Related papers: Adams Bashforth Moulton Solver for Inversion and E…
The paper presents a numerical analysis of the class of mathematical models of linear fractional oscillators, which is the Cauchy problem for a differential equation with derivatives of fractional orders in the sense of Gerasimov-Caputo. A…
Rectified-flow-based diffusion transformers like FLUX and OpenSora have demonstrated outstanding performance in the field of image and video generation. Despite their robust generative capabilities, these models often struggle with…
Flow and diffusion models achieve high-fidelity, high-resolution image synthesis, but often require many function evaluations (NFEs) at sampling time. Existing acceleration methods either require additional training through distillation or…
This work proposes a conformable fractional predictor-corrector algorithm for solving conformable fractional differential equations. Fractional calculus is finding applications in various scientific fields, but existing numerical methods…
This study addresses the critical challenge of error accumulation in spatio-temporal auto-regressive (AR) predictions within scientific machine learning models by exploring temporal integration schemes and adaptive multi-step rollout…
Multiphase flows are an important class of fluid flow and their study facilitates the development of diverse applications in industrial, natural, and biomedical systems. We consider a model that uses a continuum description of both phases…
Recent advances in flow-based generative models have enabled training-free, text-guided image editing by inverting an image into its latent noise and regenerating it under a new target conditional guidance. However, existing methods…
This paper presents the development of an Adaptive Algebraic Multiscale Solver for Compressible flow (C-AMS) in heterogeneous porous media. Similar to the recently developed AMS for incompressible (linear) flows [Wang et al., JCP, 2014],…
The alternating direction multiplier method (ADMM) is widely used in computer graphics for solving optimization problems that can be nonsmooth and nonconvex. It converges quickly to an approximate solution, but can take a long time to…
In this paper, our objective is primarily to use adaptive inverse-quadratic (IQ) and inverse-multi-quadratic (IMQ) radial basis function (RBF) interpolation techniques to develop an enhanced Adam-Bashforth and Adam-Moulton methods. By…
The Potts model has many applications. It is equivalent to some min-cut and max-flow models. Primal-dual algorithms have been used to solve these problems. Due to the special structure of the models, convergence proof is still a difficult…
Diffusion probabilistic models (DPMs) have been shown to generate high-quality images without the need for delicate adversarial training. However, the current sampling process in DPMs is prone to violent shaking. In this paper, we present a…
In clinical practice, full imaging is not always feasible, often due to complex acquisition protocols, stringent privacy regulations, or specific clinical needs. However, missing MR modalities pose significant challenges for tasks like…
We present a generalization of the Adams-Bashforth-Moulton predictor-corrector numerical integration methods to an adaptive grid. The step size may be chosen dynamically in order to maintain a desired relative magnitude of error in each…
Numerical simulation of multi-component flow systems characterized by the simultaneous presence of pressure-velocity coupling and pressure-density coupling dominated regions remains a significant challenge in computational fluid dynamics.…
This study presents an advanced sharp-interface immersed boundary method (IBM) integrated with the blastFOAM library on the OpenFOAM platform for high-speed compressible flow simulations. The developed solver extends the existing IBM…
In this work, we introduce the novel application of the adaptive mesh refinement (AMR) technique in the global stability analysis of incompressible flows. The design of an accurate mesh for transitional flows is crucial. Indeed, an…
Objective: The study aims to address the challenge of aligning Standard Fundus Images (SFIs) and Ultra-Widefield Fundus Images (UWFIs), which is difficult due to their substantial differences in viewing range and the amorphous appearance of…
The alternating direction method of multipliers (ADMM) is a powerful splitting algorithm for linearly constrained convex optimization problems. In view of its popularity and applicability, a growing attention is drawn towards the ADMM in…
This paper presents a parallel and fully conservative adaptive mesh refinement (AMR) implementation of a finite-volume-based kinetic solver for compressible flows. Time-dependent H-type refinement is combined with a two-population…