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This paper presents a novel Differential Evolution algorithm for protein folding optimization that is applied to a three-dimensional AB off-lattice model. The proposed algorithm includes two new mechanisms. A local search is used to improve…
We propose and analyze novel adaptive algorithms for the numerical solution of elliptic partial differential equations with parametric uncertainty. Four different marking strategies are employed for refinement of stochastic Galerkin finite…
We propose a randomized a posteriori error estimator for reduced order approximations of parametrized (partial) differential equations. The error estimator has several important properties: the effectivity is close to unity with prescribed…
We present an a posteriori error estimate based on equilibrated stress reconstructions for the finite element approximation of a unilateral contact problem with weak enforcement of the contact conditions. We start by proving a guaranteed…
This paper is concerned with a posteriori error bounds for linear transport equations and related questions of contriving corresponding adaptive solution strategies in the context of Discontinuous-Petrov-Galerkin schemes. After indicating…
In this paper we present a new family of rules for numerical integration. This family has up to half the error of the widely used Newton-Cotes rules when a sufficient number of points is evaluated and also much better numerical stability…
A nonlinear adaptive procedure for optimising both the schemes in time and space is proposed in view of increasing the numerical efficiency and reducing the computational time. The method is based on a four-parameter family of schemes we…
In this paper, we propose and analyze a fast two-point gradient algorithm for solving nonlinear ill-posed problems, which is based on the sequential subspace optimization method. A complete convergence analysis is provided under the…
We present an iterative inverse reinforcement learning algorithm to infer optimal cost functions in continuous spaces. Based on a popular maximum entropy criteria, our approach iteratively finds a weight improvement step and proposes a…
In this paper, based on the combination of tensor neural network and a posteriori error estimator, a novel type of machine learning method is proposed to solve high-dimensional boundary value problems with homogeneous and non-homogeneous…
This paper is concerned with a numerical solution to the scattering of a time-harmonic electromagnetic wave by a bounded and impenetrable obstacle in three dimensions. The electromagnetic wave propagation is modeled by a boundary value…
First order optimization algorithms play a major role in large scale machine learning. A new class of methods, called adaptive algorithms, were recently introduced to adjust iteratively the learning rate for each coordinate. Despite great…
We derive an anisotropic a posteriori error estimate for the adaptive conforming Virtual Element approximation of a paradigmatic two-dimensional elliptic problem. In particular, we introduce a quasi-interpolant operator and exploit its…
We discuss adaptive mesh point selection for the solution of scalar IVPs. We consider a method that is optimal in the sense of the speed of convergence, and aim at minimizing the local errors. Although the speed of convergence cannot be…
We revisit adaptive time stepping, one of the classical topics of numerical analysis and computational engineering. While widely used in application and subject of many theoretical works, a complete understanding is still missing. Apart…
Automatic algorithms attempt to provide approximate solutions that differ from exact solutions by no more than a user-specified error tolerance. This paper describes an automatic, adaptive algorithm for approximating the solution to a…
We propose and analyze a posteriori error estimators for an optimal control problem that involves an elliptic partial differential equation as state equation and a control variable that enters the state equation as a coefficient; pointwise…
In this paper we propose third-order methods for composite convex optimization problems in which the smooth part is a three-times continuously differentiable function with Lipschitz continuous third-order derivatives. The methods are…
This work aims to introduce a heuristic timestep-adaptive algorithm for Computational Fluid Dynamics (CFD) and Fluid-Structure Interaction (FSI) problems where the flow is dominated by the pressure. In such scenarios, many time-adaptive…
We develop proper correction formulas at the starting $k-1$ steps to restore the desired $k^{\rm th}$-order convergence rate of the $k$-step BDF convolution quadrature for discretizing evolution equations involving a fractional-order…