Related papers: Single-ensemble multilevel Monte Carlo for discret…
In this paper we consider the filtering of partially observed multi-dimensional diffusion processes that are observed regularly at discrete times. This is a challenging problem which requires the use of advanced numerical schemes based upon…
In this paper we present a new approach to control variates for improving computational efficiency of Ensemble Monte Carlo. We present the approach using simulation of paths of a time-dependent nonlinear stochastic equation. The core idea…
To minimise systematic errors in Monte Carlo simulations of charged particles, long range electrostatic interactions have to be calculated accurately and efficiently. Standard approaches, such as Ewald summation or the naive application of…
Estimating risk measures such as large loss probabilities and Value-at-Risk is fundamental in financial risk management and often relies on computationally intensive nested Monte Carlo methods. While Multi-Level Monte Carlo (MLMC)…
An algorithm is proposed to solve robust control problems constrained by partial differential equations with uncertain coefficients, based on the so-called MG/OPT framework. The levels in this MG/OPT hierarchy correspond to discretization…
We present simple conditions under which the limiting genealogical process associated with a class of interacting particle systems with non-neutral selection mechanisms, as the number of particles grows, is a time-rescaled Kingman…
In this article we develop a multi-grid multi-level Monte Carlo (MGMLMC) method for the stochastic Stokes-Darcy interface model with random hydraulic conductivity both in the porous media domain and on the interface. Because the randomness…
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…
The subsurface flow is usually subject to uncertain porous media structures. In most cases, however, we only have partial knowledge about the porous media properties. A common approach is to model the uncertain parameters of porous media as…
We present a multi-level Monte Carlo (MLMC) algorithm with adaptively refined meshes and accurately computed stopping-criteria utilizing adjoint-based a posteriori error analysis for differential equations. This is in contrast to classical…
The ensemble Kalman inversion is widely used in practice to estimate unknown parameters from noisy measurement data. Its low computational costs, straightforward implementation, and non-intrusive nature makes the method appealing in various…
Computing risk measures of a financial portfolio comprising thousands of derivatives is a challenging problem because (a) it involves a nested expectation requiring multiple evaluations of the loss of the financial portfolio for different…
We interpret uncertainty in a model for seismic wave propagation by treating the model parameters as random variables, and apply the Multilevel Monte Carlo (MLMC) method to reduce the cost of approximating expected values of selected,…
In this paper, we consider the filtering problem for partially observed diffusions, which are regularly observed at discrete times. We are concerned with the case when one must resort to time-discretization of the diffusion process if the…
Combinatorial optimization problems play crucial roles in real-world applications, and many studies from a physics perspective have contributed to specialized hardware for high-speed computation. However, some combinatorial optimization…
The ensemble Kalman filter (EnKF) is a method for combining a dynamical model with data in a sequential fashion. Despite its widespread use, there has been little analysis of its theoretical properties. Many of the algorithmic innovations…
We propose a Multilevel Monte-Carlo (MLMC) method for computing entropy measure valued solutions of hyperbolic conservation laws. Sharp bounds for the narrow convergence of MLMC for the entropy measure valued solutions are proposed. An…
In the stochastic gradient descent (SGD) for sequential simulations such as the neural stochastic differential equations, the Multilevel Monte Carlo (MLMC) method is known to offer better theoretical computational complexity compared to the…
This paper considers the problem of optimizing the average tracking error for an elliptic partial differential equation with an uncertain lognormal diffusion coefficient. In particular, the application of the multilevel quasi-Monte Carlo…
Markov chain Monte Carlo (MCMC) methods generate samples that are asymptotically distributed from a target distribution of interest as the number of iterations goes to infinity. Various theoretical results provide upper bounds on the…