Related papers: Multivariate error modeling and uncertainty quanti…
As the size of engineered systems grows, problems in reliability theory can become computationally challenging, often due to the combinatorial growth in the cut sets. In this paper we demonstrate how Multilevel Monte Carlo (MLMC) - a…
Many inverse problems in nuclear fusion and high-energy astrophysics research, such as the optimization of tokamak reactor geometries or the inference of black hole parameters from interferometric images, necessitate high-dimensional…
Monte Carlo methods play a central role in particle physics, where they are indispensable for simulating scattering processes, modeling detector responses, and performing multi-dimensional integrals. However, traditional Monte Carlo methods…
This paper proposes a new theory and methodology to tackle the problem of unifying distributed analyses and inferences on shared parameters from multiple sources, into a single coherent inference. This surprisingly challenging problem…
The modeling and uncertainty quantification of closed curves is an important problem in the field of shape analysis, and can have significant ramifications for subsequent statistical tasks. Many of these tasks involve collections of closed…
We consider Global Sensitivity Analysis for Monte Carlo radiation transport applications. GSA is usually combined with Uncertainty Quantification, where the latter quantifies the variability of a model output in the presence of uncertain…
Among Bayesian methods, Monte-Carlo dropout provides principled tools for evaluating the epistemic uncertainty of neural networks. Its popularity recently led to seminal works that proposed activating the dropout layers only during…
Mathematical models simulate various events under different conditions, enabling an early overview of the system to be implemented in practice, reducing the waste of resources and in less time. In project optimization, these models play a…
Accurate dose calculation is vitally important for proton therapy. Pencil beam (PB) model-based dose calculation is fast but inaccurate due to the approximation when dealing with inhomogeneities. Monte Carlo (MC) dose calculation is the…
Uncertainty Quantification (UQ) is essential in probabilistic machine learning models, particularly for assessing the reliability of predictions. In this paper, we present a systematic framework for estimating both epistemic and aleatoric…
Knowing the uncertainty associated with the output of a deep neural network is of paramount importance in making trustworthy decisions, particularly in high-stakes fields like medical diagnosis and autonomous systems. Monte Carlo Dropout…
The Reduced-Basis Control-Variate Monte-Carlo method was introduced recently in [S. Boyaval and T. Leli\`evre, CMS, 8 2010] as an improved Monte-Carlo method, for the fast estimation of many parametrized expected values at many parameter…
Population Monte Carlo (PMC) sampling methods are powerful tools for approximating distributions of static unknowns given a set of observations. These methods are iterative in nature: at each step they generate samples from a proposal…
Physics-based simulations and learning-based models are vital for complex robotics tasks like deformable object manipulation and liquid handling. However, these models often struggle with accuracy due to epistemic uncertainty or the…
Computer simulations of photon transport through an absorbing and/or scattering medium form an important research tool in astrophysics. Nearly all software codes performing such simulations for three-dimensional geometries employ the Monte…
We have developed an Uncertainty Quantification process for multistep pipelines and applied it to the ACORN particle tracking pipeline. All our experiments are made using the TrackML open dataset. Using the Monte Carlo Dropout method, we…
We discuss the improvement in the accuracy of a Monte Carlo integration that can be obtained by optimization of the `a-priori weights' of the various channels. These channels may be either the strata in a stratified-sampling approach, or…
It is highly desirable to know how uncertain a model's predictions are, especially for models that are complex and hard to understand as in deep learning. Although there has been a growing interest in using deep learning methods in…
Particle physics simulations are the cornerstone of nuclear engineering applications. Among them radiotherapy (RT) is crucial for society, with 50% of cancer patients receiving radiation treatments. For the most precise targeting of tumors,…
Monte Carlo event generators are an essential tool for data analysis in collider physics. To include subleading quantum corrections, these generators often need to produce negative weight events, which leads to statistical dilution of the…