Related papers: Dynamic Data-driven Bayesian GMsFEM
Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…
Nonlinear differential equations (DEs) are used in a wide range of scientific problems to model complex dynamic systems. The differential equations often contain unknown parameters that are of scientific interest, which have to be estimated…
Identifying a low-dimensional informed parameter subspace offers a viable path to alleviating the dimensionality challenge in the sampled-based solution to large-scale Bayesian inverse problems. This paper introduces a novel gradient-based…
Trial-based economic evaluations are typically performed on cross-sectional variables, derived from the responses for only the completers in the study, using methods that ignore the complexities of utility and cost data (e.g. skewness and…
Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they allow for the quantification of uncertainties and enable…
In this paper, we propose a multiscale method for the Darcy-Forchheimer model in highly heterogeneous porous media. The problem is solved in the framework of generalized multiscale finite element methods (GMsFEM) combined with a multipoint…
This paper proposes a non-intrusive, data-driven reduced-order modeling framework for stochastic optimal control problems governed by partial differential equations. The control problem is formulated with a quadratic cost functional and…
In this paper, we propose oversampling strategies in the Generalized Multiscale Finite Element Method (GMsFEM) framework. The GMsFEM, which has been recently introduced in [12], allows solving multiscale parameter-dependent problems at a…
Degradation data are essential for determining the reliability of high-end products and systems, especially when covering multiple degradation characteristics (DCs). Modern degradation studies not only measure these characteristics but also…
Accurate numerical simulations of interaction between fluid and solid play an important role in applications. The task is challenging in practical scenarios as the media are usually highly heterogeneous with very large contrast. To overcome…
In many scientific fields, the generation and evolution of data are governed by partial differential equations (PDEs) which are typically informed by established physical laws at the macroscopic level to describe general and predictable…
Analysis of heterogeneous patterns in complex spatio-temporal data finds usage across various domains in applied science and engineering, including training autonomous vehicles to navigate in complex traffic scenarios. Motivated by…
In this paper, we consider the numerical solution of poroelasticity problems that are of Biot type and develop a general algorithm for solving coupled systems. We discuss the challenges associated with mechanics and flow problems in…
In the presence of modeling errors, the mainstream Bayesian methods seldom give a realistic account of uncertainties as they commonly underestimate the inherent variability of parameters. This problem is not due to any misconception in the…
Well-established methods for the solution of stochastic partial differential equations (SPDEs) typically struggle in problems with high-dimensional inputs/outputs. Such difficulties are only amplified in large-scale applications where even…
In this paper, we consider local multiscale model reduction for problems with multiple scales in space and time. We developed our approaches within the framework of the Generalized Multiscale Finite Element Method (GMsFEM) using space-time…
We develop a Bayesian graphical modeling framework for functional data for correlated multivariate random variables observed over a continuous domain. Our method leads to graphical Markov models for functional data which allows the graphs…
In this paper, we propose a multiscale empirical interpolation method for solving nonlinear multiscale partial differential equations. The proposed method combines empirical interpolation techniques and local multiscale methods, such as the…
Dynamic Bayesian networks (DBNs) are increasingly used in healthcare due to their ability to model complex temporal relationships in patient data while maintaining interpretability, an essential feature for clinical decision-making.…
In this paper, we develop a multiscale finite element method for solving flows in fractured media. Our approach is based on Generalized Multiscale Finite Element Method (GMsFEM), where we represent the fracture effects on a coarse grid via…