Related papers: Multilevel Monte Carlo for quantum mechanics on a …
In the context of Monte Carlo sampling for lattice models, the complexity of the energy landscape often leads to Markov chains being trapped in local optima, thereby increasing the correlation between samples and reducing sampling…
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…
The Multilevel Monte Carlo method is an efficient variance reduction technique. It uses a sequence of coarse approximations to reduce the computational cost in uncertainty quantification applications. The method is nowadays often considered…
In this article we consider computing expectations w.r.t.~probability laws associated to a certain class of stochastic systems. In order to achieve such a task, one must not only resort to numerical approximation of the expectation, but…
This article considers the sequential Monte Carlo (SMC) approximation of ratios of normalizing constants associated to posterior distributions which in principle rely on continuum models. Therefore, the Monte Carlo estimation error and the…
Tailoring the performance of next-generation high entropy materials requires a deep understanding of the competition between entropy-driven random solid solution and enthalpy-driven chemical ordering. Investigating such order and disorder…
Monte Carlo experiments produce samples in order to estimate features of a given distribution. However, simultaneous estimation of means and quantiles has received little attention, despite being common practice. In this setting we…
Nested Monte Carlo is widely used for risk estimation, but its efficiency is limited by the discontinuity of the indicator function and high computational cost. This paper proposes a nested Multilevel Monte Carlo (MLMC) method combined with…
Many problems require to approximate an expected value by some kind of Monte Carlo (MC) sampling, e.g. molecular dynamics (MD) or simulation of stochastic reaction models (also termed kinetic Monte Carlo (kMC)). Often, we are furthermore…
The equilibrium configuration of a plasma in an axially symmetric reactor is described mathematically by a free boundary problem associated with the celebrated Grad--Shafranov equation. The presence of uncertainty in the model parameters…
On the base of a Feynman-Kac--type formula involving Poisson stochastic processes, recently a Monte Carlo algorithm has been introduced, which describes exactly the real- or imaginary-time evolution of many-body lattice quantum systems. We…
We consider the computational efficiency of Monte Carlo (MC) and Multilevel Monte Carlo (MLMC) methods applied to partial differential equations with random coefficients. These arise, for example, in groundwater flow modelling, where a…
We introduce a Monte Carlo method, as a modification of existing cluster algorithms, which allows simulations directly on systems of infinite size, and for quantum models also at beta=infinity. All two-point functions can be obtained,…
Sampling the three-dimensional (3D) spin glass -- i.e., generating equilibrium configurations of a 3D lattice with quenched random couplings -- is widely regarded as one of the central and long-standing open problems in statistical physics.…
Due to the intrinsic complexity of the quantum many-body problem, quantum Monte Carlo algorithms and their corresponding Monte Carlo configurations can be defined in various ways. Configurations corresponding to few Feynman diagrams often…
Ensemble Kalman methods solve problems in domains such as filtering and inverse problems with interacting particles that evolve over time. For computationally expensive problems, the cost of attaining a high accuracy quickly becomes…
Monte Carlo is one of the most useful methods to study the quantum Hall problems. In this paper, we introduce a fast lattice Monte Carlo method based on a mathematically exact reformulation of the torus quantum Hall problems from continuum…
Methods for generating sequences of surrogates approximating fine scale models of two-phase random heterogeneous media are presented that are designed to adaptively control the modeling error in key quantities of interest (QoIs). For…
This paper proposes a new multilevel Monte Carlo (MLMC) method for the ergodic SDEs which do not satisfy the contractivity condition. By introducing the change of measure technique, we simulate the path with contractivity and add the…
In this paper we investigate how the complexity of chaotic phase spaces affect the efficiency of importance sampling Monte Carlo simulations. We focus on a flat-histogram simulation of the distribution of finite-time Lyapunov exponent in a…