相关论文: Multi-fidelity uncertainty quantification for homo…

We present a novel approach which aims at high-performance uncertainty quantification for cardiac electrophysiology simulations. Employing the monodomain equation to model the transmembrane potential inside the cardiac cells, we evaluate…

Engineering problems are often characterized by significant uncertainty in their material parameters. A typical example coming from geotechnical engineering is the slope stability problem where the soil's cohesion is modeled as a random…

The efficient approximation of quantity of interest derived from PDEs with lognormal diffusivity is a central challenge in uncertainty quantification. In this study, we propose a multilevel quasi-Monte Carlo framework to approximate…

Uncertainty quantification (UQ) methods for Large Language Models (LLMs) encompass a variety of approaches, with two major types being particularly prominent: information-based, which focus on model confidence expressed as token…

A central challenge in scientific machine learning (ML) is the correct representation of physical systems governed by multi-regime behaviours. In these scenarios, standard data analysis techniques often fail to capture the nature of the…

Microstructural heterogeneity affects the macro-scale behavior of materials. Conversely, load distribution at the macro-scale changes the microstructural response. These up-scaling and down-scaling relations are often modeled using…

Markov chain Monte Carlo (MCMC) is an established approach for uncertainty quantification and propagation in scientific applications. A key challenge in applying MCMC to scientific domains is computation: the target density of interest is…

In this paper, we construct a combined multiscale finite element method (MsFEM) using the Local Orthogonal Decomposition (LOD) technique to solve the multiscale problems which may have singularities in some special portions of the…

Large molecular representation models pre-trained on massive unlabeled data have shown great success in predicting molecular properties. However, these models may tend to overfit the fine-tuning data, resulting in over-confident predictions…

Airfoil icing is a severe safety hazard in aviation and causes power losses on wind turbines. The precise shape of the ice formation is subject to large uncertainties, so uncertainty quantification (UQ) is needed for a reliable prediction…

This paper addresses the efficient solution of linear systems arising from curl-conforming finite element discretizations of $H(\mathrm{curl})$ elliptic problems with heterogeneous coefficients. We first employ the discrete form of a…

In this paper, we provide an analysis of a recently proposed multicontinuum homogenization technique. The analysis differs from those used in classical homogenization methods for several reasons. First, the cell problems in multicontinuum…

Deploying deep learning models in safety-critical applications remains a very challenging task, mandating the provision of assurances for the dependable operation of these models. Uncertainty quantification (UQ) methods estimate the model's…

We design a finite element method (FEM) for a membrane model of liquid crystal polymer networks (LCNs). This model consists of a minimization problem of a non-convex stretching energy. We discuss properties of this energy functional such as…

The recent progress of using graph based encoding of crystal structures for high throughput material property prediction has been quite successful. However, using a single modality model prevents us from exploiting the advantages of an…

Machine learning interatomic potentials (MLIPs) enable accurate atomistic modelling, but reliable uncertainty quantification (UQ) remains elusive. In this study, we investigate two UQ strategies, ensemble learning and D-optimality, within…

In this paper, a validation and uncertainty quantification (VUQ) framework for the Eulerian-Eulerian two-fluid-model based multiphase-computational fluid dynamics solver (MCFD) is formulated. The framework aims to answer the question: how…

The crystal plasticity finite element method (CPFEM) is used to investigate the coupling between the cylindrical void growth or collapse and grain refinement in face-centered cubic (FCC) single crystals. A 2D plane strain model with one…

We propose a novel $hp$-multilevel Monte Carlo method for the quantification of uncertainties in the compressible Navier-Stokes equations, using the Discontinuous Galerkin method as deterministic solver. The multilevel approach exploits…

We study statistical model checking of continuous-time stochastic hybrid systems. The challenge in applying statistical model checking to these systems is that one cannot simulate such systems exactly. We employ the multilevel Monte Carlo…