Related papers: Stochastic estimation of Green's functions with ap…
Transport properties of strongly correlated quantum systems are of central interest in condensed matter, ultracold atoms and in dense plasmas. There, the proper treatment of strong correlations poses a great challenge to theory. Here, we…
We introduce a guided stochastic sampling method that augments sampling from diffusion models with physics-based guidance derived from partial differential equation (PDE) residuals and observational constraints, ensuring generated samples…
Partial differential equations are often used to model various physical phenomena, such as heat diffusion, wave propagation, fluid dynamics, elasticity, electrodynamics and image processing, and many analytic approaches or traditional…
Macroscopic traffic flow is stochastic, but the physics-informed deep learning methods currently used in transportation literature embed deterministic PDEs and produce point-valued outputs; the stochasticity of the governing dynamics plays…
We apply a recently proposed Green Function Monte Carlo to the study of Hamiltonian lattice gauge theories. This class of algorithms computes quantum vacuum expectation values by averaging over a set of suitable weighted random walkers. By…
Scheduling control problems for a family of unitary networks under heavy traffic with general interarrival and service times, probabilistic routing and an infinite horizon discounted linear holding cost are studied. Diffusion control…
Treating the fermionic ground state problem as a constrained stochastic optimization problem, a formalism for fermionic quantum Monte Carlo is developed that makes no reference to a trial wavefunction. Exchange symmetry is enforced by…
We formulate a new model for transport in stochastic media with long-range spatial correlations where exponential attenuation (controlling the propagation part of the transport) becomes power law. Direct transmission over optical distance…
This paper is concerned with the study of Green's functions for one dimensional diffusions with constant diffusion coefficient and linear time inhomogeneous drift. It is well know that the whole line Green's function is given by a Gaussian.…
We discuss stochastic representations of advection diffusion equations with variable diffusivity, stochastic integrals of motion and generalized relative entropies.
In this paper, we propose and analyze a new stochastic homogenization method for diffusion equations with random and fast oscillatory coefficients. In the proposed method, the homogenized solutions are sought through a two-stage procedure.…
This paper presents a windowed Green function (WGF) method for the numerical solution of problems of elastic scattering by "locally-rough surfaces" (i.e., local perturbations of a half space), under either Dirichlet or Neumann boundary…
The distributed computing analysis of the accuracy of automodel solutions for the Green's function of a wide class of superdiffusive transport of perturbation on a uniform background is carried out. The approximate automodel solutions have…
We present a real-time second-order Green's function (GF) method for computing excited states in molecules and nanostructures, with a computational scaling of $O(N_{\rm e}^3$), where $N_{\rm e}$ is the number of electrons. The cubic scaling…
Stochastic diffusion equations are crucial for modeling a range of physical phenomena influenced by uncertainties. We introduce the generalized finite difference method for solving these equations. Then, we examine its consistency,…
Several widely used methods for the calculation of band structures and photo emission spectra, such as the GW approximation, rely on Many-Body Perturbation Theory. They can be obtained by iterating a set of functional differential equations…
A domain integral method employing a specific Green's function (i.e., incorporating some features of the global problem of wave propagation in an inhomogeneous medium) is developed for solving direct and inverse scattering problems relative…
The disorder averaged single-particle Green's function of electrons subject to a time-dependent random potential with long-range spatial correlations is calculated by means of bosonization in arbitrary dimensions. For static disorder our…
We present the variational multiscale (VMS) method for partial differential equations (PDEs) with stochastic coefficients and source terms. We use it as a method for generating accurate coarse-scale solutions while accounting for the effect…
We consider stochastic impulse control problems where the process is driven by a general one-dimensional diffusion. We shall show a new mathematical characterization of the value function as a linear function in a certain transformed space.…