Related papers: Advances in the Simulation and Modeling of Complex…

Deep Gaussian processes (DGPs) are increasingly popular as predictive models in machine learning (ML) for their non-stationary flexibility and ability to cope with abrupt regime changes in training data. Here we explore DGPs as surrogates…

First of all, this paper presents some improvements of DSMC method in the form of new schemes and approaches, that, for a wide class of problems, increase performance and reduce the demands on computer resources. The most important…

Deep Gaussian processes (DGPs) are popular surrogate models for complex nonstationary computer experiments. DGPs use one or more latent Gaussian processes (GPs) to warp the input space into a plausibly stationary regime, then use typical GP…

Graph Neural Networks (GNNs) have recently become increasingly popular due to their ability to learn complex systems of relations or interactions arising in a broad spectrum of problems ranging from biology and particle physics to social…

Flexible elastic structures, such as beams, rods, ribbons, plates, and shells, exhibit complex nonlinear dynamical behaviors that are central to a wide range of engineering and scientific applications, including soft robotics, deployable…

We propose a stochastic conditional gradient method (CGM) for minimizing convex finite-sum objectives formed as a sum of smooth and non-smooth terms. Existing CGM variants for this template either suffer from slow convergence rates, or…

Advancing research in the emerging field of deep graph learning requires new tools to support tensor computation over graphs. In this paper, we present the design principles and implementation of Deep Graph Library (DGL). DGL distills the…

Knowledge Graphs (KGs) have proven highly effective for recommendation systems by capturing latent item relationships, while recent integration of Large Language Models (LLMs) has further enhanced semantic understanding and addressed…

Differential equations (DEs) are crucial for modeling the evolution of natural or engineered systems. Traditionally, the parameters in DEs are adjusted to fit data from system observations. However, in fields such as politics, economics,…

Traffic flow prediction is a typical spatio-temporal prediction problem and has a wide range of applications. The core challenge lies in modeling the underlying complex spatio-temporal dependencies. Various methods have been proposed, and…

The Gaussian graphical model (GGM) incorporates an undirected graph to represent the conditional dependence between variables, with the precision matrix encoding partial correlation between pair of variables given the others. To achieve…

Graph Retrieval-Augmented Generation (GRAG or Graph RAG) architectures aim to enhance language understanding and generation by leveraging external knowledge. However, effectively capturing and integrating the rich semantic information…

Learning distributions of graphs can be used for automatic drug discovery, molecular design, complex network analysis, and much more. We present an improved framework for learning generative models of graphs based on the idea of deep state…

Differential Dynamic Microscopy (DDM) is the combination of optical microscopy to statistical analysis to obtain information about the dynamical behaviour of a variety of samples spanning from soft matter physics to biology. In DDM, the…

Dynamic Text-Attribute Graphs (DyTAGs), characterized by time-evolving graph interactions and associated text attributes, are prevalent in real-world applications. Existing methods, such as Graph Neural Networks (GNNs) and Large Language…

Generative modeling of graphs with spatial structure is essential across many applications from computer graphics to spatial genomics. Recent flow-based generative models have achieved impressive results by gradually adding and then…

Estimating the structure of directed acyclic graphs (DAGs) of features (variables) plays a vital role in revealing the latent data generation process and providing causal insights in various applications. Although there have been many…

Dynamic Mode Decomposition (DMD) is a data-driven technique to identify a low dimensional linear time invariant dynamics underlying high-dimensional data. For systems in which such underlying low-dimensional dynamics is time-varying, a…

Dynamic text-attributed graphs (DyTAGs) are prevalent in various real-world scenarios, where each node and edge are associated with text descriptions, and both the graph structure and text descriptions evolve over time. Despite their broad…

Gaussian processes provide a compact representation for modeling and estimating an unknown function, that can be updated as new measurements of the function are obtained. This paper extends this powerful framework to the case where the…