Related papers: A Posteriori Error Estimates for Adaptive QM/MM Co…
In this paper, we present several new a posteriori error estimators and two adaptive mixed finite element methods \textsf{AMFEM1} and \textsf{AMFEM2} for the Hodge Laplacian problem in finite element exterior calculus. We prove that…
This work reviews goal-oriented a posteriori error control, adaptivity and solver control for finite element approximations to boundary and initial-boundary value problems for stationary and non-stationary partial differential equations,…
The adaptive perturbation chooses a non-standard decomposition. The Hamiltonian becomes a sum of solvable and perturbation parts. We calculate the spectrum using the adaptive perturbation method at the leading-order to compare to numerical…
This work proposes an adaptive framework to solve a robust structural shape optimization problem governed by linear elasticity models that account for uncertainties in the loading and material inputs. A posteriori error estimators are…
This paper develops a novel sequential Monte Carlo (SMC) approach for joint state and parameter estimation that can deal efficiently with abruptly changing parameters which is a common case when tracking maneuvering targets. The approach…
Understanding the theoretical capabilities and limitations of quantum machine learning (QML) models to solve machine learning tasks is crucial to advancing both quantum software and hardware developments. Similarly to the classical setting,…
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 the a posteriori error estimation for convection-diffusion-reaction equations in both diffusion-dominated and convection/reaction-dominated regimes. We present an explicit hybrid estimator, which, in each regime, is proved to be…
This work derives a residual-based a posteriori error estimator for reduced models learned with non-intrusive model reduction from data of high-dimensional systems governed by linear parabolic partial differential equations with control…
Recent advances in adaptive Markov chain Monte Carlo (AMCMC) include the need for regional adaptation in situations when the optimal transition kernel is different across different regions of the sample space. Motivated by these findings,…
The recent work [Kurz et al., Numer. Math., 147 (2021)] proposed functional a posteriori error estimates for boundary element methods (BEMs) together with a related adaptive mesh-refinement strategy. Unlike most a posteriori BEM error…
The basis generation in reduced order modeling usually requires multiple high-fidelity large-scale simulations that could take a huge computational cost. In order to accelerate these numerical simulations, we introduce a FOM/ROM hybrid…
In this work we study a residual based a posteriori error estimation for the CutFEM method applied to an elliptic model problem. We consider the problem with non-polygonal boundary and the analysis takes into account the geometry and data…
Inexact alternating direction multiplier methods (ADMMs) are developed for solving general separable convex optimization problems with a linear constraint and with an objective that is the sum of smooth and nonsmooth terms. The approach…
The atomistic-to-continuum (a/c) coupling methods, also known as the quasicontinuum (QC) methods, are a important class of concurrent multisacle methods for modeling and simulating materials with defects. The a/c methods aim to balance the…
Mixed atomistic and continuum methods offer the possibility of carrying out simulations of material properties at both larger length scales and longer times than direct atomistic calculations. The quasi-continuum method links atomistic and…
In this note we address the question of whether any any quantum computational model that allows adaptive measurements can be simulated by a model that allows postselected measurements. We argue in the favor of this question and prove that…
This paper introduces posterior mean matching (PMM), a new method for generative modeling that is grounded in Bayesian inference. PMM uses conjugate pairs of distributions to model complex data of various modalities like images and text,…
We define an a posteriori verification procedure that enables to control and certify PGD-based model reduction techniques applied to parametrized linear elliptic or parabolic problems. Using the concept of constitutive relation error, it…
This work presents a new adaptive approach for the numerical simulation of a phase-field model for fractures in nearly incompressible solids. In order to cope with locking effects, we use a recently proposed mixed form where we have a…