Related papers: Multigoal-oriented error estimation and mesh adapt…
This work is concerned with the derivation of a robust a posteriori error estimator for a discontinuous Galerkin method discretisation of linear non-stationary convection-diffusion initial/boundary value problems and with the implementation…
We consider the general problem of learning a predictor that satisfies multiple objectives of interest simultaneously, a broad framework that captures a range of specific learning goals including calibration, regret, and multiaccuracy. We…
Motivated by problems in contact mechanics, we propose a duality approach for computing approximations and associated a posteriori error bounds to solutions of variational inequalities of the first kind. The proposed approach improves upon…
Many real world applications can be framed as multi-objective optimization problems, where we wish to simultaneously optimize for multiple criteria. Bayesian optimization techniques for the multi-objective setting are pertinent when the…
This article investigates residual a posteriori error estimates and adaptive mesh refinements for time-dependent boundary element methods for the wave equation. We obtain reliable estimates for Dirichlet and acoustic boundary conditions…
We present a novel technique for amortized posterior estimation using Normalizing Flows trained with likelihood-weighted importance sampling. This approach allows for the efficient inference of theoretical parameters in high-dimensional…
Multi-objective optimization (MOO) aims to optimize multiple, possibly conflicting objectives with widespread applications. We introduce a novel interacting particle method for MOO inspired by molecular dynamics simulations. Our approach…
We recently demonstrated the reduction of the unified continuum and variational multiscale formulation to a computationally efficient fluid-structure interaction (FSI) formulation via three sound modeling assumptions pertaining to the…
Modern techniques for physical simulations rely on numerical schemes and mesh-refinement methods to address trade-offs between precision and complexity, but these handcrafted solutions are tedious and require high computational power.…
A computational approach is introduced for the study of the rheological properties of complex fluids and soft materials. The approach allows for a consistent treatment of microstructure elastic mechanics, hydrodynamic coupling, thermal…
We derive and discuss a posteriori error estimators for Galerkin and collocation IGA boundary element methods for weakly-singular integral equations of the first-kind in 2D. While recent own work considered the Faermann residual error…
In the expanding landscape of AI-enabled robotics, robust quantification of predictive uncertainties is of great importance. Three-dimensional (3D) object detection, a critical robotics operation, has seen significant advancements; however,…
The immersed boundary method is a mathematical framework for modeling fluid-structure interaction. This formulation describes the momentum, viscosity, and incompressibility of the fluid-structure system in Eulerian form, and it uses…
A novel method for complex fluid-structure interaction (FSI) involving large structural deformation and motion is proposed. The new approach is based on a hybrid fluid formulation that combines the advantages of purely Eulerian (fixed-grid)…
We present a scale-bridging approach based on a multi-fidelity (MF) machine-learning (ML) framework leveraging Gaussian processes (GP) to fuse atomistic computational model predictions across multiple levels of fidelity. Through the…
A unified fluid-structure interaction (FSI) formulation is presented for solid, liquid and mixed membranes. Nonlinear finite elements (FE) and the generalized-alpha scheme are used for the spatial and temporal discretization. The membrane…
We present a loosely-coupled partitioned scheme for a benchmark problem in fluid-composite structure interaction. The benchmark problem proposed here consists of an incompressible, viscous fluid interacting with a composite structure that…
This work derives a posteriori error estimate of polygonal finite element methods based on Wachspress barycentric coordinates. In particular, we prove that the classical residual-based a posteriori error estimator is both an upper and lower…
Stochastic gradient methods are scalable for solving large-scale optimization problems that involve empirical expectations of loss functions. Existing results mainly apply to optimization problems where the objectives are one- or two-level…
This work is devoted to the study of a posteriori error estimation and adaptivity in parabolic problems with a particular focus on spatial discontinuous Galerkin (dG) discretisations. We begin by deriving an a posteriori error estimator for…