Related papers: Multifidelity Methods for Uncertainty Quantificati…
The rigorous quantification of uncertainty in geophysical inversions is a challenging problem. Inversions are often ill-posed and the likelihood surface may be multi-modal; properties of any single mode become inadequate uncertainty…
The nonlocal Cahn-Hilliard (NCH) equation with nonlocal diffusion operator is more suitable for the simulation of microstructure phase transition than the local Cahn-Hilliard (LCH) equation. In this paper, based on the exponential…
Bayesian inference in the presence of an intractable likelihood function is computationally challenging. When following a Markov chain Monte Carlo (MCMC) approach to approximate the posterior distribution in this context, one typically…
Methods that bypass analytical evaluations of the likelihood function have become an indispensable tool for statistical inference in many fields of science. These so-called likelihood-free methods rely on accepting and rejecting simulations…
Fast and accurate predictions of uncertainties in the computed dose are crucial for the determination of robust treatment plans in radiation therapy. This requires the solution of particle transport problems with uncertain parameters or…
Fiber orientation is decisive for the mechanical performance of composite materials. During manufacturing, variations in material and process parameters can influence fiber orientation. We employ multilevel polynomial surrogates to model…
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…
For many complex simulation tasks spanning areas such as healthcare, engineering, and finance, Monte Carlo (MC) methods are invaluable due to their unbiased estimates and precise error quantification. Nevertheless, Monte Carlo simulations…
As modern neural networks get more complex, specifying a model with high predictive performance and sound uncertainty quantification becomes a more challenging task. Despite some promising theoretical results on the true posterior…
We present a "module-based hybrid" Uncertainty Quantification (UQ) framework for general nonlinear multi-physics simulation. The proposed methodology, introduced in [\hyperlink{ref1}{1}], supports the independent development of each…
A generalized version of the fidelity susceptibility of single-band and multi-orbital Hubbard models is systematically studied using single-site dynamical mean-field theory in combination with a hybridization expansion continuous-time…
While multilevel Monte Carlo (MLMC) methods for the numerical approximation of partial differential equations with random coefficients enjoy great popularity, combinations with spatial adaptivity seem to be rare. We present an adaptive MLMC…
Real-world black-box optimization often involves time-consuming or costly experiments and simulations. Multi-fidelity optimization (MFO) stands out as a cost-effective strategy that balances high-fidelity accuracy with computational…
In this article we offer some modification of Monte-Carlo method for multiple parametric integral computation and solving of a linear integral Fredholm equation of a second kind (well posed problem). We prove that the rate of convergence of…
We propose a multi-fidelity Bayesian optimization (MF-BO) framework that integrates computational fluid dynamics (CFD) evaluations with Gaussian-process surrogates to efficiently navigate the accuracy-cost trade-off induced by mesh…
Markov chain Monte Carlo (MCMC) methods are a powerful but computationally expensive way of performing non-parametric Bayesian inference. MCMC proposals which utilise gradients, such as Hamiltonian Monte Carlo (HMC), can better explore the…
We consider a class of finite time horizon nonlinear stochastic optimal control problem, where the control acts additively on the dynamics and the control cost is quadratic. This framework is flexible and has found applications in many…
When a system undergoes a quantum phase transition, the ground-state wave-function shows a change of nature, which can be monitored using the fidelity concept. We introduce two Quantum Monte Carlo schemes that allow the computation of…
We introduce a multi-fidelity estimator of covariance matrices that employs the log-Euclidean geometry of the symmetric positive-definite manifold. The estimator fuses samples from a hierarchy of data sources of differing fidelities and…
Traditional deep learning (DL) models are powerful classifiers, but many approaches do not provide uncertainties for their estimates. Uncertainty quantification (UQ) methods for DL models have received increased attention in the literature…