Related papers: Propagation and reconstruction of re-entry uncerta…

Uncertainty analysis in the outcomes of model predictions is a key element in decision-based material design to establish confidence in the models and evaluate the fidelity of models. Uncertainty Propagation (UP) is a technique to determine…

Numerical continuation techniques are powerful tools that have been extensively used to identify particular solutions of nonlinear dynamical systems and enable trajectory design in chaotic astrodynamics problems such as the Circular…

Estimating the probability of collision between spacecraft is crucial for risk management and collision-avoidance strategies. Current methods often rely on Gaussian assumptions and simplifications, which can be inaccurate in highly…

Macroscopically heterogeneous materials, characterised mostly by comparable heterogeneity lengthscale and structural sizes, can no longer be modelled by deterministic approach instead. It is convenient to introduce stochastic approach with…

Starting from considerations about meaning and subsequent use of asymmetric uncertainty intervals of experimental results, we review the issue of uncertainty propagation. We show that, using a probabilistic approach (the so-called Bayesian…

Uncertainty estimation, which provides a means of building explainable neural networks for medical imaging applications, have mostly been studied for single deep learning models that focus on a specific task. In this paper, we propose a…

A multifidelity method for the nonlinear propagation of uncertainties in the presence of stochastic accelerations is presented. The proposed algorithm treats the uncertainty propagation (UP) problem by separating the propagation of the…

This paper addresses the problem of quantification and propagation of uncertainties associated with dependence modeling when data for characterizing probability models are limited. Practically, the system inputs are often assumed to be…

Propagating uncertainties introduced by chemical reaction rate parameters to high-fidelity numerical simulations of complex combustion devices is necessary to ascertain impact on computational predictions. However, the high cost of detailed…

A family of semi-intrusive uncertainty propagation (UP) methods for multiscale models is introduced. The methods are semi-intrusive in the sense that inspection of the model is limited up to the level of the single scale systems, and…

Most approximations for stochastic differential equations with high-dimensional, non-Gaussian inputs suffer from a rapid (e.g., exponential) increase of computational cost, an issue known as the curse of dimensionality. In astrodynamics,…

Uncertainty in large language model (LLM)-based systems is often studied at the level of a single model output, yet deployed LLM applications are compound systems in which uncertainty is transformed and reused across model internals,…

This paper addresses uncertainty propagation on unimodular matrix Lie groups that have a surjective exponential map. We derive the exact formula for the propagation of mean and covariance in a continuous-time setting from the governing…

Modelling uncertainty in Machine Learning models is essential for achieving safe and reliable predictions. Most research on uncertainty focuses on output uncertainty (predictions), but minimal attention is paid to uncertainty at inputs. We…

We propose a method to outer bound forward reachable sets on finite horizons for uncertain nonlinear systems with polynomial dynamics. This method makes use of time-dependent polynomial storage functions that satisfy appropriate dissipation…

In this paper, we address the problem of uncertainty propagation through nonlinear stochastic dynamical systems. More precisely, given a discrete-time continuous-state probabilistic nonlinear dynamical system, we aim at finding the sequence…

We propose a new approach for propagating stable probability distributions through neural networks. Our method is based on local linearization, which we show to be an optimal approximation in terms of total variation distance for the ReLU…

We present a proximal algorithm that performs a variational recursion on the space of joint probability measures to propagate the stochastic uncertainties in power system dynamics over high dimensional state space. The proposed algorithm…

We apply a recursive approach to the continuity equation of the Madelung fluid resulting in a propagation equation for particle probability densities. This propagation equation can be used to propagate particle distributions in the presence…

In this work we present a nonparametric approach, which works on minimal assumptions, to reconstruct the cosmic expansion of the Universe. We propose to combine a locally weighted scatterplot smoothing method and a simulation-extrapolation…