Related papers: Point spread function approximation of high rank H…

Hessian-free training has become a popular parallel second or- der optimization technique for Deep Neural Network training. This study aims at speeding up Hessian-free training, both by means of decreasing the amount of data used for…

This paper is concerned with the analysis of the kernel-based algorithm for gain function approximation in the feedback particle filter. The exact gain function is the solution of a Poisson equation involving a probability-weighted…

We construct deterministic particle solutions for linear and fast diffusion equations using a nonlocal approximation. We exploit the $2$-Wasserstein gradient flow structure of the equations in order to obtain the nonlocal approximating PDEs…

In this paper, we extend the class of kernel methods, the so-called diffusion maps (DM) and ghost point diffusion maps (GPDM), to solve the time-dependent advection-diffusion PDE on unknown smooth manifolds without and with boundaries. The…

In this work, we propose a SPH interpolating Kernel reformulation suitable also to treat free edge boundaries in the computational domain. Application to both inviscid and viscous stationary low compressibility accretion disc models in…

Point processes model the distribution of random point sets in mathematical spaces, such as spatial and temporal domains, with applications in fields like seismology, neuroscience, and economics. Existing statistical and machine learning…

Localization microscopy enables imaging with resolutions that surpass the conventional optical diffraction limit. Notably, the MINFLUX method achieves super-resolution by shaping the excitation point-spread function (PSF) to minimize the…

Point spread function (PSF) engineering has been pivotal in the remarkable progress made in high-resolution imaging in the last decades. However, the diversity in PSF structures attainable through existing engineering methods is limited.…

Simulated images are essential in algorithm development and instrument testing for optical telescopes. During real observations, images obtained by optical telescopes are affected by spatially variable point spread functions (PSFs), a…

A main science goal for the Large Synoptic Survey Telescope (LSST) is to measure the cosmic shear signal from weak lensing to extreme accuracy. One difficulty, however, is that with the short exposure time ($\simeq$15 seconds) proposed, the…

The knowledge of the point spread function (PSF) of imaging instruments represents a fundamental requirement for astronomical observations. The Herschel PACS PSFs delivered by the instrument control centre are obtained from observations of…

In this study, we propose Shortcut Fine-Tuning (SFT), a new approach for addressing the challenge of fast sampling of pretrained Denoising Diffusion Probabilistic Models (DDPMs). SFT advocates for the fine-tuning of DDPM samplers through…

Score-based generative models (SGMs) have recently emerged as a promising class of generative models. However, a fundamental limitation is that their inference is very slow due to a need for many (e.g., 2000) iterations of sequential…

Nonlinear function estimation is core to modern machine learning applications. In this paper, to perform nonlinear function estimation, we reduce a nonlinear inverse problem to a linear one using a polynomial kernel expansion. These kernels…

We consider minimizing finite-sum and expectation objective functions via Hessian-averaging based subsampled Newton methods. These methods allow for gradient inexactness and have fixed per-iteration Hessian approximation costs. The recent…

In this paper, we explore provable acceleration of diffusion models without any additional retraining. Focusing on the task of approximating a target data distribution in $\mathbb{R}^d$ to within $\varepsilon$ total-variation distance, we…

We propose a new technique for constructing low-rank approximations of matrices that arise in kernel methods for machine learning. Our approach pairs a novel automatically constructed analytic expansion of the underlying kernel function…

Context. Future weak lensing surveys, such as the Euclid mission, will attempt to measure the shapes of billions of galaxies in order to derive cosmological information. These surveys will attain very low levels of statistical error, and…

This paper considers distributed optimization problems, where each agent cooperatively minimizes the sum of local objective functions through the communication with its neighbors. The widely adopted distributed gradient method in solving…

This work proposes and analyzes a generalized acceleration technique for decreasing the computational complexity of using stochastic collocation (SC) methods to solve partial differential equations (PDEs) with random input data. The SC…