1,111 research outputs found
Sufficient conditions for unique global solutions in optimal control of semilinear equations with nonlinearity
We consider a semilinear elliptic optimal control problem possibly
subject to control and/or state constraints. Generalizing previous work we
provide a condition which guarantees that a solution of the necessary first
order conditions is a global minimum. A similiar result also holds at the
discrete level where the corresponding condition can be evaluated explicitly.
Our investigations are motivated by G\"unter Leugering, who raised the question
whether our previous results can be extended to the nonlinearity
. We develop a corresponding analysis and present several
numerical test examples demonstrating its usefulness in practice
GivEn -- Shape Optimization for Gas Turbines in Volatile Energy Networks
This paper describes the project GivEn that develops a novel multicriteria
optimization process for gas turbine blades and vanes using modern "adjoint"
shape optimization algorithms. Given the many start and shut-down processes of
gas power plants in volatile energy grids, besides optimizing gas turbine
geometries for efficiency, the durability understood as minimization of the
probability of failure is a design objective of increasing importance. We also
describe the underlying coupling structure of the multiphysical simulations and
use modern, gradient based multicriteria optimization procedures to enhance the
exploration of Pareto-optimal solutions
State-of-the-art in aerodynamic shape optimisation methods
Aerodynamic optimisation has become an indispensable component for any aerodynamic design over the past 60 years, with applications to aircraft, cars, trains, bridges, wind turbines, internal pipe flows, and cavities, among others, and is thus relevant in many facets of technology. With advancements in computational power, automated design optimisation procedures have become more competent, however, there is an ambiguity and bias throughout the literature with regards to relative performance of optimisation architectures and employed algorithms. This paper provides a well-balanced critical review of the dominant optimisation approaches that have been integrated with aerodynamic theory for the purpose of shape optimisation. A total of 229 papers, published in more than 120 journals and conference proceedings, have been classified into 6 different optimisation algorithm approaches. The material cited includes some of the most well-established authors and publications in the field of aerodynamic optimisation. This paper aims to eliminate bias toward certain algorithms by analysing the limitations, drawbacks, and the benefits of the most utilised optimisation approaches. This review provides comprehensive but straightforward insight for non-specialists and reference detailing the current state for specialist practitioners
Automatic differentiation in machine learning: a survey
Derivatives, mostly in the form of gradients and Hessians, are ubiquitous in
machine learning. Automatic differentiation (AD), also called algorithmic
differentiation or simply "autodiff", is a family of techniques similar to but
more general than backpropagation for efficiently and accurately evaluating
derivatives of numeric functions expressed as computer programs. AD is a small
but established field with applications in areas including computational fluid
dynamics, atmospheric sciences, and engineering design optimization. Until very
recently, the fields of machine learning and AD have largely been unaware of
each other and, in some cases, have independently discovered each other's
results. Despite its relevance, general-purpose AD has been missing from the
machine learning toolbox, a situation slowly changing with its ongoing adoption
under the names "dynamic computational graphs" and "differentiable
programming". We survey the intersection of AD and machine learning, cover
applications where AD has direct relevance, and address the main implementation
techniques. By precisely defining the main differentiation techniques and their
interrelationships, we aim to bring clarity to the usage of the terms
"autodiff", "automatic differentiation", and "symbolic differentiation" as
these are encountered more and more in machine learning settings.Comment: 43 pages, 5 figure
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