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In this paper, we apply a recently developed nonparametric modeling approach, the "diffusion forecast", to predict the time-evolution of Fourier modes of turbulent dynamical systems. While the diffusion forecasting method assumes the…
In this paper, a two-dimensional Dirichlet-to-Neumann (DtN) finite element method (FEM) is developed to analyze the scattering of SH guided waves due to an interface delamination in a bi-material plate. During the finite element analysis,…
Representation learning is all about discovering the hidden modular attributes that generate the data faithfully. We explore the potential of Denoising Diffusion Probabilistic Model (DM) in unsupervised learning of the modular attributes.…
Machine learning methods, such as diffusion models, are widely explored as a promising way to accelerate high-fidelity fluid dynamics computation via a super-resolution process from faster-to-compute low-fidelity input. However, existing…
Low-dose Computed Tomography (LDCT) reconstruction is an important task in medical image analysis. Recent years have seen many deep learning based methods, proved to be effective in this area. However, these methods mostly follow a…
Previous raw image-based low-light image enhancement methods predominantly relied on feed-forward neural networks to learn deterministic mappings from low-light to normally-exposed images. However, they failed to capture critical…
We develop unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations $$ \partial_t u-\mathfrak{L}[\varphi(u)]=f(x,t) \qquad\text{in}\qquad \mathbb{R}^N\times(0,T), $$…
Diffusion models have shown superior performance on unsupervised anomaly detection tasks. Since trained with normal data only, diffusion models tend to reconstruct normal counterparts of test images with certain noises added. However, these…
Denoising diffusion models have emerged as a dominant paradigm in image generation. Discretizing image data into tokens is a critical step for effectively integrating images with Transformer and other architectures. Although the Denoising…
We present a forward-modelling simulation framework designed to model the data products from the Dark Energy Survey (DES). This forward-model process can be thought of as a transfer function -- a mapping from cosmological and astronomical…
A prominent paradigm for graph neural networks is based on the message-passing framework. In this framework, information communication is realized only between neighboring nodes. The challenge of approaches that use this paradigm is to…
We develop a unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations $$ \partial_t u-\mathfrak{L}^{\sigma,\mu}[\varphi(u)]=f \quad\quad\text{in}\quad\quad…
A popular approach to sample a diffusion-based generative model is to solve an ordinary differential equation (ODE). In existing samplers, the coefficients of the ODE solvers are pre-determined by the ODE formulation, the reverse discrete…
Denosing diffusion model, as a generative model, has received a lot of attention in the field of image generation recently, thanks to its powerful generation capability. However, diffusion models have not yet received sufficient research in…
Deep Ensemble (DE) approach is a straightforward technique used to enhance the performance of deep neural networks by training them from different initial points, converging towards various local optima. However, a limitation of this…
Out-of-distribution (OOD) detection is a crucial part of deploying machine learning models safely. It has been extensively studied with a plethora of methods developed in the literature. This problem is tackled with an OOD score…
For faster sampling and higher sample quality, we propose DiNof ($\textbf{Di}$ffusion with $\textbf{No}$rmalizing $\textbf{f}$low priors), a technique that makes use of normalizing flows and diffusion models. We use normalizing flows to…
In this work, we consider the numerical solution of an initial boundary value problem for the distributed order time fractional diffusion equation. The model arises in the mathematical modeling of ultra-slow diffusion processes observed in…
Deep learning has revolutionized the field of computer vision by introducing large scale neural networks with millions of parameters. Training these networks requires massive datasets and leads to intransparent models that can fail to…
We study solution techniques for an evolution equation involving second order derivative in time and the spectral fractional powers, of order $s \in (0,1)$, of symmetric, coercive, linear, elliptic, second-order operators in bounded domains…