Algorithmic Differentiation for Discontinuous Payoffs

2017 ◽  
Author(s):  
Roberto Daluiso ◽  
Giorgio Facchinetti
Keyword(s):  
Algorithmic Differentiation ◽  
Discontinuous Payoffs

ALGORITHMIC DIFFERENTIATION FOR DISCONTINUOUS PAYOFFS

2018 ◽  
Vol 21 (04) ◽  
pp. 1850019 ◽  
Author(s):  
ROBERTO DALUISO ◽  
GIORGIO FACCHINETTI
Keyword(s):  
Monte Carlo ◽  
Execution Time ◽  
Natural Extension ◽  
General Technique ◽  
Algorithmic Differentiation ◽  
Financial Products ◽  
Discontinuous Payoffs

We present a general technique to compute the sensitivities of the Monte Carlo prices of discontinuous financial products. It is a natural extension of the pathwise adjoints method, which would require an almost-surely differentiable payoff; the efficiency of the latter method when many sensitivities must be calculated is preserved. We show empirically that the new algorithm is competitive in terms of accuracy and execution time when compared to benchmarks obtained by smoothing of the payoff, which benchmarks are biased and require a nonobvious tuning of their parameters.

Forced Response Sensitivity Analysis Using an Adjoint Harmonic Balance Solver

2018 ◽  
Author(s):  
Anna Engels-Putzka ◽  
Jan Backhaus ◽  
Christian Frey
Keyword(s):  
Frequency Domain ◽  
Harmonic Balance ◽  
Unsteady Aerodynamics ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Algorithmic Differentiation ◽  
Design And Optimization ◽  
Initial Application ◽  
Reverse Mode ◽  
Geometric Changes

This paper describes the development and initial application of an adjoint harmonic balance solver. The harmonic balance method is a numerical method formulated in the frequency domain which is particularly suitable for the simulation of periodic unsteady flow phenomena in turbomachinery. Successful applications of this method include unsteady aerodynamics as well as aeroacoustics and aeroelasticity. Here we focus on forced response due to the interaction of neighboring blade rows. In the CFD-based design and optimization of turbomachinery components it is often helpful to be able to compute not only the objective values — e.g. performance data of a component — themselves, but also their sensitivities with respect to variations of the geometry. An efficient way to compute such sensitivities for a large number of geometric changes is the application of the adjoint method. While this is frequently used in the context of steady CFD, it becomes prohibitively expensive for unsteady simulations in the time domain. For unsteady methods in the frequency domain, the use of adjoint solvers is feasible, but still challenging. The present approach employs the reverse mode of algorithmic differentiation (AD) to construct a discrete adjoint of an existing harmonic balance solver in the framework of an industrially applied CFD code. The paper discusses implemen-tational issues as well as the performance of the adjoint solver, in particular regarding memory requirements. The presented method is applied to compute the sensitivities of aeroelastic objectives with respect to geometric changes in a turbine stage.

scholarly journals Improving the FLORIS wind plant model for compatibility with gradient-based optimization

2017 ◽  
Vol 41 (5) ◽  
pp. 313-329 ◽  
Author(s):  
Jared J Thomas ◽  
Pieter MO Gebraad ◽  
Andrew Ning
Keyword(s):  
Steady State ◽  
Wind Turbine ◽  
Case Studies ◽  
Wind Farm ◽  
Optimization Problems ◽  
Algorithmic Differentiation ◽  
Function Calls ◽  
Gradient Based ◽  
Wake Model ◽  
Yaw Angle

The FLORIS (FLOw Redirection and Induction in Steady-state) model, a parametric wind turbine wake model that predicts steady-state wake characteristics based on wind turbine position and yaw angle, was developed for optimization of control settings and turbine locations. This article provides details on changes made to the FLORIS model to make the model more suitable for gradient-based optimization. Changes to the FLORIS model were made to remove discontinuities and add curvature to regions of non-physical zero gradient. Exact gradients for the FLORIS model were obtained using algorithmic differentiation. A set of three case studies demonstrate that using exact gradients with gradient-based optimization reduces the number of function calls by several orders of magnitude. The case studies also show that adding curvature improves convergence behavior, allowing gradient-based optimization algorithms used with the FLORIS model to more reliably find better solutions to wind farm optimization problems.

scholarly journals On the Use of Recursive Evaluation of Derivatives and Padé Approximation to Solve the Blasius Problem

2016 ◽  
Vol 2016 ◽  
pp. 1-5
Author(s):  
Asai Asaithambi
Keyword(s):  
Differential Equation ◽  
Computational Effort ◽  
Navier Stokes ◽  
Series Solutions ◽  
Third Order ◽  
Navier Stokes Equation ◽  
Order Problem ◽  
Algorithmic Differentiation ◽  
Blasius Problem ◽  
Recursive Evaluation

The Blasius problem is one of the well-known problems in fluid mechanics in the study of boundary layers. It is described by a third-order ordinary differential equation derived from the Navier-Stokes equation by a similarity transformation. Crocco and Wang independently transformed this third-order problem further into a second-order differential equation. Classical series solutions and their Padé approximants have been computed. These solutions however require extensive algebraic manipulations and significant computational effort. In this paper, we present a computational approach using algorithmic differentiation to obtain these series solutions. Our work produces results superior to those reported previously. Additionally, using increased precision in our calculations, we have been able to extend the usefulness of the method beyond limits where previous methods have failed.

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