energia: Monte Carlo method

Evidence: 100 • authority: 72

Monte Carlo methods, also called the Monte Carlo experiments or Monte Carlo simulations, are a broad class of computational algorithms based on repeated random sampling for obtaining numerical results, conceptualized by Polish mathematician Stanisław Ulam. The underlying concept is to use randomness to solve deterministic problems. Monte Carlo methods are mainly used in three distinct problem classes: optimization, numerical integration, and non-uniform random variate generation, available for modeling phenomena with significant input uncertainties, e.g. risk assessments for nuclear power plants. Monte Carlo methods are often implemented using computer simulations. They can provide approxim…

Evidence: 64 • authority: 92

Bayesian-calibrated global sensitivity analysis for mathematical models using generative AI.. We present a generative modeling framework for global sensitivity analysis (GSA) in complex systems characterized by strong and potentially high-dimensional parameter correlations. Traditional variance-based GSA methods rely on the assumption of independent inputs, which rarely holds for Bayesian-calibrated models. While recent extensions using Rosenblatt transformations and Shapley effects theoretically address this limitation, their implementation requires accurate conditional sampling from correlated joint distributions, a task that remains challenging. Existing solutions suffer from restrictive…

Evidence: 64 • authority: 72

Approximate Bayesian computation (ABC) constitutes a class of computational methods rooted in Bayesian statistics that can be used to estimate the posterior distributions of model parameters. In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quantifies the support data lend to particular values of parameters and to choices among different models. For simple models, an analytical formula for the likelihood function can typically be derived. However, for more complex models, an analytical formula might be elusive or the likelihood function might be c…

Evidence: 54 • authority: 72

Particle filters, also known as sequential Monte Carlo methods, are a set of Monte Carlo algorithms used to find approximate solutions for filtering problems for nonlinear state-space systems, such as signal processing and Bayesian statistical inference. The filtering problem consists of estimating the internal states in dynamical systems when partial observations are made and random perturbations are present in the sensors as well as in the dynamical system. The objective is to compute the posterior distributions of the states of a Markov process, given the noisy and partial observations. The term "particle filters" was first coined in 1996 by Pierre Del Moral about mean-field interacting…

Evidence: 45 • authority: 92

Thermo-Electro-Mechanical Vibration Analysis of Microbeams with Non-Ideal Boundary Conditions.. In this study, the vibration characteristics of microbeams subjected to thermal loads and electric field effects under non-ideal boundary conditions were investigated. The non-ideal boundary conditions are modeled as a linear combination of ideal fixed and simply supported boundary conditions. The weighting factor, k, is defined as a measure of deviation from the ideal boundary conditions. To determine the influence of the boundary conditions, both non-ideal fixed and non-ideal simply supported beams were examined. The equations of motion of the system are derived using Hamilton's principle, and…

Evidence: 45 • authority: 92

End-to-end robust system discovery in electrical dynamical systems using scientific machine learning.. System discovery is an important part of the power systems asset management process. In this paper, we introduce an end-to-end approach for robust system discovery for a class of electrical dynamical systems with polynomial dynamics. To that end, we provide a theoretical analysis of the problem setting and the solution approach using a particular Scientific Machine Learning method called Physics-Informed Machine Learning. We introduce model architecture and training and validation methods for deterministic as well as probabilistic approaches to predict the solution to pertinent inverse pro…