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We propose a new time quantifiable Monte Carlo (MC) method to simulate the thermally induced magnetization reversal for an isolated single domain particle system. The MC method involves the determination of density of states, and the use of…
Finite element model updating is challenging because 1) the problem is oftentimes underdetermined while the measurements are limited and/or incomplete; 2) many combinations of parameters may yield responses that are similar with respect to…
The Markov Decision Process (MDP) is a popular framework for sequential decision-making problems, and uncertainty quantification is an essential component of it to learn optimal decision-making strategies. In particular, a Bayesian…
Monte Carlo algorithms are frequently used in atomistic simulations, including for computation of magnetic parameter temperature dependences in multiscale simulations. Even though parallelization strategies for Monte Carlo simulations of…
The study of animal behavioural states inferred through hidden Markov models and similar state switching models has seen a significant increase in popularity in recent years. The ability to account for varying levels of behavioural scale…
The widespread adoption of machine learning surrogate models has significantly improved the scale and complexity of systems and processes that can be explored accurately and efficiently using atomistic modeling. However, the inherently…
Computer models, aiming at simulating a complex real system, are often calibrated in the light of data to improve performance. Standard calibration methods assume that the optimal values of calibration parameters are invariant to the model…
The development of large databases of material properties, together with the availability of powerful computers, has allowed machine learning (ML) modeling to become a widely used tool for predicting material performances. While confidence…
We present new methodologies for Bayesian inference on the rate parameters of a discretely observed continuous-time Markov jump processes with a countably infinite state space. The usual method of choice for inference, particle Markov chain…
The change in materials properties subjected to irradiation by highly energetic particles strongly depends on the irradiation dose rate. Atomistic simulations can in principle be used to predict microstructural evolution where experimental…
The basic problem in equilibrium statistical mechanics is to compute phase space average, in which Monte Carlo method plays a very important role. We begin with a review of nonlocal algorithms for Markov chain Monte Carlo simulation in…
In nuclear reactor system design and safety analysis, the Best Estimate plus Uncertainty (BEPU) methodology requires that computer model output uncertainties must be quantified in order to prove that the investigated design stays within…
Predicting how materials behave under realistic conditions requires understanding the statistical distribution of atomic configurations on crystal lattices, a problem central to alloy design, catalysis, and the study of phase transitions.…
The present paper describes the development of a novel and comprehensive computational framework to simulate solidification problems in materials processing, specifically casting processes. Heat transfer, solidification and fluid flow due…
Bayesian methods which utilize Bayes' theorem to update the knowledge of desired parameters after each measurement, are used in a wide range of quantum science. For various applications in quantum science, efficiently and accurately…
Multimodal structures in the sampling density (e.g. two competing phases) can be a serious problem for traditional Markov Chain Monte Carlo (MCMC), because correct sampling of the different structures can only be guaranteed for infinite…
This paper presents a fast algorithm for estimating hidden states of Bayesian state space models. The algorithm is a variation of amortized simulation-based inference algorithms, where a large number of artificial datasets are generated at…
We examine a constrained Markov decision process under uncertain transition probabilities, with the uncertainty modeled as deviations from observed transition probabilities. We construct the uncertainty set associated with the deviations…
A theoretical analysis is given of the equation of motion method, due to Alben et al., to compute the eigenvalue distribution (density of states) of very large matrices. The salient feature of this method is that for matrices of the kind…
Two non-intrusive uncertainty propagation approaches are proposed for the performance analysis of engineering systems described by expensive-to-evaluate deterministic computer models with parameters defined as interval variables. These…