Related papers: Reduced Order Model Enhanced Source Iteration with…

Inverse problems are pervasive mathematical methods in inferring knowledge from observational and experimental data by leveraging simulations and models. Unlike direct inference methods, inverse problem approaches typically require many…

A data-driven projection-based reduced-order model (ROM) for nonlinear thermal radiative transfer (TRT) problems is presented. The TRT ROM is formulated by (i) a hierarchy of low-order quasidiffusion (aka variable Eddington factor)…

While super-resolution (SR) methods based on diffusion models exhibit promising results, their practical application is hindered by the substantial number of required inference steps. Recent methods utilize degraded images in the initial…

An adaptive projection-based reduced-order model (ROM) formulation is presented for model-order reduction of problems featuring chaotic and convection-dominant physics. An efficient method is formulated to adapt the basis at every time-step…

Fine-tuning large language models is essential for task-specific adaptation, yet it remains computationally prohibitive. Parameter-Efficient Fine-Tuning (PEFT) methods have emerged as a solution, but current approaches typically ignore the…

The current study aims to evaluate and investigate the development of projection-based reduced-order models (ROMs) for efficient and accurate RDE simulations. Specifically, we focus on assessing the projection-based ROM construction…

A novel method for solving the linear radiative transport equation (RTE) in a three-dimensional homogeneous medium is proposed and illustrated with numerical examples. The method can be used with an arbitrary phase function A(s,s') with the…

Semi-discrete optimal transport (SOT), which maps a continuous probability measure to a discrete one, is a fundamental problem with wide-ranging applications. Entropic regularization is often employed to solve the SOT problem, leading to a…

A posteriori reduced-order models (ROM), e.g. based on proper orthogonal decomposition (POD), are essential to affordably tackle realistic parametric problems. They rely on a trustful training set, that is a family of full-order solutions…

Reduced-order modeling (ROM) commonly refers to the construction, based on a few solutions (referred to as snapshots) of an expensive discretized partial differential equation (PDE), and the subsequent application of low-dimensional…

Text-to-image generation powered by Diffusion Transformers (DiTs) has made remarkable strides, yet remote sensing (RS) synthesis lags behind due to two barriers: the absence of a domain-specialized DiT prior and the prohibitive cost of…

We begin by briefly surveying some results on the convergence of the Stochastic Gradient Descent (SGD) Method, proved in a companion paper by the present authors. These results are based on viewing SGD as a version of Stochastic…

Despite its huge number of variants, standard Low-Rank Adaptation (LoRA) is still a dominant technique for parameter-efficient fine-tuning (PEFT). Nonetheless, it faces persistent challenges, including the pre-selection of an optimal rank…

An adaptive approach to using reduced-order models as surrogates in PDE-constrained optimization is introduced that breaks the traditional offline-online framework of model order reduction. A sequence of optimization problems constrained by…

We study synthetic aperture radar (SAR) imaging and motion estimation of complex scenes consisting of stationary and moving targets. We use the classic SAR setup with a single antenna emitting signals and receiving the echoes from the…

Radars provide robust perception of vehicle surroundings by effectively functioning in poor light and adverse weather conditions. Synthetic aperture radar (SAR) algorithms are employed to address the limited angular resolution of radars by…

In applications of diffusion models, controllable generation is of practical significance, but is also challenging. Current methods for controllable generation primarily focus on modifying the score function of diffusion models, while Mean…

Motivated by single-particle cryo-electron microscopy, multi-reference alignment (MRA) models the task of recovering an unknown signal from multiple noisy observations corrupted by random rotations. The standard approach,…

In this paper, we propose an equation-based parametric Reduced Order Model (ROM), whose accuracy is improved with data-driven terms added into the reduced equations. These additions have the aim of reintroducing contributions that in…

Reed-Solomon (RS) codes are widely used to correct errors in storage systems. Finding the error locator polynomial is one of the key steps in the error correction procedure of RS codes. Modular Approach (MA) is an effective algorithm for…