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We study the Bayesian inverse problem for inferring the log-normal slowness function of the eikonal equation given noisy observation data on its solution at a set of spatial points. We study approximation of the posterior probability…
The inhomogeneous cooling state describing the hydrodynamic behavior of a freely evolving granular gas strongly confined between two parallel plates is studied, using a Boltzmann kinetic equation derived recently. By extending the idea of…
Wind tunnel tests of 2D rough cylinders are presented. The goal is to simulate the alternate vortex shedding in flow regimes encountered in wind engineering applications, where the full scale Reynolds number is larger than the one that can…
The statistical evidence (or marginal likelihood) is a key quantity in Bayesian statistics, allowing one to assess the probability of the data given the model under investigation. This paper focuses on refining the power posterior approach…
The main purpose of percolation theory is to model phase transitions in a variety of random systems, which is highly valuable in fields related to materials physics, biology, or otherwise unrelated areas like oil extraction or even quantum…
Bayesian filtering deals with computing the posterior distribution of the state of a stochastic dynamic system given noisy observations. In this paper, motivated by applications in counter-adversarial systems, we consider the following…
Stochastic inverse problems considered in this article consist of estimating the probability distributions of intrinsically random inputs of computer models. These estimations are based on observable outputs affected by model noise, and…
The probability density function (PDF) of the gas density in turbulent supersonic flows is investigated with high-resolution numerical simulations. In a systematic study, we compare the density statistics of compressible turbulence driven…
We introduce a computational framework to statistically infer thermophysical properties of any given wall from in-situ measurements of air temperature and surface heat fluxes. The proposed framework uses these measurements, within a…
Reservoir computing is applied to model the large-scale evolution and the resulting low-order turbulence statistics of a two-dimensional turbulent Rayleigh-B\'{e}nard convection flow at a Rayleigh number ${\rm Ra}=10^7$ and a Prandtl number…
This article delves into a numerical exploration of two-dimensional, incompressible, laminar flow within a confined diverging jet. The study aims to understand how variations in the inlet opening fraction and Reynolds number affect the heat…
We propose a method for estimating the posterior distribution of a standard geostatistical model. After choosing the model formulation and specifying a prior, we use normal mixture densities to approximate the posterior distribution. The…
This paper introduces an approach to endow generative diffusion processes the ability to satisfy and certify compliance with constraints and physical principles. The proposed method recast the traditional sampling process of generative…
In this paper we demonstrate a computational method to solve the inverse scattering problem for a star-shaped, smooth, penetrable obstacle in 2D. Our method is based on classical ideas from computational geometry. First, we approximate the…
In this paper, we study a fast approximate inference method based on expectation propagation for exploring the posterior probability distribution arising from the Bayesian formulation of nonlinear inverse problems. It is capable of…
The convective instability in a plane liquid layer with time-dependent temperature profile is investigated by means of a general method suitable for linear stability analysis of an unsteady basic flow. The method is based on a non-normal…
This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian…
Mantle convection simulations are an essential tool for understanding how rocky planets evolve. However, the poorly known input parameters to these simulations, the non-linear dependence of transport properties on pressure and temperature,…
In this paper, we employ a Bayesian approach to uncertainty quantification of computer simulations used to assess the probability of rare events. As a case study, we assess the reliability of an Earth reentry capsule for sample return…
The linear inverse source and scattering problems are studied from the perspective of compressed sensing, in particular the idea that sufficient incoherence and sparsity guarantee uniqueness of the solution. By introducing the sensor as…