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We present new analytical and numerical results for the elliptic-parabolic system of partial differential equations proposed by Hu and Cai, which models the formation of biological transport networks. The model describes the pressure field…

We introduce TopoX, a Python software suite that provides reliable and user-friendly building blocks for computing and machine learning on topological domains that extend graphs: hypergraphs, simplicial, cellular, path and combinatorial…

The open-source PyNX toolkit [Favre-Nicolin et al (2011) arXiv:1010.2641, Mandula et al (2016)] has been extended to provide tools for coherent X-ray imaging data analysis and simulation. All calculations can be executed on graphical…

Simulation of multiphase flow in porous media is crucial for the effective management of subsurface energy and environment related activities. The numerical simulators used for modeling such processes rely on spatial and temporal…

In this paper, we extend the reinterpreted discrete fracture model for flow simulation of fractured porous media containing flow blocking barriers on non-conforming meshes. The methodology of the approach is to modify the traditional…

Conventional physically based rendering (PBR) pipelines generate photorealistic images through computationally intensive light transport simulations. Although recent deep learning approaches leverage diffusion model priors with geometry…

The paper studies a finite element method for computing transport and diffusion along evolving surfaces. The method does not require a parametrization of a surface or an extension of a PDE from a surface into a bulk outer domain. The…

In recent years, deep learning methods, exemplified by Physics-Informed Neural Networks (PINNs), have been widely applied to the numerical solution of differential equations. However, these methods may suffer from limited accuracy, high…

Two-scale models pose a promising approach in simulating reactive flow and transport in evolving porous media. Classically, homogenized flow and transport equations are solved on the macroscopic scale, while effective parameters are…

Diffusion transformers have recently delivered strong text-to-image generation around 1K resolution, but we show that extending them to native 4K across diverse aspect ratios exposes a tightly coupled failure mode spanning positional…

We introduce CORTEX, an algorithmic framework designed for large-scale brain simulation. Leveraging the computational capacity of the Fugaku Supercomputer, CORTEX maximizes available problem size and processing performance. Our primary…

In this study, we propose a unified, general framework for the direct discontinuous Galerkin methods. In the new framework, the antiderivative of the nonlinear diffusion matrix is not needed. This allows a simple definition of the numerical…

We construct transported PDEs on self-similar fractal domains from reference equations posed on the unit interval, and derive explicit self-similar interacting particle systems that approximate the resulting dynamics. The construction…

This work focuses on model preparation for electrostatic simulations of CAD designs to realize a rapid virtual prototyping concept. We present a boundary element method (BEM) allowing discontinuous fields between surfaces. The corresponding…

We present the recent development of hybridizable and embedded discontinuous Galerkin (DG) methods for wave propagation problems in fluids, solids, and electromagnetism. In each of these areas, we describe the methods, discuss their main…

Computer algebra methods for analyzing reaction networks often rely on the assumption of mass-action kinetics, which transform the governing ODEs into polynomial systems amenable to techniques such as Gr\"obner basis computation and related…

In this paper, we introduce our open source implementation of the Coupled Discrete Unified Gas Kinetic Scheme (CDUGKS) of https://journals.aps.org/pre/abstract/10.1103/PhysRevE.98.053310, a phase space scheme capable of handling a wide…

Partial differential equation (PDE) simulation holds extensive significance in scientific research. Currently, the integration of deep neural networks to learn solution operators of PDEs has introduced great potential. In this paper, we…

Over the past few years, neural network methods have evolved in various directions for approximating partial differential equations (PDEs). A promising new development is the integration of neural networks with classical numerical…

We introduce a framework to intertwine dynamical processes of different nature, each with its own distinct network topology, using a multilayer network approach. As an example of collective phenomena emerging from the interactions of…