Related papers: THE CONVERGENCE OF CHAOTIC INTEGRALS
We analyse convergence of a micro-macro acceleration method for the Monte Carlo simulation of stochastic differential equations with time-scale separation between the (fast) evolution of individual trajectories and the (slow) evolution of…
Dynamical zeta functions provide a powerful method to analyze low dimensional dynamical systems when the underlying symbolic dynamics is under control. On the other hand even simple one dimensional maps can show an intricate structure of…
A statistical learning approach for parametric PDEs related to Uncertainty Quantification is derived. The method is based on the minimization of an empirical risk on a selected model class and it is shown to be applicable to a broad range…
The efficiency of Monte Carlo samplers is dictated not only by energetic effects, such as large barriers, but also by entropic effects that are due to the sheer volume that is sampled. The latter effects appear in the form of an entropic…
We use extensive Monte Carlo transfer matrix calculations on infinite strips of widths $L$ up to 30 lattice spacing and a finite-size scaling analysis to obtain critical exponents and conformal anomaly number $c$ for the two-dimensional…
By means of a variational approach we find new series representations both for well known mathematical constants, such as $\pi$ and the Catalan constant, and for mathematical functions, such as the Riemann zeta function. The series that we…
Improvements beyond the primitive approximation in the path integral Monte Carlo method are explored both in a model problem and in real systems. Two different strategies are studied: the Richardson extrapolation on top of the path integral…
We compute the rate of convergence of forward, backward and central finite difference $\theta$-schemes for linear PDEs with an arbitrary odd order spatial derivative term. We prove convergence of the first or second order for smooth and…
A fast method for dynamic aperture (DA) optimization of storage rings has been developed through the use of reversal integration. While chaotic dynamical systems have exact time-reversal symmetry, numerical forward integration differs from…
The Diffusion Monte Carlo method with constant number of walkers, also called Stochastic Reconfiguration as well as Sequential Monte Carlo, is a widely used Monte Carlo methodology for computing the ground-state energy and wave function of…
In this work, an intelligent controller is employed to the chaos control problem in a nonlinear pendulum. The adopted approach is based on the sliding mode control strategy and enhanced by an adaptive fuzzy algorithm to cope with modeling…
Many stochastic differential equations that occur in financial modelling do not satisfy the standard assumptions made in convergence proofs of numerical schemes that are given in textbooks, i.e., their coefficients and the corresponding…
The exponential trapezoidal rule is proposed and analyzed for the numerical integration of semilinear integro-differential equations. Although the method is implicit, the numerical solution is easily obtained by standard fixed-point…
Motivated by recent developments in conformal field theory (CFT), we devise a Quantum Monte Carlo (QMC) method to calculate the moments of the partially transposed reduced density matrix at finite temperature. These are used to construct…
A recent approach to the Beck-Fiala conjecture, a fundamental problem in combinatorics, has been to understand when random integer matrices have constant discrepancy. We give a complete answer to this question for two natural models:…
This paper addresses the challenging computational problem of estimating intractable expectations over discrete domains. Existing approaches, including Monte Carlo and Russian Roulette estimators, are consistent but often require a large…
In this work, we establish $\mathrm{L}^2$-exponential convergence for a broad class of Piecewise Deterministic Markov Processes recently proposed in the context of Markov Process Monte Carlo methods and covering in particular the Randomized…
Recent progress on the theory of variational hypocoercivity established that Randomized Hamiltonian Monte Carlo -- at criticality -- can achieve pronounced acceleration in its convergence and hence sampling performance over diffusive…
The present work introduces an efficient Monte Carlo algorithm for continuum percolation composed of randomly-oriented rectangles. By conducting extensive simulations, we report high precision percolation thresholds for a variety of…
We consider the numerical solution of scalar, nonlinear degenerate convection-diffusion problems with random diffusion coefficient and with random flux functions. Building on recent results on the existence, uniqueness and continuous…