Related papers: Uncertainty quantification for random domains usin…
Recursive Marginal Quantization (RMQ) allows fast approximation of solutions to stochastic differential equations in one-dimension. When applied to two factor models, RMQ is inefficient due to the fact that the optimization problem is…
Bayesian optimization is a class of global optimization techniques. In Bayesian optimization, the underlying objective function is modeled as a realization of a Gaussian process. Although the Gaussian process assumption implies a random…
Inverse problems play a key role in modern image/signal processing methods. However, since they are generally ill-conditioned or ill-posed due to lack of observations, their solutions may have significant intrinsic uncertainty. Analysing…
In this paper, we address the probabilistic error quantification of a general class of prediction methods. We consider a given prediction model and show how to obtain, through a sample-based approach, a probabilistic upper bound on the…
Monte Carlo methods are widely used for approximating complicated, multidimensional integrals for Bayesian inference. Population Monte Carlo (PMC) is an important class of Monte Carlo methods, which utilizes a population of proposals to…
A new Quantum Monte-Carlo (QMC) approach is proposed to investigate low-lying states of nuclei within the shell model. The formalism relies on a variational symmetry-restored wave-function to guide the underlying Brownian motion. Sign/phase…
The incorporation of systematic uncertainties into confidence interval calculations has been addressed recently in a paper by Conrad et al. (Physical Review D 67 (2003) 012002). In their work, systematic uncertainities in detector…
We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters. If the system dynamics is expensive to compute, standard sampling…
Optimizing the design of complex systems requires navigating interdependent decisions, heterogeneous components, and multiple objectives. Our monotone theory of co-design offers a compositional framework for addressing this challenge,…
Neural networks (NNs) are currently changing the computational paradigm on how to combine data with mathematical laws in physics and engineering in a profound way, tackling challenging inverse and ill-posed problems not solvable with…
We consider the problem of providing optimal uncertainty quantification (UQ) --- and hence rigorous certification --- for partially-observed functions. We present a UQ framework within which the observations may be small or large in number,…
This work describes a domain embedding technique between two non-matching meshes used for generating realizations of spatially correlated random fields with applications to large-scale sampling-based uncertainty quantification. The goal is…
The uncertainty quantification (UQ) for partial differential equations (PDEs) with random parameters is important for science and engineering. Forward UQ quantifies the impact of random parameters on the solution or the quantity-of-interest…
In this work we propose an Uncertainty Quantification methodology for sedimentary basins evolution under mechanical and geochemical compaction processes, which we model as a coupled, time-dependent, non-linear, monodimensional (depth-only)…
Quality-Diversity optimisation (QD) has proven to yield promising results across a broad set of applications. However, QD approaches struggle in the presence of uncertainty in the environment, as it impacts their ability to quantify the…
Latent variable models have been playing a central role in psychometrics and related fields. In many modern applications, the inference based on latent variable models involves one or several of the following features: (1) the presence of…
Recursive marginal quantization (RMQ) allows the construction of optimal discrete grids for approximating solutions to stochastic differential equations in d-dimensions. Product Markovian quantization (PMQ) reduces this problem to d…
In this paper we introduce concepts from uncertainty quantification (UQ) and numerical analysis for the efficient evaluation of stochastic high dimensional Newton iterates. In particular, we develop complex analytic regularity theory of the…
Quantifying uncertainty of machine learning model predictions is essential for reliable decision-making, especially in safety-critical applications. Recently, uncertainty quantification (UQ) theory has advanced significantly, building on a…
Uncertainty quantification is a key aspect in many tasks such as model selection/regularization, or quantifying prediction uncertainties to perform active learning or OOD detection. Within credal approaches that consider modeling…