Related papers: Numerical analytic continuation of Euclidean data
We compare and discuss the respective efficiency of three methods (with two variants for each of them), based respectively on Taylor (Maclaurin) series, Pad\'{e} approximants and conformal mappings, for solving quasi-analytically a…
The analytic continuation of imaginary-time quantum Monte Carlo data to extract real-frequency spectra remains a key problem in connecting theory with experiment. Here we present a fast and efficient stochastic optimization method (FESOM)…
Many fields of physics use quantum Monte Carlo techniques, but struggle to estimate dynamic spectra via the analytic continuation of imaginary-time quantum Monte Carlo data. One of the most ubiquitous approaches to analytic continuation is…
This study explores the use of neural network-based analytic continuation to extract spectra from Monte Carlo data. We apply this technique to both synthetic and Monte Carlo-generated data. The training sets for neural networks are…
Numerical continuation methods for deterministic dynamical systems have been one of the most successful tools in applied dynamical systems theory. Continuation techniques have been employed in all branches of the natural sciences as well as…
We develop a method for multidimensional optimisation using flow equations. This method is based on homotopy continuation in combination with a maximum entropy approach. Extrema of the optimising functional correspond to fixed points of the…
Control-based continuation (CBC) is a general and systematic method to probe the dynamics of nonlinear experiments. In this paper, CBC is combined with a novel continuation algorithm that is robust to experimental noise and enables the…
Resummation methods using continued functions are implemented to converge divergent series appearing in perturbation problems related to continuous phase transitions in field theories. In some cases, better convergence properties are…
We study the problem of recovering a globally consistent Euclidean embedding of data, given only a local distance graph and propose a method that optimally represents these distances. The method operates solely on a neighborhood graph…
In this note, a classification of Homogenization-Based Numerical Methods and (in particular) of Numerical Methods that are based on the Two-Scale Convergence is done. In this classification stand: Direct Homogenization-Based Numerical…
We numerically test the method of non-sequential recursive pair substitutions to estimate the entropy of an ergodic source. We compare its performance with other classical methods to estimate the entropy (empirical frequencies, return…
In this paper we study numerical positivity and contractivity in the infinite norm of Crank-Nicolson method when it is applied to the diffusion equation with homogeneous Dirichlet boundary conditions. For this purpose, the amplification…
We develop a framework for extracting non-polynomial analytic functions of density matrices in randomized measurement experiments by a method of analytical continuation. A central advantage of this approach, dubbed stabilized analytic…
The extraction of spectral densities from Euclidean correlators evaluated on the lattice is an important problem, as these quantities encode physical information on scattering amplitudes, finite-volume spectra, inclusive decay rates, and…
In this paper we discuss the reliability of two computational methods (numerical integration on Cartesian grids, and population analysis) used for evaluating scalar quantities related to the nature of electronic transitions. These…
Analytic continuation is an essential step in extracting information about the dynamical properties of physical systems from quantum Monte Carlo (QMC) simulations. Different methods for analytic continuation have been proposed and are still…
This work addresses the problem of simulating Gaussian random fields that are continuously indexed over a class of metric graphs, termed graphs with Euclidean edges, being more general and flexible than linear networks. We introduce three…
We introduce a general framework for undirected graphical models. It generalizes Gaussian graphical models to a wide range of continuous, discrete, and combinations of different types of data. The models in the framework, called exponential…
We present a novel approach for the reconstruction of spectra from Euclidean correlator data that makes close contact to modern Bayesian concepts. It is based upon an axiomatically justified dimensionless prior distribution, which in the…
Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by…