adjoint is achieved whilst maintaining the flexibility of the discrete adjoint. It is demonstrated how the obtained adjoint system may be utilized to optimize a thermoacoustic configuration by determining the optimal damper setting for an annular combustor.

Nonlinear Schrodinger Equation-Based Adjoint Sensitivity Analysis

2021 ◽  
Vol 35 (11) ◽  
pp. 1342-1343
Author(s):  
Mahmoud Maghrabi ◽  
Mohamed Bakr ◽  
Shiva Kumar
Keyword(s):  
Sensitivity Analysis ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Adjoint System ◽  
Nonlinear Schrodinger Equation ◽  
Design Parameters ◽  
Adjoint Sensitivity Analysis ◽  
Adjoint Sensitivity ◽  
Nonlinear Schrödinger

A general nonlinear adjoint sensitivity analysis (ASA) approach for the time-dependent nonlinear Schrodinger equation (NLSE) is presented. The proposed algorithm estimates the sensitivities of a desired objective function with respect to all design parameters using only one extra adjoint system simulation. The approach efficiency is shown here through a numerical example.

scholarly journals Adjoint Variable Method for the Study of Combined Active and Passive Magnetic Shielding

2008 ◽  
Vol 2008 ◽  
pp. 1-15 ◽  
Author(s):  
Peter Sergeant ◽  
Ivan Cimrák ◽  
Valdemar Melicher ◽  
Luc Dupré ◽  
Roger Van Keer
Keyword(s):  
Adjoint System ◽  
Design Sensitivity ◽  
Computational Effort ◽  
Magnetic Shielding ◽  
Adjoint Variable Method ◽  
Adjoint Variable ◽  
Cpu Time ◽  
Gradient Optimization ◽  
Sensitivity Approach ◽  
Active Shield

For shielding applications that cannot sufficiently be shielded by only a passive shield, it is useful to combine a passive and an active shield. Indeed, the latter does the “finetuning” of the field reduction that is mainly caused by the passive shield. The design requires the optimization of the geometry of the passive shield, the position of all coils of the active shield, and the real and imaginary components of the currents (when working in the frequency domain). As there are many variables, the computational effort for the optimization becomes huge. An optimization using genetic algorithms is compared with a classical gradient optimization and with a design sensitivity approach that uses an adjoint system. Several types of active and/or passive shields with constraints are designed. For each type, the optimization was carried out by all three techniques in order to compare them concerning CPU time and accuracy.

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