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For hyperbolic conservation laws, traditional methods and physics-informed neural networks (PINNs) often encounter difficulties in capturing sharp discontinuities and maintaining temporal consistency. To address these challenges, we…

We present a new, first-order, flux-conservative formulation of relativistic viscous hydrodynamics in the BDNK framework, applicable to conformal and nonconformal fluids at zero chemical potential. Focusing on the conformal case in 1+1…

Real-time tool segmentation is an essential component in computer-assisted surgical systems. We propose a novel real-time automatic method based on Fully Convolutional Networks (FCN) and optical flow tracking. Our method exploits the…

This study enhances the application of Physics-Informed Neural Networks (PINNs) for modeling discontinuous solutions in both hydrodynamics and relativistic hydrodynamics. Conventional PINNs, trained with partial differential equation…

We present a novel physics-informed deep learning framework for solving steady-state incompressible flow on multiple sets of irregular geometries by incorporating two main elements: using a point-cloud based neural network to capture…

We introduce an extended discontinuous Galerkin discretization of hyperbolic-parabolic problems on multidimensional semi-infinite domains. Building on previous work on the one-dimensional case, we split the strip-shaped computational domain…

Two dimensional (2D) peak finding is a common practice in data analysis for physics experiments, which is typically achieved by computing the local derivatives. However, this method is inherently unstable when the local landscape is…

Atrial Fibrillation (AF) is a common electro-physiological cardiac disorder that causes changes in the anatomy of the atria. A better characterization of these changes is desirable for the definition of clinical biomarkers, furthermore,…

To mitigate the detection performance drop caused by domain shift, we aim to develop a novel few-shot adaptation approach that requires only a few target domain images with limited bounding box annotations. To this end, we first observe…

In the physically non viscous fluid dynamics, "shock capturing" methods adopt either an artificial viscosity contribution or an appropriate Riemann solver algorithm. These techniques are necessary to solve the strictly hyperbolic Euler…

The detection of abnormal behaviours in crowded scenes has to deal with many challenges. This paper presents an efficient method for detection and localization of anomalies in videos. Using fully convolutional neural networks (FCNs) and…

We propose a new data-driven method to learn the dynamics of an unknown hyperbolic system of conservation laws using deep neural networks. Inspired by classical methods in numerical conservation laws, we develop a new conservative form…

In recent work, Li et al.\ (Comm.\ Math.\ Sci., 7:81-107, 2009) developed a diffuse-domain method (DDM) for solving partial differential equations in complex, dynamic geometries with Dirichlet, Neumann, and Robin boundary conditions. The…

We prove that for the two-dimensional steady complete compressible Euler system, with given uniform upcoming supersonic flows, the following three fundamental flow patterns (special solutions) in gas dynamics involving transonic shocks are…

Accurate yet efficient surrogate models are essential for large-scale simulations of partial differential equations (PDEs), particularly for uncertainty quantification (UQ) tasks that demand hundreds or thousands of evaluations. We develop…

Smoothed particle hydrodynamics (SPH) is omnipresent in modern engineering and scientific disciplines. SPH is a class of Lagrangian schemes that discretize fluid dynamics via finite material points that are tracked through the evolving…

In this work, we propose a novel selective discontinuity sensor approach for numerical simulations of the compressible Navier-Stokes equations. Since transformation to characteristic space is already a common approach to reduce…

In this paper, we propose a fast fully convolutional neural network (FCNN) for crowd segmentation. By replacing the fully connected layers in CNN with 1 by 1 convolution kernels, FCNN takes whole images as inputs and directly outputs…

In our prior work [arXiv:2109.09316], neural network methods with inputs based on domain of dependence and a converging sequence were introduced for solving one dimensional conservation laws, in particular the Euler systems. To predict a…

Hydrodynamical numerical methods that converge with high-order hold particular promise for astrophysical studies, as they can in principle reach prescribed accuracy goals with higher computational efficiency than standard second- or…