Related papers: Goal-oriented error estimation and adaptivity in M…
Multilevel sampling methods, such as multilevel and multifidelity Monte Carlo, multilevel stochastic collocation, or delayed acceptance Markov chain Monte Carlo, have become standard uncertainty quantification (UQ) tools for a wide class of…
The cost- and memory-efficient numerical simulation of coupled volume-based multi-physics problems like flow, transport, wave propagation and others remains a challenging task with finite element method (FEM) approaches. Goal-oriented space…
Model-based deep reinforcement learning has achieved success in various domains that require high sample efficiencies, such as Go and robotics. However, there are some remaining issues, such as planning efficient explorations to learn more…
A higher-order accurate finite element method is proposed which uses automatically generated meshes based on implicit level-set data for the description of boundaries and interfaces in two and three dimensions. The method is an alternative…
In this paper we propose a method for the construction of locally conservative flux fields from Generalized Multiscale Finite Element Method (GMsFEM) pressure solutions. The flux values are obtained from an element-based postprocessing…
Motivated by modern applications such as computerized adaptive testing, sequential rank aggregation, and heterogeneous data source selection, we study the problem of active sequential estimation, which involves adaptively selecting…
Parameter-efficient fine-tuning (PEFT) has emerged as an effective method for adapting pre-trained language models to various tasks efficiently. Recently, there has been a growing interest in transferring knowledge from one or multiple…
The aggregated unfitted finite element method (AgFEM) is a methodology recently introduced in order to address conditioning and stability problems associated with embedded, unfitted, or extended finite element methods. The method is based…
The challenges in feature selection, particularly in balancing model accuracy, interpretability, and computational efficiency, remain a critical issue in advancing machine learning methodologies. To address these complexities, this study…
The adaptive nonconforming Morley finite element method (FEM) approximates a regular solution to the von K\'{a}rm\'{a}n equations with optimal convergence rates for sufficiently fine triangulations and small bulk parameter in the D\"orfler…
Although the existing max-value entropy search (MES) is based on the widely celebrated notion of mutual information, its empirical performance can suffer due to two misconceptions whose implications on the exploration-exploitation trade-off…
Structural learning, a method to estimate the parameters for discrete energy minimization, has been proven to be effective in solving computer vision problems, especially in 3D scene parsing. As the complexity of the models increases,…
We introduce a new estimator, CRE-GMM, which exploits the correlated random effects (CRE) approach within the generalised method of moments (GMM), specifically applied to level equations, GMM-lev. It has the advantage of estimating the…
Numerical homogenization for mechanical multiscale modeling by means of the finite element method (FEM) is an elegant way of obtaining structure-property relations, if the behavior of the constituents of the lower scale is well understood.…
As cloud services become increasingly integral to modern IT infrastructure, ensuring hardware reliability is essential to sustain high-quality service. Memory failures pose a significant threat to overall system stability, making accurate…
In this paper, we develop an adaptive high-order surface finite element method (FEM) incorporating the spectral deferred correction method for chain contour discretization to solve polymeric self-consistent field equations on general curved…
The Multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty Quantification (UQ) in Partial Differential Equation (PDE) models, combining model computations at different levels…
Pixel- and voxel-based representations of microstructures obtained from tomographic imaging methods is an established standard in computational materials science. The corresponding highly resolved, uniform discretitization in numerical…
In this paper, we analyze the convergence of the operator-compressed multiscale finite element method (OC MsFEM) for Schr\"{o}dinger equations with general multiscale potentials in the semiclassical regime. In the OC MsFEM the multiscale…
We present EDGE, a general-purpose, misconception-aware adaptive learning framework composed of four stages: Evaluate (ability and state estimation), Diagnose (posterior infer-ence of misconceptions), Generate (counterfactual item…