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The Green function has a complex dependence upon its underlying domain and differential operator. We briefly review Hadamard's formula for the first variation of the Green function due to a perturbation of the domain. We then take a…
Approximating wind flows using computational fluid dynamics (CFD) methods can be time-consuming. Creating a tool for interactively designing prototypes while observing the wind flow change requires simpler models to simulate faster. Instead…
We study large deviations in the Langevin dynamics, with damping of order $\e^{-1}$ and noise of order $1$, as $\e\downarrow 0$. The damping coefficient is assumed to be state dependent. We proceed first with a change of time and then, we…
This paper investigates the numerical modeling of a time-dependent heat transmission problem by the convolution quadrature boundary element method. It introduces the latest theoretical development into the error analysis of the numerical…
Use energy-based model for bridge-type innovation. The loss function is explained by the game theory, the logic is clear and the formula is simple and clear. Thus avoid the use of maximum likelihood estimation to explain the loss function…
Seismic inverse modeling is a common method in reservoir prediction and it plays a vital role in the exploration and development of oil and gas. Conventional seismic inversion method is difficult to combine with complicated and abstract…
Recently, a first-order differentiator based on time-varying gains was introduced in the literature, in its non recursive form, for a class of differentiable signals $y(t)$, satisfying $|\ddot{y}(t)|\leq L(t-t_0)$, for a known function…
An end-to-end strategy for hybrid quantum-classical computations of Green's functions in many-body systems is presented and applied to the pairing model. The scheme makes explicit use of the spectral representation of the Green's function,…
A new domain decomposition method for Maxwell's equations in conductive media is presented. Using this method reconstruction algorithms are developed for determination of dielectric permittivity function using time-dependent scattered data…
We present a method for analytic continuation of retarded Green functions, including Euclidean Green functions computed using lattice QCD. The method is based on conformal maps and construction of an interpolation function which is analytic…
During the past three years, Wapenaar, Snieder, Broggini and others have developed an algorithm to compute the Green's function for any point inside a medium to points on the surface from measurements on that surface only. Their algorithm…
Implicit generative models have the capability to learn arbitrary complex data distributions. On the downside, training requires telling apart real data from artificially-generated ones using adversarial discriminators, leading to unstable…
While working within the spatial domain can pose problems associated with ill-conditioned scores caused by power-law decay, recent advances in diffusion-based generative models have shown that transitioning to the wavelet domain offers a…
This study focuses on inverting time-domain airborne electromagnetic data in 2D by training a neural-network to understand the relationship between data and conductivity, thereby removing the need for expensive forward modeling during the…
In this paper, we establish a priori estimates for the positive solutions to a higher-order fractional Laplace equation on a bounded domain by a blowing-up and rescaling argument. To overcome the technical difficulty due to the high-order…
Latent force models (LFM) are principled approaches to incorporating solutions to differential equations within non-parametric inference methods. Unfortunately, the development and application of LFMs can be inhibited by their computational…
We consider an outward degenerate drifted Brownian motion in the quarter plane with oblique reflections on the boundaries. In this article, we explicitly compute the Laplace transforms of the Green's functions associated with the process.…
This work considers a time domain inverse acoustic obstacle scattering problem due to passive data. Motivated by the Helmholtz-Kirchhoff identity in the frequency domain, we propose to relate the time domain measurement data in passive…
We put forward a general approach for calculating the quantum energy level shift for emitter in arbitrary nanostructures, in which the energy level shift is expressed by the sum of the real part of the scattering photon Green function (GF)…
Normalizing flows attempt to model an arbitrary probability distribution through a set of invertible mappings. These transformations are required to achieve a tractable Jacobian determinant that can be used in high-dimensional scenarios.…