Related papers: Surrogate-based multilevel Monte Carlo methods for…
Variational quantum algorithms are a class of techniques intended to be used on near-term quantum computers. The goal of these algorithms is to perform large quantum computations by breaking the problem down into a large number of shallow…
We propose a quantum Monte Carlo approach to solve the ground state many-body Schrodinger equation for the electronic ground state. The method combines optimization from variational Monte Carlo and propagation from auxiliary field quantum…
Running a reliability analysis on engineering problems involving complex numerical models can be computationally very expensive, requiring advanced simulation methods to reduce the overall numerical cost. Gaussian process based active…
Exact Solov'ev equilibria for arbitrary plasma cross-sections are calculated using a constrained least-squares method. The boundary, with or without $X$-points, can be specified with an arbitrarily large number of constraints to ensure an…
We study statistical model checking of continuous-time stochastic hybrid systems. The challenge in applying statistical model checking to these systems is that one cannot simulate such systems exactly. We employ the multilevel Monte Carlo…
The efficient simulation of the mean value of a non-linear functional of the solution to a linear stochastic partial differential equation (SPDE) with additive Gaussian noise is considered. A Galerkin finite element method is employed along…
Kinetic equations play a major rule in modeling large systems of interacting particles. Uncertainties may be due to various reasons, like lack of knowledge on the microscopic interaction details or incomplete informations at the boundaries.…
In this work we present a robust and accurate arbitrary order solver for the fixed-boundary plasma equilibria in toroidally axisymmetric geometries. To achieve this we apply the mimetic spectral element formulation presented in [56] to the…
Machine learning-based surrogate models have emerged as more efficient alternatives to numerical solvers for physical simulations over complex geometries, such as car bodies. Many existing models incorporate the simulation mesh as an…
Recent advancements in Markov chain Monte Carlo (MCMC) sampling and surrogate modelling have significantly enhanced the feasibility of Bayesian analysis across engineering fields. However, the selection and integration of surrogate models…
In axisymmetric fusion reactors, the equilibrium magnetic configuration can be expressed in terms of the solution to a semi-linear elliptic equation known as the Grad-Shafranov equation, the solution of which determines the poloidal…
We tackle the problem of quantifying failure probabilities for expensive deterministic computer experiments with stochastic inputs under a fixed budget. The computational cost of the computer simulation prohibits direct Monte Carlo (MC) and…
We present a hybrid method for time-dependent particle transport problems that combines Monte Carlo (MC) estimation with deterministic solutions based on discrete ordinates. For spatial discretizations, the MC algorithm computes a piecewise…
Global optimization of expensive functions has important applications in physical and computer experiments. It is a challenging problem to develop efficient optimization scheme, because each function evaluation can be costly and the…
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…
We propose and investigate a new multi-level Monte Carlo scheme for numerical solutions of the kinetic Boltzmann equation for neutral species in edge plasmas. In particular, this method explicitly exploits a key structural property of…
The multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty quantification in PDE models. It combines approximations at different levels of accuracy using a hierarchy of…
Markov chain Monte Carlo methods for exponential family models with intractable normalizing constant, such as the exchange algorithm, require simulations of the sufficient statistics at every iteration of the Markov chain, which often…
Surrogate models are statistical or conceptual approximations for more complex simulation models. In this context, it is crucial to propagate the uncertainty induced by limited simulation budget and surrogate approximation error to…
In this paper the application of the multi-level Monte Carlo (MLMC) method on numerical simulations of turbulent flows with uncertain parameters is investigated. Several strategies for setting up the MLMC method are presented, and the…