相关论文: Automated shape differentiation in the Unified For…
We introduce new results about the shape derivatives of scalar- and vector-valued functions, extending the results from (Dogan-Nochetto 2012) to more general surface energies. They consider surface energies defined as integrals over…
Automatic differentiation is everywhere, but there exists only minimal documentation of how it works in complex arithmetic beyond stating "derivatives in $\mathbb{C}^d$" $\cong$ "derivatives in $\mathbb{R}^{2d}$" and, at best, shallow…
This paper introduces a new approach for the computation of electromagnetic field derivatives, up to any order, with respect to the material and geometric parameters of a given geometry, in a single Finite-Difference Time-Domain (FDTD)…
Derivatives play a critical role in computational statistics, examples being Bayesian inference using Hamiltonian Monte Carlo sampling and the training of neural networks. Automatic differentiation is a powerful tool to automate the…
For an educational purpose we develop the Python package AutoFreeFem which generates all ingredients for shape optimization with non-linear multi-physics in FreeFEM++ and also outputs the expressions for use in LaTex. As an input, the…
Shape optimization approaches to inverse design offer low-dimensional, physically-guided parameterizations of structures by representing them as combinations of shape primitives. However, on discretized rectilinear simulation grids,…
We propose a new approach to heap analysis through an abstract domain of automata, called automatic shapes. The abstract domain uses a particular kind of automata, called quantified data automata on skinny trees (QSDAs), that allows to…
In this short note, we propose an unified method to derive formulas for derivations conjugated by exponential functions on an almost complex manifold. In v3, we corrected some mistakes in previous versions.
We aim at computing the derivative of the solution to a parametric optimization problem with respect to the involved parameters. For a class broader than that of strongly convex functions, this can be achieved by automatic differentiation…
Building on the observation that reverse-mode automatic differentiation (AD) -- a generalisation of backpropagation -- can naturally be expressed as pullbacks of differential 1-forms, we design a simple higher-order programming language…
We show how to use extended word series in the reduction of continuous and discrete dynamical systems to normal form and in the computation of formal invariants of motion in Hamiltonian systems. The manipulations required involve complex…
A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of multivector and multiform fields is presented using algebraic and analytical tools developed in previous papers.
Weighted pushdown automata (WPDAs) are at the core of many natural language processing tasks, like syntax-based statistical machine translation and transition-based dependency parsing. As most existing dynamic programming algorithms are…
We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse…
Extracting finite state automata (FSAs) from black-box models offers a powerful approach to gaining interpretable insights into complex model behaviors. To support this pursuit, we present a weighted variant of Angluin's (1987)…
This contribution proposes a new formulation to efficiently compute directional derivatives of order one to fourth. The formulation is based on automatic differentiation implemented with dual numbers. Directional derivatives are particular…
A study of assisted problem solving formalized via decompositions of deterministic finite automata is initiated. The landscape of new types of decompositions of finite automata this study uncovered is presented. Languages with various…
In model-driven engineering (MDE), UML class diagrams serve as a way to plan and communicate between developers. However, it is complex and resource-consuming. We propose an automated approach for the extraction of UML class diagrams from…
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…
This article deals with a particular class of shape and topology optimization problems: the optimized design is a region $G$ of the boundary $\partial \Omega$ of a given domain $\Omega$, which supports a particular type of boundary…