Related papers: Learning Algorithms for Coarsening Uncertainty Spa…
In this work, we present methodologies for the quantification of confidence in bottom-up coarse-grained models for molecular and macromolecular systems. Coarse-graining methods have been extensively used in the past decades in order to…
While deep neural networks have become the go-to approach in computer vision, the vast majority of these models fail to properly capture the uncertainty inherent in their predictions. Estimating this predictive uncertainty can be crucial,…
Although Gaussian processes (GPs) with deep kernels have been successfully used for meta-learning in regression tasks, its uncertainty estimation performance can be poor. We propose a meta-learning method for calibrating deep kernel GPs for…
A stochastic approach based on generalized Polynomial Chaos (gPC) is used to quantify the error in Large-Eddy Simulation (LES) of a spatially-evolving mixing layer flow and its sensitivity to different simulation parameters, viz. the grid…
In this work, we present a novel nonlocal nonlinear coarse grid approximation using a machine learning algorithm. We consider unsaturated and two-phase flow problems in heterogeneous and fractured porous media, where mathematical models are…
Numerical homogenization and multiscale finite element methods construct effective properties on a coarse grid by solving local problems and extracting the average effective properties from these local solutions. In some cases, the…
The local geometrical randomness of metal foams brings complexities to the performance prediction of porous structures. Although the relative density is commonly deemed as the key factor, the stochasticity of internal cell sizes and shapes…
We propose a stochastic multiscale finite element method (StoMsFEM) to solve random elliptic partial differential equations with a high stochastic dimension. The key idea is to simultaneously upscale the stochastic solutions in the physical…
We develop a new coarse-scale approximation strategy for the nonlinear single-continuum Richards equation as an unsaturated flow over heterogeneous non-periodic media, using the online generalized multiscale finite element method (online…
Due to the high computational load of modern numerical simulation, there is a demand for approaches that would reduce the size of discrete problems while keeping the accuracy reasonable. In this work, we present an original algorithm to…
In the present work, a multi-scale framework for neural network enhanced methods is proposed for approximation of function and solution of partial differential equations (PDEs). By introducing the multi-scale concept, the total solution of…
Neural networks predictions are unreliable when the input sample is out of the training distribution or corrupted by noise. Being able to detect such failures automatically is fundamental to integrate deep learning algorithms into robotics.…
We present an ``equation-free'' multiscale approach to the simulation of unsteady diffusion in a random medium. The diffusivity of the medium is modeled as a random field with short correlation length, and the governing equations are cast…
In this paper we use the GeneralizedMultiscale Finite ElementMethod (GMsFEM) framework, introduced in [20], in order to solve nonlinear elliptic equations with high-contrast coefficients. The proposed solution method involves linearizing…
We propose a method for reducing the spatial discretization error of coarse computational fluid dynamics (CFD) problems by enhancing the quality of low-resolution simulations using deep learning. We feed the model with fine-grid data after…
Partial differential equations (PDEs) involving high contrast and oscillating coefficients are common in scientific and industrial applications. Numerical approximation of these PDEs is a challenging task that can be addressed, for example,…
In this paper we consider the numerical upscaling of the Brinkman equation in the presence of high-contrast permeability fields. We develop and analyze a robust and efficient Generalized Multiscale Finite Element Method (GMsFEM) for the…
Due to the wide range of timescales that are present in macromolecular systems, hierarchical multiscale strategies are necessary for their computational study. Coarse-graining (CG) allows to establish a link between different system…
This work is directed to uncertainty quantification of homogenized effective properties for composite materials with complex, three dimensional microstructure. The uncertainties arise in the material parameters of the single constituents as…
Uncertainty quantification is an important and challenging problem in deep learning. Previous methods rely on dropout layers which are not present in modern deep architectures or batch normalization which is sensitive to batch sizes. In…