相关论文: Efficient numerical method for predicting nonlinea…
We introduce stochastic models for continuous-time evolution of angles and develop their estimation. We focus on studying Langevin diffusions with stationary distributions equal to well-known distributions from directional statistics, since…
In the last three decades, powerful computer-assisted techniques have been developed in order to validate a posteriori numerical solutions of semilinear elliptic problems of the form $\Delta u +f(u,\nabla u) = 0$. By studying a well chosen…
Guided diffusion is a technique for conditioning the output of a diffusion model at sampling time without retraining the network for each specific task. One drawback of diffusion models, however, is their slow sampling process. Recent…
(abridged) Imaging observations are generally affected by a fluctuating background of speckles, a particular problem when detecting faint stellar companions at small angular separations. Knowing the distribution of the speckle intensities…
Ultrafast-optical-pump -- structural-probe measurements, including ultrafast electron and x-ray scattering, provide direct experimental access to the fundamental timescales of atomic motion, and are thus foundational techniques for studying…
Modern optical flow methods make use of salient scene feature points detected and matched within the scene as a basis for sparse-to-dense optical flow estimation. Current feature detectors however either give sparse, non uniform point…
We propose a novel framework for the systematic design of lensless imaging systems based on the hyperuniform random field solutions of nonlinear reaction-diffusion equations from pattern formation theory. Specifically, we introduce a new…
The reported results for ultrasonic wave attenuation constant ({\alpha}) in pure water show noticeable inconsistency in magnitude. A "Propagating-Wave" model analysis of the most popular pulse-echo technique indicates that this is a…
Spectral methods for solving partial differential equations (PDEs) and stochastic partial differential equations (SPDEs) often use Fourier or polynomial spectral expansions on either uniform and non-uniform grids. However, while very widely…
The spark plasma sintering (SPS) process, a key technology for advanced material manufacturing, demands accurate and efficient simulation tools to capture the complex electro-thermal-mechanical interactions inherent in powder materials.…
We present a real-time propagation method for computing linear and nonlinear optical properties of molecules based on the Bethe-Salpeter equation. The method follows the time evolution of the one-particle density matrix under an external…
Image enhancement holds extensive applications in real-world scenarios due to complex environments and limitations of imaging devices. Conventional methods are often constrained by their tailored models, resulting in diminished robustness…
We develop the Fourier-Laplace Inversion of the Perturbation Theory (FLIPT), a novel numerically exact "black box" method to compute perturbative expansions of the density matrix with rigorous convergence conditions. Specifically, the FLIPT…
We propose a new theoretical framework that exploits convolution kernels to transform a Volterra-type path-dependent (non-Markovian) stochastic process into a standard (Markovian) diffusion process. Remarkably, it is also possible to go…
A Gaussian process (GP)-based methodology is proposed to emulate complex dynamical computer models (or simulators). The method relies on emulating the numerical flow map of the system over an initial (short) time step, where the flow map is…
Bayesian inference provides a principled way of estimating the parameters of a stochastic process that is observed discretely in time. The overdamped Brownian motion of a particle confined in an optical trap is generally modelled by the…
We demonstrate a strategy for simulating wide-range X-ray scattering patterns, which spans the small- and wide scattering angles as well as the scattering angles typically used for Pair Distribution Function (PDF) analysis. Such simulated…
Due to the nonlocal feature of fractional differential operators, the numerical solution to fractional partial differential equations usually requires expensive memory and computation costs. This paper develops a fast scheme for fractional…
X-ray free electron laser (XFEL) experiments have brought unique capabilities and opened new directions in research, such as creating new states of matter or directly measuring atomic motion. One such area is the ability to use finely…
The goal of this paper is to propose two nonlinear variational models for obtaining a refined motion estimation from an image sequence. Both the proposed models can be considered as a part of a generalized framework for an accurate…