相关论文: A Nonlinear Hyperbolic Model for Radiative Transfe…

Solution of Helmholtz equation with impedance boundary condition on finite interval is equivalently reformulated as steady state of initial boundary value problem for first order hyperbolic system of partial differential equations.…

In this paper, we present a systematic stability analysis of the quadrature-based moment method (QBMM) for the one-dimensional Boltzmann equation with BGK or Shakhov models. As reported in recent literature, the method has revealed its…

The progress in hyperbolic neural networks (HNNs) research is hindered by their absence of inductive bias mechanisms, which are essential for generalizing to new tasks and facilitating scalable learning over large datasets. In this paper,…

We provide two new classes of moment models for linear kinetic equations in slab and three-dimensional geometry. They are based on classical finite elements and low-order discontinuous-Galerkin approximations on the unit sphere. We…

Linear kinetic transport equations play a critical role in optical tomography, radiative transfer and neutron transport. The fundamental difficulty hampering their efficient and accurate numerical resolution lies in the high dimensionality…

This paper introduces a method of calculating and rendering shapes in a non-Euclidean 2D space. In order to achieve this, we developed a physics and graphics engine that uses hyperbolic trigonometry to calculate and subsequently render the…

In this paper, we intend to bring together the hyperbolic spinors, which are useful frameworks from mathematics to physics, and both spacelike and timelike framed curves in Minkowski 3-space $\mathbb{R}_1^3$, which are new type attractive…

The interaction of neural networks with physical equations offers a wide range of applications. We provide a method which enables a neural network to transform objects subject to given physical constraints. Therefore an U-Net architecture…

Stable, accurate, divergence-free simulation of magnetized supersonic turbulence is a severe test of numerical MHD schemes and has been surprisingly difficult to achieve due to the range of flow conditions present. Here we present a new,…

In many cases, analytic solutions of partial differential equations may not be possible. For practical problems, it is more reasonable to carry out computational solutions. However, the standard grid in the finite difference approximation…

The Standard Model of elementary particle physics is one of the most successful models of contemporary theoretical physics being in full agreement with experiments. However, its mathematical structure deserves further investigations both…

In this paper, we present a regularization to 1D Grad's moment system to achieve global hyperbolicity. The regularization is based on the observation that the characteristic polynomial of the Jacobian of the flux in Grad's moment system is…

Large language models (LLMs) have achieved remarkable success and demonstrated superior performance across various tasks, including natural language processing (NLP), weather forecasting, biological protein folding, text generation, and…

Hyperbolic geometry has emerged as an effective latent space for representing complex networks, owing to its ability to capture hierarchical organization and heterogeneous connectivity patterns using low-dimensional embeddings. As a result,…

High-dimensional multiplex graphs are characterized by their high number of complementary and divergent dimensions. The existence of multiple hierarchical latent relations between the graph dimensions poses significant challenges to…

The ability of Machine-Learning (ML) based model components to generalize to the previously unseen inputs, and the resulting stability of the models that use these components, has been receiving a lot of recent attention, especially when it…

As more and more numerical and analytical solutions to the linear neutron transport equation become available, verification of numerical results is increasingly important. This presentation concerns the development of another benchmark for…

Recent works have demonstrated promising performances of neural networks on hyperbolic spaces and symmetric positive definite (SPD) manifolds. These spaces belong to a family of Riemannian manifolds referred to as symmetric spaces of…

This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The…

Continuum mechanics simulators, numerically solving one or more partial differential equations, are essential tools in many areas of science and engineering, but their performance often limits application in practice. Recent modern machine…