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Machine learning models struggle with generalization when encountering out-of-distribution (OOD) samples with unexpected distribution shifts. For vision tasks, recent studies have shown that test-time adaptation employing diffusion models…
Abstract. The advancement of deep learning has coincided with the proliferation of both models and available data. The surge in dataset sizes and the subsequent surge in computational requirements have led to the development of the Dataset…
The decentralized gradient descent (DGD) algorithm, and its sibling, diffusion, are workhorses in decentralized machine learning, distributed inference and estimation, and multi-agent coordination. We propose a novel, principled framework…
This article performs a unified convergence analysis of a variety of numerical methods for a model of the miscible displacement of one incompressible fluid by another through a porous medium. The unified analysis is enabled through the…
Masked diffusion models (MDMs) have emerged as a popular research topic for generative modeling of discrete data, thanks to their superior performance over other discrete diffusion models, and are rivaling the auto-regressive models (ARMs)…
In this work, we investigate the $hp$-discontinuous Galerkin (DG) time-stepping method for the generalized Burgers-Huxley equation with memory, a non-linear advection-diffusion-reaction problem featuring weakly singular kernels. We derive a…
In this article we consider the numerical approximation of the convection-diffusion-reaction equation. One of the main challenges of designing a numerical method for this problem is that boundary layers occurring in the convection-dominated…
This paper explores the residual based a posteriori error estimations for the generalized Burgers-Huxley equation (GBHE) featuring weakly singular kernels. Initially, we present a reliable and efficient error estimator for both the…
We present a higher order space-time unfitted finite element method for convection-diffusion problems on coupled (surface and bulk) domains. In that way, we combine a method suggested by Heimann, Lehrenfeld, Preu{\ss} (SIAM J. Sci. Comput.…
We developed a statistical inference method applicable to a broad range of generalized linear models (GLMs) in high-dimensional settings, where the number of unknown coefficients scales proportionally with the sample size. Although a…
Recently proposed generative models for discrete data, such as Masked Diffusion Models (MDMs), exploit conditional independence approximations to reduce the computational cost of popular Auto-Regressive Models (ARMs), at the price of some…
A hydrogeological model for the spread of pollution in an aquifer is considered. The model consists in a convection-diffusion-reaction equation involving the dispersion tensor which depends nonlinearly of the fluid velocity. We introduce an…
Gradient-based approximate inference methods, such as Stein variational gradient descent (SVGD), provide simple and general-purpose inference engines for differentiable continuous distributions. However, existing forms of SVGD cannot be…
We propose and analyze a time-stepping discontinuous Petrov-Galerkin method combined with the continuous conforming finite element method in space for the numerical solution of time-fractional subdiffusion problems. We prove the existence,…
Diffusion models are distinguished by their exceptional generative performance, particularly in producing high-quality samples through iterative denoising. While current theory suggests that the number of denoising steps required for…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…
Solving partial differential equations (PDEs) on fine spatio-temporal scales for high-fidelity solutions is critical for numerous scientific breakthroughs. Yet, this process can be prohibitively expensive, owing to the inherent complexities…
Recent advances in generative modeling with diffusion processes (DPs) enabled breakthroughs in image synthesis. Despite impressive image quality, these models have various prompt compliance problems, including low recall in generating…
In this work we address the analysis of the stationary generalized Burgers-Huxley equation (a nonlinear elliptic problem with anomalous advection) and propose conforming, nonconforming and discontinuous Galerkin finite element methods for…
Convection-diffusion-reaction equations are a class of second-order partial differential equations widely used to model phenomena involving the change of concentration/population of one or more substances/species distributed in space.…