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

A promising approach to investigating high-dimensional problems is to identify their intrinsically low-dimensional features, which can be achieved through recently developed techniques for effective low-dimensional representation of…

We study evolution equations on networks that can be modeled by means of hyperbolic systems. We extend our previous findings in \cite{KraMugNic20} by discussing well-posedness under rather general transmission conditions that might be…

Guided wave modes in a symmetric slab waveguide formed by an isotropic dielectric layer with cubic nonlinear response placed in the hyperbolic surrounding medium are investigated theoretically. Optical axis of the hyperbolic medium is…

Binary Neural Network (BNN) converts full-precision weights and activations into their extreme 1-bit counterparts, making it particularly suitable for deployment on lightweight mobile devices. While binary neural networks are typically…

Backward compatible representation learning enables updated models to integrate seamlessly with existing ones, avoiding to reprocess stored data. Despite recent advances, existing compatibility approaches in Euclidean space neglect the…

Models for shallow water flow often assume that the lateral velocity is constant over the water height. The recently derived shallow water moment equations are an extension of these standard shallow water equations. The extended models…

Probabilistic Latent Variable Models (LVMs) excel at modeling complex, high-dimensional data through lower-dimensional representations. Recent advances show that equipping these latent representations with a Riemannian metric unlocks…

Numerous phenomenological nuclear models have been proposed to describe specific observables within different regions of the nuclear chart. However, developing a unified model that describes the complex behavior of all nuclei remains an…

Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases, e.g., hierarchical structures benefit from hyperbolic…

Ultrafast accurate physical layer models are essential for designing, optimizing and managing ultrawideband optical transmission systems. We present a closed-form GN/EGN model based on a recent analytical breakthrough, improving…

Many complex networks exhibit hierarchical, tree-like structures, making hyperbolic space a natural candidate wherein to learn representations of them. Based on this observation, Hyperbolic Graph Neural Networks (HGNNs) have been widely…

The set of benchmark solutions used in the thermal radiative transfer community suffer some coverage gaps, in particular nonlinear, non-equilibrium problems. Also, there are no non-equilibrium, optically thick benchmarks. These shortcomings…

Uncertainty Quantification through stochastic spectral methods is rising in popularity. We derive a modification of the classical stochastic Galerkin method, that ensures the hyperbolicity of the underlying hyperbolic system of partial…

Rapid advancements in machine learning (ML) are transforming materials science by significantly speeding up material property calculations. However, the proliferation of ML approaches has made it challenging for scientists to keep up with…

While Hyperbolic Graph Neural Network (HGNN) has recently emerged as a powerful tool dealing with hierarchical graph data, the limitations of scalability and efficiency hinder itself from generalizing to deep models. In this paper, by…

In this paper, we investigate steady states of shallow water moment equations including bottom topographies. We derive a new hyperbolic shallow water moment model based on linearized moment equations that allows for a simple assessment of…

In this paper we will consider the peridynamic equation of motion which is described by a second order in time partial integro-differential equation. This equation has recently received great attention in several fields of Engineering…

This study presents novel predictive models using Graph Neural Networks (GNNs) for simulating thermal dynamics in Laser Powder Bed Fusion (L-PBF) processes. By developing and validating Single-Laser GNN (SL-GNN) and Multi-Laser GNN (ML-GNN)…

The recent success of State-Space Models (SSMs) in sequence modeling has motivated their adaptation to graph learning, giving rise to Graph State-Space Models (GSSMs). However, existing GSSMs operate by applying SSM modules to sequences…

This paper proposes an Adaptive-Growth Randomized Neural Network (AG-RaNN) method for computing multivalued solutions of nonlinear first-order PDEs with hyperbolic characteristics, including quasilinear hyperbolic balance laws and…