Related papers: Adjoint approach to calculating shape gradients fo…
The goal of this paper is to give a comprehensive and short review on how to compute the first and second order topological derivative and potentially higher order topological derivatives for PDE constrained shape functionals. We employ the…
It is common to manufacture an object by decomposing it into parts that can be assembled. This decomposition is often required by size limits of the machine, the complex structure of the shape, etc. To make it possible to easily assemble…
In general, standard necessary optimality conditions cannot be formulated in a straightforward manner for semi-smooth shape optimization problems. In this paper, we consider shape optimization problems constrained by variational…
An adjoint method to calculate the gradient of island width in stellarators is presented and applied to a set of magnetic field configurations. The underlying method of calculation of the island width is that of Cary & Hanson (1991) (with a…
An adjoint-based shape optimization method for solid bodies subjected to both rarefied and continuum gas flows is proposed. The gas-kinetic BGK equation with the diffuse-reflection boundary condition is used to describe the multiscale gas…
Momentum-based gradients are essential for optimizing advanced machine learning models, as they not only accelerate convergence but also advance optimizers to escape stationary points. While most state-of-the-art momentum techniques utilize…
This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifically, we address the computation of geodesics and geodesic…
Seismic traveltime tomography represents a popular and useful tool for unravelling the structure of the subsurface across the scales. In this work we address the case where the forward model is represented by the eikonal equation and derive…
In this work, the role which three-dimensional shaping plays in the generation of rotational transform in toroidal magnetically confinement devices is explored. The susceptance matrix as defined by Strand & Houlberg (2001) is presented and…
Multivariate functions encountered in high-dimensional uncertainty quantification problems often vary most strongly along a few dominant directions in the input parameter space. We propose a gradient-based method for detecting these…
Gradient methods are widely used in optimization problems. In practice, while the smoothness parameter can be estimated utilizing techniques such as backtracking, estimating the strong convexity parameter remains a challenge; moreover, even…
This work is motivated by the monitoring of conductive clogging deposits in steam generator at the level of support plates. One would like to use monoaxial coils measurements to obtain estimates on the clogging volume. We propose a 3D shape…
In structural optimization, both parameters and shape are relevant for the model performance. Yet, conventional optimization techniques usually consider either parameters or the shape separately. This work addresses this problem by…
The development of inverse design, where computational optimization techniques are used to design devices based on certain specifications, has led to the discovery of many compact, non-intuitive structures with superior performance. Among…
Working within the class of piecewise constant conductivities, the inverse problem of electrical impedance tomography can be recast as a shape optimization problem where the discontinuity interface is the unknown. Using Gr\"oger's…
We introduce a new approach for estimating the 3D pose and the 3D shape of an object from a single image. Given a training set of view exemplars, we learn and select appearance-based discriminative parts which are mapped onto the 3D model…
A range of optimization cases of two-dimensional Stefan problems, solved using a tracking-type cost-functional, is presented. A level set method is used to capture the interface between the liquid and solid phases and an immersed boundary…
A variational approach to the reconstruction of a shape (2D simple manifolds) as triangulated surface from given level set using shape gradients is presented. It involves an energy functional that depends on the local shape characteristics…
Understanding how the release of stored magnetic energy contributes to the generation of non-thermal high energy particles during solar flares is an important open problem in solar physics. Magnetic reconnection plays a fundamental role in…
This study demonstrates how the adjoint-based framework traditionally used to compute gradients in PDE optimization problems can be extended to handle general constraints on the state variables. This is accomplished by constructing a…