Related papers: Instance-optimal goal-oriented adaptivity
In this work, we develop an adaptive algorithm for the efficient numerical solution of the minimum compliance problem in topology optimization. The algorithm employs the phase field approximation and continuous density field. The adaptive…
We present a powerful general framework for designing data-dependent optimization algorithms, building upon and unifying recent techniques in adaptive regularization, optimistic gradient predictions, and problem-dependent randomization. We…
In this paper, we analyze the convergence and optimality of a standard adaptive nonconforming linear element method for the Stokes problem. After establishing a special quasi--orthogonality property for both the velocity and the pressure in…
In this paper, we present a unified analysis of both convergence and optimality of adaptive mixed finite element methods for a class of problems when the finite element spaces and corresponding a posteriori error estimates under…
We consider a linear elliptic PDE and a quadratic goal functional. The goal-oriented adaptive FEM algorithm (GOAFEM) solves the primal as well as a dual problem, where the goal functional is always linearized around the discrete primal…
We study the problem of causal structure learning when the experimenter is limited to perform at most $k$ non-adaptive experiments of size $1$. We formulate the problem of finding the best intervention target set as an optimization problem,…
We consider linear reaction-diffusion equations posed on unbounded domains, and discretized by adaptive Lagrange finite elements. To obtain finite-dimensional spaces, it is necessary to introduce a truncation boundary, whereby only a…
In this work, we apply multi-goal oriented error estimation to the finite element method. In particular, we use the dual weighted residual method and apply it to a model problem. This model problem consist of locally different coercive…
We consider finite element approximations of ill-posed elliptic problems with conditional stability. The notion of {\emph{optimal error estimates}} is defined including both convergence with respect to mesh parameter and perturbations in…
In this paper, we study the non-monotone adaptive submodular maximization problem subject to a cardinality constraint. We first revisit the adaptive random greedy algorithm proposed in \citep{gotovos2015non}, where they show that this…
This paper is devoted to the convergence and optimality analysis of the adaptive Morley element method for the fourth order elliptic problem. A new technique is developed to establish a quasi-orthogonality which is crucial for the…
In this paper we prove the optimal convergence of a standard adaptive scheme based on edge finite elements for the approximation of the solutions of the eigenvalue problem associated with Maxwell's equations. The proof uses the known…
In this paper, we discuss adaptive approximations of an elliptic eigenvalue optimization problem in a phase-field setting by a conforming finite element method. An adaptive algorithm is proposed and implemented in several two dimensional…
With this paper, we contribute to the growing research area of feature-based analysis of bio-inspired computing. In this research area, problem instances are classified according to different features of the underlying problem in terms of…
We consider goal-oriented optimal design of experiments for infinite-dimensional Bayesian linear inverse problems governed by partial differential equations (PDEs). Specifically, we seek sensor placements that minimize the posterior…
In this work, we derive a reliable and efficient residual-typed error estimator for the finite element approximation of a 2d cathodic protection problem governed by a steady-state diffusion equation with a nonlinear boundary condition. We…
The purpose of this work is the design and analysis of a reliable and efficient a posteriori error estimator for the so-called pointwise tracking optimal control problem. This linear-quadratic optimal control problem entails the…
We extend the ideas of Diening, Kreuzer, and Stevenson [Instance optimality of the adaptive maximum strategy, Found. Comput. Math. (2015)], from conforming approximations of the Poisson problem to nonconforming Crouzeix-Raviart…
Modern large-scale statistical models require to estimate thousands to millions of parameters. This is often accomplished by iterative algorithms such as gradient descent, projected gradient descent or their accelerated versions. What are…
This paper presents a new parameter estimation algorithm for the adaptive control of a class of time-varying plants. The main feature of this algorithm is a matrix of time-varying learning rates, which enables parameter estimation error…