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Pixel-space diffusion has re-emerged as a promising alternative to latent-space generation because it avoids the representation bottleneck introduced by VAEs. Yet most existing methods still treat image generation as a frequency-homogeneous…
HyperNetX (HNX) is an open source Python library for the analysis and visualization of complex network data modeled as hypergraphs. Initially released in 2019, HNX facilitates exploratory data analysis of complex networks using algebraic…
Understanding and controlling diffusion processes in complex networks is critical across domains ranging from epidemiology to information science. Here, we present ExDiff, an interactive and modular computational framework that integrates…
We present a first numerical study of transport phenomena involving chemically reactive species, modeled by advection-diffusion-reaction systems with flow fields governed by Darcy's law. Among the various discretisation approaches, we…
BridgeNet is a novel hybrid framework that integrates convolutional neural networks with physics-informed neural networks to efficiently solve non-linear, high-dimensional Fokker-Planck equations (FPEs). Traditional PINNs, which typically…
We develop a novel physics informed deep learning approach for solving nonlinear drift-diffusion equations on metric graphs. These models represent an important model class with a large number of applications in areas ranging from transport…
We propose SymPlex, a reinforcement learning framework for discovering analytical symbolic solutions to partial differential equations (PDEs) without access to ground-truth expressions. SymPlex formulates symbolic PDE solving as…
Physics-informed neural networks (PINNs) have successfully addressed various computational physics problems based on partial differential equations (PDEs). However, while tackling issues related to irregularities like singularities and…
The mass flow rate of Poiseuille flow of rarefied gas through long ducts of two-dimensional cross-sections with arbitrary shape are critical in the pore-network modeling of gas transport in porous media. In this paper, for the first time,…
Non-linear convection-reaction-diffusion (CRD) partial differential equations (PDEs) are crucial for modeling complex phenomena in fields such as biology, ecology, population dynamics, physics, and engineering. Numerical approximation of…
This article presents a multi-physics methodology for the numerical simulation of physical systems that involve the non-linear interaction of multi-phase reactive fluids and elastoplastic solids, inducing high strain-rates and high…
This work concerns the numerical solution of a coupled system of self-consistent reaction-drift-diffusion-Poisson equations that describes the macroscopic dynamics of charge transport in photoelectrochemical (PEC) solar cells with reactive…
Molecular dynamics simulations play an increasingly important role in the rational design of (nano)-materials and in the study of biomacromolecules. However, generating input files and realistic starting coordinates for these simulations is…
Fine-scale simulation of complex systems governed by multiscale partial differential equations (PDEs) is computationally expensive and various multiscale methods have been developed for addressing such problems. In addition, it is…
This work proposes a unified $hp$-adaptivity framework for hybridized discontinuous Galerkin (HDG) method for a large class of partial differential equations (PDEs) of Friedrichs' type. In particular, we present unified $hp$-HDG…
We present a computational framework for modeling large-scale particle-laden flows in complex domains with the goal of enabling simulations in medical-image derived patient specific geometries. The framework is based on a volume-filtered…
We present a numerical method to model the dynamics of inextensible biomembranes in a quasi-Newtonian incompressible flow, which better describes hemorheology in the small vasculature. We consider a level set model for the fluid-membrane…
This paper presents PipeFusion, an innovative parallel methodology to tackle the high latency issues associated with generating high-resolution images using diffusion transformers (DiTs) models. PipeFusion partitions images into patches and…
With the recent proliferation of heterogeneous, GPU-accelerated supercomputers, high-order computational fluid dynamics (CFD) simulations of complex, turbulent flows are more accessible than ever. To leverage the computing power of these…
Integro-differential equations, analyzed in this work, comprise an important class of models of continuum media with nonlocal interactions. Examples include peridynamics, population and opinion dynamics, the spread of disease models, and…