相关论文: A Nonlinear Hyperbolic Model for Radiative Transfe…
Geometric representation learning has recently shown great promise in several machine learning settings, ranging from relational learning to language processing and generative models. In this work, we consider the problem of performing…
Recent papers in the graph machine learning literature have introduced a number of approaches for hyperbolic representation learning. The asserted benefits are improved performance on a variety of graph tasks, node classification and link…
This dissertation presents a new coupled electro-mechanical model that is an improvement on the classical parallel-plate approximation. The model employs a hyperbolic function to account for the beam deformed shape and electrostatic field.…
Various neuroimaging studies suffer from small sample size problem which often limit their reliability. Meta-analysis addresses this challenge by aggregating findings from different studies to identify consistent patterns of brain activity.…
In this paper, we take a data-driven approach and apply machine learning to the moment closure problem for radiative transfer equation in slab geometry. Instead of learning the unclosed high order moment, we propose to directly learn the…
We make a brief historical review to the moment model reduction to the kinetic equations, particularly the Grad's moment method for Boltzmann equation. The focus is on the hyperbolicity of the reduced model, which is essential to the…
Localized cavity resonances due to nanostructures at material surfaces can greatly enhance radiative heat transfer (RHT) between two closely placed bodies owing to stretching of cavity states in momentum space beyond light line. Based on…
We introduce hyperbolic attention networks to endow neural networks with enough capacity to match the complexity of data with hierarchical and power-law structure. A few recent approaches have successfully demonstrated the benefits of…
This study focuses on solving the numerical challenges of imposing absorbing boundary conditions for dynamic simulations in the material point method (MPM). To attenuate elastic waves leaving the computational domain, the current work…
Moment equations offer a compelling alternative to the kinetic description of plasmas, gases, and liquids. Their simulation requires fewer degrees of freedom than phase space models, yet it can still incorporate kinetic effects to a certain…
The eigenvalue problem of quantum many-body systems is a fundamental and challenging subject in condensed matter physics, since the dimension of the Hilbert space (and hence the required computational memory and time) grows exponentially as…
Graph embedding techniques are useful to characterize spectral signature relations for hyperspectral images. However, such images consists of disjoint classes due to spatial details that are often ignored by existing graph computing tools.…
Nonlinear diffusion equations of spectral transfer are systematically derived for anisotropic magnetohydrodynamics in the regime of wave turbulence. The background of the analysis is the asymptotic Alfv\'en wave turbulence equations from…
In this paper we study hyperbolic and parabolic nonlinear partial differential equation models, which describe the evolution of two intersecting pedestrian flows. We assume that individuals avoid collisions by sidestepping, which is encoded…
Hyperbolic geometry has recently found applications in social networks, machine learning and computational biology. With the increasing popularity, questions about the best representations of hyperbolic spaces arise, as each representation…
Generative network models play an important role in algorithm development, scaling studies, network analysis, and realistic system benchmarks for graph data sets. A complex network model gaining considerable popularity builds random…
Network embedding is a fervid topic in current networks science and observes that most real complex systems can be embedded in hidden metrics space and emerge as the geometrical property, where the geometric distance between nodes…
As they carry great potential for modeling complex interactions, graph neural network (GNN)-based methods have been widely used to predict quantum mechanical properties of molecules. Most of the existing methods treat molecules as molecular…
In this paper, we describe a numerical method to solve numerically the weakly dispersive fully nonlinear Serre-Green-Naghdi (SGN) celebrated model. Namely, our scheme is based on reliable finite volume methods, proven to be very effective…
Embedding the data in hyperbolic spaces can preserve complex relationships in very few dimensions, thus enabling compact models and improving efficiency of machine learning (ML) algorithms. The underlying idea is that hyperbolic…