相关论文: Pre-Shape Calculus: Foundations and Application to…
Shape priors have long been known to be effective when reconstructing 3D shapes from noisy or incomplete data. When using a deep-learning based shape representation, this often involves learning a latent representation, which can be either…
The structure theorem of Hadamard-Zol\'esio states that the derivative of a shape functional is a distribution on the boundary of the domain depending only on the normal perturbations of a smooth enough boundary. Actually the domain…
State-of-the-art classical optimization solvers set a high bar for quantum computers to deliver utility in this domain. Here, we introduce a quantum preconditioning approach based on the quantum approximate optimization algorithm. It…
A generalized prefactorization of compact schemes aimed at reducing the stencil and improving the computational efficiency is proposed here in the framework of transport equations. By the prefactorization introduced here, the computational…
When solving partial differential equations using classical schemes such as finite difference or finite volume methods, sufficiently fine meshes and carefully designed schemes are required to achieve high-order accuracy of numerical…
A broad class of hybrid quantum-classical algorithms known as "variational algorithms" have been proposed in the context of quantum simulation, machine learning, and combinatorial optimization as a means of potentially achieving a quantum…
In this paper we study an abstract framework for computing shape derivatives of functionals subject to PDE constraints. We revisit the Lagrangian approach using the implicit function theorem in an abstract setting tailored for applications…
In the context of the optimization of rotating electric machines, many different objective functions are of interest and considering this during the optimization is of crucial importance. While evolutionary algorithms can provide a Pareto…
This paper provides a theoretical and numerical comparison of classical first-order splitting methods for solving smooth convex optimization problems and cocoercive equations. From a theoretical point of view, we compare convergence rates…
Complex non-local behavior makes designing high efficiency and multifunctional metasurfaces a significant challenge. While using libraries of meta-atoms provide a simple and fast implementation methodology, pillar to pillar interaction…
Representing a 3D shape with a set of primitives can aid perception of structure, improve robotic object manipulation, and enable editing, stylization, and compression of 3D shapes. Existing methods either use simple parametric primitives…
Nowadays, high-speed machining is usually used for production of hardened material parts with complex shapes such as dies and molds. In such parts, tool paths generated for bottom machining feature with the conventional parallel plane…
A unified explicit form for difference formulas to approximate the fractional and classical derivatives is presented. The formula gives finite difference approximations for any classical derivatives with a desired order of accuracy at nodal…
Shape optimization under uncertainty (OUU) is computationally intensive for classical PDE-based methods due to the high cost of repeated sampling-based risk evaluation across many uncertainty realizations and varying geometries, while…
The goal of this tutorial is to introduce key models, algorithms, and open questions related to the use of optimization methods for solving problems arising in machine learning. It is written with an INFORMS audience in mind, specifically…
We introduce a Monte Carlo method for computing derivatives of the solution to a partial differential equation (PDE) with respect to problem parameters (such as domain geometry or boundary conditions). Derivatives can be evaluated at…
Classical dimensional analysis is one of the cornerstones of qualitative physics and is also used in the analysis of engineering systems, for example in engineering design. The basic power product relationship in dimensional analysis is…
This article investigates the application of computer vision and graph-based models in solving mesh-based partial differential equations within high-performance computing environments. Focusing on structured, graded structured, and…
The problem of finding of analytical gradients (derivatives over atoms coordinates) of solvation energies can be decomposed on two subtasks: at the first stage we search for parameters of the superficial devices (three coordinates, three…
Recent advances in quantum computers are demonstrating the ability to solve problems at a scale beyond brute force classical simulation. As such, a widespread interest in quantum algorithms has developed in many areas, with optimization…