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We propose a numerical approach for solving conjugate heat transfer problems using the finite volume method. This approach combines a semi-implicit scheme for fluid flow, governed by the incompressible Navier-Stokes equations, with an…
We consider the inverse problem of reconstructing the interior boundary curve of a doubly connected domain from the knowledge of the temperature and the thermal flux on the exterior boundary curve. The use of the Laguerre transform in time…
Tungsten is a promising candidate material for plasma-facing armour components in future fusion reactors. A key concern is irradiation-induced degradation of its normally excellent thermal transport properties. In this comprehensive study,…
We propose a novel approach to numerically approximate McKean-Vlasov stochastic differential equations (MV-SDE) using stochastic gradient descent (SGD) while avoiding the use of interacting particle systems (IPS) {and the associated…
The diffusion approximation of stochastic gradient descent (SGD) in current literature is only valid on a finite time interval. In this paper, we establish the uniform-in-time diffusion approximation of SGD, by only assuming that the…
Complex object wave recovery from single-shot interference pattern is an important practical problem in interferometry and digital holography. The most popular single-shot interferogram analysis method involves Fourier filtering of…
Diffusion models have advanced from text-to-image (T2I) to image-to-image (I2I) generation by incorporating structured inputs such as depth maps, enabling fine-grained spatial control. However, existing methods either train separate models…
Many real-world data are sequentially collected over time and often exhibit skewed class distributions, resulting in imbalanced data streams. While existing approaches have explored several strategies, such as resampling and reweighting,…
The balancing domain decomposition methods (BDDC) are originally introduced for symmetric positive definite systems and have been extended to the nonsymmetric positive definite system from the linear finite element discretization of…
The intensive computational burden of Stable Diffusion (SD) for text-to-image generation poses a significant hurdle for its practical application. To tackle this challenge, recent research focuses on methods to reduce sampling steps, such…
Smoothed dissipative particle dynamics (SDPD) is a widely used particle-based method for modelling soft matter systems at mesoscopic and macroscopic scales, offering thermodynamic consistency and direct control over the fluid's transport…
Latest diffusion-based methods for many image restoration tasks outperform traditional models, but they encounter the long-time inference problem. To tackle it, this paper proposes a Wavelet-Based Diffusion Model (WaveDM). WaveDM learns the…
This paper proposes a novel approach to spectral computed tomography (CT) material decomposition that uses the recent advances in generative diffusion models (DMs) for inverse problems. Spectral CT and more particularly photon-counting CT…
In this paper, the focus is on the reconstruction of a diffusive field and the localization of the underlying driving sources on arbitrary graphs by observing a significantly smaller subset of vertices of the graph uniformly in time.…
Sparse-view Computed Tomography (CT) image reconstruction is a promising approach to reduce radiation exposure, but it inevitably leads to image degradation. Although diffusion model-based approaches are computationally expensive and suffer…
In this paper, we describe a stable finite element formulation for advection-diffusion-reaction problems that allows for robust automatic adaptive strategies to be easily implemented. We consider locally vanishing, heterogeneous, and…
Standard Latent Diffusion Models rely on a complex, three-part architecture consisting of a separate encoder, decoder, and diffusion network, which are trained in multiple stages. This modular design is computationally inefficient, leads to…
Generative diffusion models have achieved remarkable success in producing high-quality images. However, these models typically operate in continuous intensity spaces, diffusing independently across pixels and color channels. As a result,…
Problems with dominant advection, discontinuities, travelling features, or shape variations are widespread in computational mechanics. However, classical linear model reduction and interpolation methods typically fail to reproduce even…
Stein Variational Gradient Descent (SVGD) is an algorithm for sampling from a target density which is known up to a multiplicative constant. Although SVGD is a popular algorithm in practice, its theoretical study is limited to a few recent…