## UQ framework for catalytic active site identification

A comprehensive UQ framework is developed to discriminate among probabilistic models corresponding to each candidate active site. Each probabilistic model consists of a microkinetic model, a probabilistic discrepancy model to account for errors between model predictions and observations, and a prior distribution over the intermediates, transition states, as well as gas molecule corrections and model Read More ...

## StackedGP – Stacked Gaussian Process

A network of independently trained Gaussian processes (StackedGP) is introduced to integrate different datasets through model composition, enhance predictions of quantities of interest through a cascade of intermediate predictions, and to propagate uncertainties through emulated dynamical systems driven by uncertain forcing variables. By using analytical first and second-order moments of a Gaussian process with uncertain Read More ...

## EnLLVM – Fast Approximate Bayesian Inference

Approximate Bayesian inference that only requires a small number of samples and can be applied to high-dimensional non-linear systems with non-Gaussian uncertainties. It leverages the machinery behind the linear latent variable models which provide significant computational speed-up. Works with intractable likelihood functions and the model can be absorbed implicitly and reflected in the uncertainty of Read More ...

## Approximate Bayesian Sensor Placement in High Dimensions

Since the cost of installing and maintaining sensors is usually high, sensor locations are always strategically selected. For those aiming at inferring certain quantities of interest (QoI), it is desirable to explore the dependency between sensor measurements and QoI. One of the most popular metric for the dependency is mutual information which naturally measures how Read More ...

## Structural Uncertainty Modeling and Predictive Validation of Unobserved Quantities

Current state-of-the-art strategies in calibrating models rely on the Kennedy and O’Hagan framework based on the external discrepancy, which fall short in providing a comprehensive uncertainty representation that can support reliable predictions of unobserved quantities of interest (QoI) and usually yield biased estimates of physical parameters. The proposed internal discrepancy representation is based on the Read More ...

## Information-Theoretic Experimental Design

We emphasise that the optimal experimental design can be obtained as a result of an information theoretic sensitivity analysis. Thus, the preferred design is where the statistical dependence between the model parameters and observables is the highest possible. It is also shown that the sequential Bayesian analysis used in the experimental design can be useful Read More ...

## Optimal Data Split for Model Validation

The decision to incorporate cross-validation into validation processes of mathematical models raises an immediate question – how should one partition the data into calibration and validation sets? We answer this question systematically: we present an algorithm to find the optimal partition of the data subject to certain constraints. While doing this, we address two critical Read More ...

## Predictive Model Selection

A predictive Bayesian model selection approach is presented to discriminate coupled models used to predict an unobserved quantity of interest (QoI). The need for accurate predictions arises in a variety of critical applications such as climate, aerospace and defense. A model problem is introduced to study the prediction yielded by the coupling of two physics/sub-components. Read More ...

## Adaptive Gaussian Mixture Models for Uncertainty Propagation and Stochastic Filtering

This is a novel method for accurate uncertainty propagation through a general nonlinear system. The basic idea of this approach is to approximate the state probability density function (pdf) by a weighted average of sufficient number of distinct local Gaussian density functions. In conventional methods, both the weights of the components and the number of Read More ...

## Decision-Centric Uncertainty Propagation

This work is concerned with providing a better approximation to the probability density function by incorporating contextual loss information, here a region of interest in state space, held by the decision maker into the uncertainty propagation process. Due to the approximations used in propagating the conditional probability density function it may happen that no or Read More ...

## Hybrid Aleatory-Epistemic Uncertainty Propagation

A new algorithm based on polynomial chaos is derived to propagate hybrid aleatory-epistemic uncertainty modeled using Dempster-Shafer structures on probability measures. This way we are able to model the ignorance when the knowledge about the system is incomplete. Aleatory uncertainty is characterized by randomness and epistemic uncertainty is characterized by the lack of knowledge. In Read More ...

## Data Assimilation and Source Estimation for CBRN incidents

CBRN = Chemical, Biological, Radiological and Nuclear. The objective is the systematic study and elucidation of the basic physico-mathematical principles underlying data assimilation in the chem-bio context, that is, the blending of chem-bio dispersion forecasts with uncertain sensor data. This problem is mathematically characterized by high dimensionality, profoundly nonlinear models, and uncertainties with non-Gaussian non-stationary Read More ...