Related papers: An Efficient Non-Intrusive Uncertainty Propagation…

Distributed parameter systems (DPS) are formulated as partial differential equations (PDE). Especially, under time-varying boundary conditions, PDE introduce force coupling. In the case of the flexible stacker crane (STC), nonlinear…

A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…

This work proposes a sampling-based (non-intrusive) approach within the context of low-rank separated representations to tackle the issue of curse-of-dimensionality associated with the solution of models, e.g., PDEs/ODEs, with…

Calibration of individual based models (IBMs), successful in modeling complex ecological dynamical systems, is often performed only ad-hoc. Bayesian inference can be used for both parameter estimation and uncertainty quantification, but its…

This paper introduces a global uncertainty propagation scheme for rigid body dynamics, through a combination of numerical parametric uncertainty techniques, noncommutative harmonic analysis, and geometric numerical integration. This method…

We introduce a general Monte Carlo method based on Nested Sampling (NS), for sampling complex probability distributions and estimating the normalising constant. The method uses one or more particles, which explore a mixture of nested…

We propose a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of parametric partial differential equations (PDEs) conditioned on partial observations, which includes,…

Uncertainty quantification based on generalized polynomial chaos has been used in many applications. It has also achieved great success in variation-aware design automation. However, almost all existing techniques assume that the parameters…

Simulating complex physical systems is crucial for understanding and predicting phenomena across diverse fields, such as fluid dynamics and heat transfer, as well as plasma physics and structural mechanics. Traditional approaches rely on…

This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…

We propose a predictor-corrector adaptive method for the simulation of hyperbolic partial differential equations (PDEs) on networks under general uncertainty in parameters, initial conditions, or boundary conditions. The approach is based…

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…

Higher order schemes for stochastic partial differential equations that do not possess commutative noise require the simulation of iterated stochastic integrals. In this work, we propose a derivative-free Milstein type scheme to approximate…

Quantifying predictive uncertainty of neural networks has recently attracted increasing attention. In this work, we focus on measuring uncertainty of graph neural networks (GNNs) for the task of node classification. Most existing GNNs model…

This work addresses the challenge of ignition timing and load control in homogeneous charge compression ignition engines operating subject to uncertainty from complex combustion dynamics and external disturbances. To handle this issue, we…

The study of uncertainty propagation is of fundamental importance in plasma physics simulations. To this end, in the present work we propose a novel stochastic Galerkin (sG) particle {method} for collisional kinetic models of plasmas under…

The non-intrusive generalized Polynomial Chaos (gPC) method is a popular computational approach for solving partial differential equations (PDEs) with random inputs. The main hurdle preventing its efficient direct application for…

The Immersed Boundary method is a simple, efficient, and robust numerical scheme for solving PDE in general domains, yet it only achieves first-order spatial accuracy near embedded boundaries. In this paper, we introduce a new high-order…

Macroscopic models for spatially extended systems under random influences are often described by stochastic partial differential equations (SPDEs). Some techniques for understanding solutions of such equations, such as estimating…

Many quantum technologies rely on high-precision dynamics, which raises the question of how these are influenced by the experimental uncertainties that are always present in real-life settings. A standard approach in the literature to…