Related papers: Robust Hybrid High-Order method on polytopal meshe…

Linear elastic fracture mechanics admit analytic solutions that have low regularity at crack tips. Current numerical methods for partial differential equations (PDEs) of this type suffer from the constraint of such low regularity, and fail…

Hyperparameter optimization (HPO) plays a central role in the automated machine learning (AutoML). It is a challenging task as the response surfaces of hyperparameters are generally unknown, hence essentially a global optimization problem.…

Poisson likelihood models have been prevalently used in imaging, social networks, and time series analysis. We propose fast, simple, theoretically-grounded, and versatile, optimization algorithms for Poisson likelihood modeling. The Poisson…

We propose a high order unfitted finite element method for solving timeharmonic Maxwell interface problems. The unfitted finite element method is based on a mixed formulation in the discontinuous Galerkin framework on a Cartesian mesh with…

We present a multiscale finite element method for a diffusion problem with rough and high contrast coefficients. The construction of the multiscale finite element space is based on the localized orthogonal decomposition methodology and it…

Meshless methods approximate operators in a specific node as a weighted sum of values in its neighbours. Higher order approximations of derivatives provide more accurate solutions with better convergence characteristics, but they come at…

We present HIghly Parallelisable Pareto Optimisation (HIPPO) -- a batch acquisition function that enables multi-objective Bayesian optimisation methods to efficiently exploit parallel processing resources. Multi-Objective Bayesian…

In this paper, we discuss an adaptive hybrid stress finite element method on quadrilateral meshes for linear elasticity problems. To deal with hanging nodes arising in the adaptive mesh refinement, we propose new transition types of hybrid…

In this present paper we consider a full divergence-free of high order virtual finite element algorithm to approximate the stationary inductionless magnetohydrodynamic model on polygonal meshes. More precisely, we choice appropriate virtual…

Electrokinetic phenomena in nanopore sensors and microfluidic devices require accurate simulation of coupled fluid-electrostatic interactions in geometrically complex domains with irregular boundaries and adaptive mesh refinement. We…

We propose a multiscale approach for an elliptic multiscale setting with general unstructured diffusion coefficients that is able to achieve high-order convergence rates with respect to the mesh parameter and the polynomial degree. The…

This contribution presents a hierarchical multigrid approach for the solution of large-scale finite cell problems on both uniform grids and multi-level hp-discretizations. The proposed scheme leverages the hierarchical nature of the basis…

In this paper we propose the first better than second order accurate method in space and time for the numerical solution of the resistive relativistic magnetohydrodynamics (RRMHD) equations on unstructured meshes in multiple space…

In the present work, we consider multi-scale computation and convergence for nonlinear time-dependent thermo-mechanical equations of inhomogeneous shells possessing temperature-dependent material properties and orthogonal periodic…

We consider the problem of distributionally robust multimodal machine learning. Existing approaches often rely on merging modalities on the feature level (early fusion) or heuristic uncertainty modeling, which downplays modality-aware…

Diffusion probabilistic models have set a new standard for generative fidelity but are hindered by a slow iterative sampling process. A powerful training-free strategy to accelerate this process is Schedule Optimization, which aims to find…

Designing high-entropy alloys (HEAs) that are both mechanically hard and possess soft magnetic properties is inherently challenging, as a trade-off is needed for mechanical and magnetic properties. In this study, we optimize HEA…

This work presents a Discrete de Rham (DDR) numerical scheme for solving linear elasticity problems on general polyhedral meshes, with a focus on preventing volumetric locking in the quasi-incompressible regime. The method is formulated as…

In this thesis, we investigate a novel local projection based stabilized conforming virtual element method for the generalized Oseen problem using equal-order element pairs on general polygonal meshes. To ensure the stability, particularly…

This research proposes to use the Moreau-Yosida envelope to stabilize the convergence behavior of bi-level Hyperparameter optimization solvers, and introduces the new algorithm called Moreau-Yosida regularized Hyperparameter Optimization…