相关论文: A numerical test of differential equations for one…
Interior point methods solve small to medium sized problems to high accuracy in a reasonable amount of time. However, for larger problems as well as stochastic problems, one needs to use first-order methods such as stochastic gradient…
In this paper, we introduce some analytical techniques to solve some classes of second order differential equations. Such classes of differential equations arise in describing some mathematical problems in Physics and Engineering.
In this paper, we propose a robust and efficient numerical method to compute the dynamics of the rotating two-component dipolar Bose-Einstein condensates (BEC). Using the rotating Lagrangian coordinates transform \cite{BMTZ2013}, we…
We use Rice's formulas in order to compute the moments of some level functionals which are linked to problems in oceanography and optics. For instance, we consider the number of specular points in one or two dimensions, the number of…
We describe the various types of singularities that can arise for second order rational mappings and we discuss the historical and present-day, practical, role the singularity confinement property plays as an integrability detector. In…
We describe an efficient scheme for evaluating higher order contributions to primordial cosmological perturbations using the "in-in" formalism, which is the basis of modern calculations of non-Gaussian and higher order contributions to the…
Moment systems arise in a wide range of contexts and applications, e.g. in network modeling of complex systems. Since moment systems consist of a high or even infinite number of coupled equations, an indispensable step in obtaining a…
An unsteady problem is considered for a space-fractional diffusion equation in a bounded domain. A first-order evolutionary equation containing a fractional power of an elliptic operator of second order is studied for general boundary…
We develop a monotone, two-scale discretization for a class of integrodifferential operators of order $2s$, $s \in (0,1)$. We apply it to develop numerical schemes, and derive pointwise convergence rates, for linear and obstacle problems…
This paper studies a new class of integration schemes for the numerical solution of semi-explicit differential-algebraic equations of differentiation index 2 in Hessenberg form. Our schemes provide the flexibility to choose different…
We use projected entangled-pair states (PEPS) to calculate the large deviations (LD) statistics of the dynamical activity of the two dimensional East model, and the two dimensional symmetric simple exclusion process (SSEP) with open…
We study differentiable mixed-moment models (full zeroth and first moment, half higher moments) for a Fokker-Planck equation in one space dimension. Mixed-moment minimum-entropy models are known to overcome the zero net-flux problem of…
In this paper, we propose a class of super-schemes for efficiently solving nonlinear unconstrained optimization problems. The proposed approach introduces two novel choices of step-size parameters, leading to efficient descent directions…
In this paper, we propose a general framework for solving high-dimensional partial differential equations with tensor networks. Our approach uses Monte-Carlo simulations to update the solution and re-estimates the new solution from samples…
We show how to compute the two-loop sunset integrals at finite volume, for non-degenerate masses and non-zero momentum. We present results for all integrals that appear in the Chiral Perturbation Therory ($\chi$PT) calculation of the…
We introduce a symbolic method for the evaluation of definite integrals containing combinations of various functions, including exponentials, logarithm and products of Bessel functions of different types. The method we develop is naturally…
We present a new method for the numerical evaluation of arbitrary loop integrals in dimensional regularization. We first derive Mellin-Barnes integral representations and apply an algorithmic technique, based on the Cauchy theorem, to…
In this work, we present a novel downscaling procedure for compositional quantities based on the Aitchison geometry. The method is able to naturally consider compositional constraints, i.e. unit-sum and positivity. We show that the method…
We present a set of efficient techniques in first-principles electronic-structure calculations utilizing the real-space finite-difference method. These techniques greatly reduce the overhead for performing integrals that involve…
In this paper we consider the possibility to use numerical simulations for a computer assisted analysis of integrability of dynamical systems. We formulate a rather general method of recovering the obstruction to integrability for the…