Related papers: Causality and Bayesian network PDEs for multiscale…

Equations governing physico-chemical processes are usually known at microscopic spatial scales, yet one suspects that there exist equations, e.g. in the form of Partial Differential Equations (PDEs), that can explain the system evolution at…

In this article, we present a novel data assimilation strategy in pore-scale imaging and demonstrate that this makes it possible to robustly address reactive inverse problems incorporating Uncertainty Quantification (UQ). Pore-scale…

We discuss a Bayesian formulation to coarse-graining (CG) of PDEs where the coefficients (e.g. material parameters) exhibit random, fine scale variability. The direct solution to such problems requires grids that are small enough to resolve…

In the estimation of the causal effect under linear Structural Causal Models (SCMs), it is common practice to first identify the causal structure, estimate the probability distributions, and then calculate the causal effect. However, if the…

Although propensity scores have been central to the estimation of causal effects for over 30 years, only recently has the statistical literature begun to consider in detail methods for Bayesian estimation of propensity scores and causal…

Although tissues are usually studied in isolation, this situation rarely occurs in biology, as cells, tissues, and organs, coexist and interact across scales to determine both shape and function. Here, we take a quantitative approach…

Correlations between fundamental microscopic properties computable from first principles, which we term canonical properties, and complex large-scale quantities of interest (QoIs) provide an avenue to predictive materials discovery. We…

We develop Bayesian nonparametric models for spatially indexed data of mixed type. Our work is motivated by challenges that occur in environmental epidemiology, where the usual presence of several confounding variables that exhibit complex…

This paper provides a critical review of the Bayesian perspective of causal inference based on the potential outcomes framework. We review the causal estimands, identification assumptions, the general structure of Bayesian inference of…

Earthquake-induced secondary ground failure hazards, such as liquefaction and landslides, result in catastrophic building and infrastructure damage as well as human fatalities. To facilitate emergency responses and mitigate losses, the U.S.…

Conceptualizing a porous media as a network of conductors sets a compromise between the oversimplifying conceptualization of the media as a bundle of capillary tubes and the computationally expensive and unobtainable detailed description of…

Existing model validation studies in geoscience often disregard or partly account for uncertainties in observations, model choices, and input parameters. In this work, we develop a statistical framework that incorporates a probabilistic…

In this paper we address the problem of learning the structure of a Bayesian network in domains with continuous variables. This task requires a procedure for comparing different candidate structures. In the Bayesian framework, this is done…

Recent technological advances have made it possible to simultaneously measure multiple protein activities at the single cell level. With such data collected under different stimulatory or inhibitory conditions, it is possible to infer the…

Machine Learning tools are nowadays widely applied extensively to the prediction of the properties of molecular materials, using datasets extracted from high-throughput computational models. In several cases of scientific and technological…

We study the significance of non-Gaussianity in the likelihood of weak lensing shear two-point correlation functions, detecting significantly non-zero skewness and kurtosis in one-dimensional marginal distributions of shear two-point…

Modeling uncertainty in deep neural networks, despite recent important advances, is still an open problem. Bayesian neural networks are a powerful solution, where the prior over network weights is a design choice, often a normal…

Significant progress has been made for assessing the influence of porosity on the performance metrics for cast components through various modeling techniques. However, a computationally efficient framework to account for porosity with…

Knowledge driven discovery of novel materials necessitates the development of the causal models for the property emergence. While in classical physical paradigm the causal relationships are deduced based on the physical principles or via…

The thesis investigates the flow of non-Newtonian fluids in porous media using pore-scale network modeling. Non-Newtonian fluids show very complex time and strain dependent behavior and may have initial yield stress. Their common feature is…