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Convection-diffusion equations arise in a variety of applications such as particle transport, electromagnetics, and magnetohydrodynamics. Simulation of the convection-dominated regime for these problems, even with high-fidelity techniques,…

We present a novel artificial diffusion method to circumvent the instabilities associated with the standard finite element approximation of convection-diffusion equations. Motivated by the micromorphic approach, we introduce an auxiliary…

A novel method to improve the accuracy of pressure field estimation from time-resolved Particle Image Velocimetry data is proposed. This method generates several new time-series of velocity field by propagating in time the original one…

Image-based 3D generation has vast applications in robotics and gaming, where high-quality, diverse outputs and consistent 3D representations are crucial. However, existing methods have limitations: 3D diffusion models are limited by…

A central challenge in Bayesian inference is efficiently approximating posterior distributions. Stein Variational Gradient Descent (SVGD) is a popular variational inference method which transports a set of particles to approximate a target…

In this work, it is shown that image reconstruction methods from ultrasonic imaging can be employed for thermographic signals. Before using these imaging methods, a virtual signal is calculated by applying a local transformation to the…

The Convected Scheme (CS) is a `forward-trajectory' semi-Lagrangian method for solution of transport equations, which has been most often applied to the kinetic description of plasmas and rarefied neutral gases. In its simplest form, the CS…

We present a sequential data assimilation algorithm based on the ensemble Kalman inversion to estimate the near-surface shear wave velocity profile and damping when heterogeneous data and a priori information that can be represented in…

A fast inverse heat conduction model (IHCM) is developed for estimating unknown properties of multi-layer composites considering internal heat generation. This work builds on the validated analytical forward models presented in Part I.…

We consider the numerical approximation of the ill-posed data assimilation problem for stationary convection-diffusion equations and extend our previous analysis in [Numer. Math. 144, 451--477, 2020] to the convection-dominated regime.…

Distribution Matching Distillation (DMD) is a widely used paradigm for accelerating inference in few-step video diffusion models. However, DMD-style video distillation faces two coupled challenges: the fake score must track a continuously…

Existing algorithms with iterations as the principle for 3D inverse heat conduction problems (IHCPs) are usually time-consuming. With the recent advancements in deep learning techniques, it is possible to apply the neural network to compute…

Real-time estimations of temperature distributions and geometric configurations are important to energy efficient buildings and the development of smarter cities. In this paper we formulate a gradient-based estimation algorithm capable of…

In this paper, based on neural networks, we develop a data-driven model for extremely fast prediction of steady-state heat convection of a hot object with arbitrary complex geometry in a two-dimensional space. According to the governing…

Diffusion models generate high-quality images but require dozens of forward passes. We introduce Distribution Matching Distillation (DMD), a procedure to transform a diffusion model into a one-step image generator with minimal impact on…

This paper introduces a novel optimization algorithm designed for nonlinear least-squares problems. The method is derived by preconditioning the gradient descent direction using the Singular Value Decomposition (SVD) of the Jacobian. This…

We present Stable Video 3D (SV3D) -- a latent video diffusion model for high-resolution, image-to-multi-view generation of orbital videos around a 3D object. Recent work on 3D generation propose techniques to adapt 2D generative models for…

The numerical approximation of an inverse problem subject to the convection--diffusion equation when diffusion dominates is studied. We derive Carleman estimates that are on a form suitable for use in numerical analysis and with explicit…

In this work the authors consider the recovery of the point source in the heat equation. The used data is the sparse boundary measurements. The uniqueness theorem of the inverse problem is given. After that, the numerical reconstruction is…

Tokenizers are a key component of state-of-the-art generative image models, extracting the most important features from the signal while reducing data dimension and redundancy. Most current tokenizers are based on KL-regularized variational…