Related papers: A Unified Framework for Structured Flow Modeling: …

Multivector fields provide an avenue for studying continuous dynamical systems in a combinatorial framework. There are currently two approaches in the literature which use persistent homology to capture changes in combinatorial dynamical…

We introduce structured decompositions, category-theoretic structures which simultaneously generalize notions from graph theory (including treewidth, layered treewidth, co-treewidth, graph decomposition width, tree independence number,…

Federated graph learning (FGL) enables collaborative training on graph data across multiple clients. As graph data increasingly contain multimodal node attributes such as text and images, multimodal federated graph learning (MM-FGL) has…

Despite their popularity, to date, the application of normalizing flows on categorical data stays limited. The current practice of using dequantization to map discrete data to a continuous space is inapplicable as categorical data has no…

We present an innovative framework for traffic dynamics analysis using High-Order Evolving Graphs, designed to improve spatio-temporal representations in autonomous driving contexts. Our approach constructs temporal bidirectional bipartite…

We present a finite element framework for the numerical prediction of cavitating turbulent flows interacting with flexible structures. The vapor-fluid phases are captured through a homogeneous mixture model, with a scalar transport equation…

We introduce a general framework for leveraging graph stream data for temporal prediction-based applications. Our proposed framework includes novel methods for learning an appropriate graph time-series representation, modeling and weighting…

Identifying the intrinsic coordinates or modes of the dynamical systems is essential to understand, analyze, and characterize the underlying dynamical behaviors of complex systems. For nonlinear dynamical systems, this presents a critical…

In real-world systems, the relationships and connections between components are highly complex. Real systems are often described as networks, where nodes represent objects in the system and edges represent relationships or connections…

Diffuse-interface theory provides a foundation for the modeling and simulation of microstructure evolution in a very wide range of materials, and for the tracking/capturing of dynamic interfaces between different materials on larger scales.…

Models for fluid deformable surfaces provide valid theories to describe the dynamics of thin fluidic sheets of soft materials. To use such models in morphogenesis and development requires to incorporate active forces. We consider active…

Generative modeling provides a powerful framework for learning data distributions. These models initially relied on probabilistic methods such as Gaussian Processes (GP) for uncertainty-aware predictions and shifted towards larger trainable…

Graphs serve as fundamental descriptors for systems composed of interacting elements, capturing a wide array of data types, from molecular interactions to social networks and knowledge graphs. In this paper, we present an exhaustive review…

We discuss a unified flow theory which in a single system of hyperbolic partial differential equations (PDEs) can describe the two main branches of continuum mechanics, fluid dynamics, and solid dynamics. The fundamental difference from the…

Federated Graph Learning (FGL) has demonstrated the advantage of training a global Graph Neural Network (GNN) model across distributed clients using their local graph data. Unlike Euclidean data (\eg, images), graph data is composed of…

Conditional Normalizing Flows (CNFs) are flexible generative models capable of representing complicated distributions with high dimensionality and large interdimensional correlations, making them appealing for structured output learning.…

Many complex real-world systems exhibit inherently intertwined temporal and spatial characteristics. Spatio-temporal knowledge graphs (STKGs) have therefore emerged as a powerful representation paradigm, as they integrate entities,…

This paper builds on the connection between graph neural networks and traditional dynamical systems. We propose continuous graph neural networks (CGNN), which generalise existing graph neural networks with discrete dynamics in that they can…

Graph neural networks trained to predict observable dynamics can be used to decompose the temporal activity of complex heterogeneous systems into simple, interpretable representations. Here we apply this framework to simulated neural…

Network theory has proven to be a powerful tool in describing and analyzing systems by modelling the relations between their constituent objects. In recent years great progress has been made by augmenting `traditional' network theory.…