Related papers: Multi-fidelity uncertainty quantification for homo…
In traffic flow modeling, incorporating uncertainty is crucial for accurately capturing the complexities of real-world scenarios. In this work we focus on kinetic models of traffic flow, where a key step is to design effective numerical…
Universal machine learning interatomic potentials (uMLIPs) have emerged as powerful tools for accelerating atomistic simulations, offering scalable and efficient modeling with accuracy close to quantum calculations. However, their…
While multilevel Monte Carlo (MLMC) methods for the numerical approximation of partial differential equations with random coefficients enjoy great popularity, combinations with spatial adaptivity seem to be rare. We present an adaptive MLMC…
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…
We introduce a multi-fidelity estimator of covariance matrices that employs the log-Euclidean geometry of the symmetric positive-definite manifold. The estimator fuses samples from a hierarchy of data sources of differing fidelities and…
This paper presents a homogenization framework for elastomeric metamaterials exhibiting long-range correlated fluctuation fields. Based on full-scale numerical simulations on a class of such materials, an ansatz is proposed that allows to…
Multi-fidelity Monte Carlo methods leverage low-fidelity and surrogate models for variance reduction to make tractable uncertainty quantification even when numerically simulating the physical systems of interest with high-fidelity models is…
A ubiquitous challenge in design space exploration or uncertainty quantification of complex engineering problems is the minimization of computational cost. A useful tool to ease the burden of solving such systems is model reduction. This…
In this paper, we address the numerical homogenization approximation of a free-boundary dam problem posed in a heterogeneous media. More precisely, we propose a generalized multiscale finite element (GMsFEM) method for the heterogeneous dam…
We interpret uncertainty in a model for seismic wave propagation by treating the model parameters as random variables, and apply the Multilevel Monte Carlo (MLMC) method to reduce the cost of approximating expected values of selected,…
Emergence of artificial intelligence techniques in biomedical applications urges the researchers to pay more attention on the uncertainty quantification (UQ) in machine-assisted medical decision making. For classification tasks, prior…
Treating uncertainties in models is essential in many fields of science and engineering. Uncertainty quantification (UQ) on complex and computationally costly numerical models necessitates a combination of efficient model solvers, advanced…
We consider the problem of modeling heterogeneous materials where micro-scale dynamics and interactions affect global behavior. In the presence of heterogeneities in material microstructure it is often impractical, if not impossible, to…
An efficient and reliable stress computation algorithm is presented, which is based on implicit integration of the local evolution equations of multiplicative finite-strain plasticity/viscoplasticity. The algorithm is illustrated by an…
Reliable uncertainty quantification (UQ) in machine learning (ML) regression tasks is becoming the focus of many studies in materials and chemical science. It is now well understood that average calibration is insufficient, and most studies…
We consider the computational efficiency of Monte Carlo (MC) and Multilevel Monte Carlo (MLMC) methods applied to partial differential equations with random coefficients. These arise, for example, in groundwater flow modelling, where a…
Deep learning models for semantic segmentation are prone to poor performance in real-world applications due to the highly challenging nature of the task. Model uncertainty quantification (UQ) is one way to address this issue of lack of…
In this paper, we develop the constraint energy minimization generalized multiscale finite element method (CEM-GMsFEM) in mixed formulation applied to parabolic equations with heterogeneous diffusion coefficients. The construction of the…
Neural networks (NNs) are currently changing the computational paradigm on how to combine data with mathematical laws in physics and engineering in a profound way, tackling challenging inverse and ill-posed problems not solvable with…
Monte Carlo techniques play a central role in statistical mechanics approaches for connecting macroscopic thermodynamic and kinetic properties to the electronic structure of a material. This paper describes the implementation of Monte Carlo…