Related papers: A shape optimization algorithm for cellular compos…
Grids are a general representation for capturing regularly-spaced information, but since they are uniform in space, they cannot dynamically allocate resolution to regions with varying levels of detail. There has been some exploration of…
This article combines shape optimization and homogenization techniques by looking for the optimal design of the microstructure in composite materials and of scaffolds. The development of materials with specific properties is of huge…
This work deals with shape optimization for contact mechanics. More specifically, the linear elasticity model is considered under the small deformations hypothesis, and the elastic body is assumed to be in contact (sliding or with Tresca…
Shape optimization with respect to eigenvalues of a cavity plays an important role in the design of new resonators or in the optimization of existing ones. In our paper, we propose a gradient-based optimization scheme, which we enhance with…
Bilevel optimization enjoys a wide range of applications in emerging machine learning and signal processing problems such as hyper-parameter optimization, image reconstruction, meta-learning, adversarial training, and reinforcement…
In this work we investigate a combination of classical PDE constrained optimization methods and a rounding strategy based on shape optimization for the identification of interfaces. The goal is to identify radioactive regions in a…
We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…
We suggest a novel shape matching algorithm for three-dimensional surface meshes of disk or sphere topology. The method is based on the physical theory of nonlinear elasticity and can hence handle large rotations and deformations.…
We propose in this paper a multilevel correction method to solve optimal control problems constrained by elliptic equations with the finite element method. In this scheme, solving optimization problem on the finest finite element space is…
Neuroscientists fit morphologically and biophysically detailed neuron simulations to physiological data, often using evolutionary algorithms. However, such gradient-free approaches are computationally expensive, making convergence slow when…
We present the design and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations. The method uses local smoothing on the refined part of the mesh. Partitioning is achieved by…
The use of multigrid and related preconditioners with the finite element method is often limited by the difficulty of applying the algorithm effectively to a problem, especially when the domain has a complex shape or adaptive refinement. We…
This investigation is motivated by the problem of optimal design of cooling elements in modern battery systems. We consider a simple model of two-dimensional steady-state heat conduction described by elliptic partial differential equations…
We present an initial implementation of a probabilistic PDE-constrained shape optimization algorithm. Our method is based on a novel probabilistic representation of the shape derivative, which is evaluated using Monte Carlo sampling; and…
Shape optimization based on shape calculus has received a lot of attention in recent years, particularly regarding the development, analysis, and modification of efficient optimization algorithms. In this paper we propose and investigate…
The ability to differentiate through optimization problems has unlocked numerous applications, from optimization-based layers in machine learning models to complex design problems formulated as bilevel programs. It has been shown that…
A wide range of modern science and engineering applications are formulated as optimization problems with a system of partial differential equations (PDEs) as constraints. These PDE-constrained optimization problems are typically solved in a…
This article addresses the research question if and how the finite cell method, an embedded domain finite element method of high order, may be used in the simulation of metal deposition to harvest its computational efficiency. This…
A method of simultaneously optimizing both the structure of neural networks and the connection weights in a single training loop can reduce the enormous computational cost of neural architecture search. We focus on the probabilistic…
We apply an unfitted HDG discretization to a model problem in shape optimization. The method proposed uses a fixed, shape regular, non-geometry conforming mesh and a high order transfer technique to deal with the curved boundaries arising…