Related papers: A probabilistic peridynamic framework with an appl…

We introduce a Monte Carlo Virtual Element estimator based on Virtual Element discretizations for stochastic elliptic partial differential equations with random diffusion coefficients. We prove estimates for the statistical approximation…

Peridynamic (PD) theory is significant and promising in engineering and materials science; however, it imposes challenges owing to the enormous computational cost caused by its nonlocality. Our main contribution, which overcomes the…

For many complex simulation tasks spanning areas such as healthcare, engineering, and finance, Monte Carlo (MC) methods are invaluable due to their unbiased estimates and precise error quantification. Nevertheless, Monte Carlo simulations…

Knowing the uncertainty in a prediction is critical when making expensive investment decisions and when patient safety is paramount, but machine learning (ML) models in drug discovery typically provide only a single best estimate and ignore…

Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…

The topic of deep learning has seen a surge of interest in recent years both within and outside of the field of Statistics. Deep models leverage both nonlinearity and interaction effects to provide superior predictions in many cases when…

We propose a variance reduction framework for variational inference using the Multilevel Monte Carlo (MLMC) method. Our framework is built on reparameterized gradient estimators and "recycles" parameters obtained from past update history in…

Numerical modeling of morphodynamics presents significant challenges in engineering due to uncertainties arising from inaccurate inputs, model errors, and limited computing resources. Accurate results are essential for optimizing strategies…

The evolution of local defects such as dislocations and cracks often determines the performance of engineering materials. For a proper description and understanding of these phenomena, one needs to descend to a very small scale, at which…

Parameter inference and uncertainty quantification are important steps when relating mathematical models to real-world observations, and when estimating uncertainty in model predictions. However, methods for doing this can be…

Computing risk measures of a financial portfolio comprising thousands of derivatives is a challenging problem because (a) it involves a nested expectation requiring multiple evaluations of the loss of the financial portfolio for different…

We quantify uncertainties in the location and magnitude of extreme pressure spots revealed from large scale multi-phase flow simulations of cloud cavitation collapse. We examine clouds containing 500 cavities and quantify uncertainties…

We consider the application of multilevel Monte Carlo methods to steady state Darcy flow in a random porous medium, described mathematically by elliptic partial differential equations with random coefficients. The levels in the multilevel…

This paper proposes a novel robust Model Predictive Control (MPC) scheme for linear discrete-time systems affected by model uncertainty described by interval matrices. The key feature of the proposed method is a bound on the uncertainty…

Accurate simulation of complex physical systems enables the development, testing, and certification of control strategies before they are deployed into the real systems. As simulators become more advanced, the analytical tractability of the…

Given (small amounts of) time-series' data from a high-dimensional, fine-grained, multiscale dynamical system, we propose a generative framework for learning an effective, lower-dimensional, coarse-grained dynamical model that is predictive…

This work presents an efficient approach for accelerating multilevel Markov Chain Monte Carlo (MCMC) sampling for large-scale problems using low-fidelity machine learning models. While conventional techniques for large-scale Bayesian…

Many large scale problems in computational fluid dynamics such as uncertainty quantification, Bayesian inversion, data assimilation and PDE constrained optimization are considered very challenging computationally as they require a large…

Turbulent flows play an important role in many scientific and technological design problems. Both Sub-Grid Scale (SGS) models in Large Eddy Simulations (LES) and Reynolds Averaged Navier Stokes (RANS) based modeling will require turbulence…

The class of $\alpha$-stable distributions enjoys multiple practical applications in signal processing, finance, biology and other areas because it allows to describe interesting and complex data patterns, such as asymmetry or heavy tails,…