Related papers: Equation-free analysis of a dynamically evolving m…
We develop algorithms built around properties of the transfer operator and Koopman operator which 1) test for possible multiscale dynamics in a given dynamical system, 2) estimate the magnitude of the time-scale separation, and finally 3)…
This chapter discusses the interplay between structure and dynamics in complex networks. Given a particular network with an endowed dynamics, our goal is to find partitions aligned with the dynamical process acting on top of the network. We…
In most domains of network analysis researchers consider networks that arise in nature with weighted edges. Such networks are routinely dichotomized in the interest of using available methods for statistical inference with networks. The…
Existing studies on the degree correlation of evolving networks typically rely on differential equations and statistical analysis, resulting in only approximate solutions due to inherent randomness. To address this limitation, we propose an…
Dynamic gene-regulatory networks are complex since the number of potential components involved in the system is very large. Estimating dynamic networks is an important task because they compromise valuable information about interactions…
Natural physical, chemical, and biological dynamical systems are often complex, with heterogeneous components interacting in diverse ways. We show how simple graph neural networks can be designed to jointly learn the interaction rules and…
We introduce a generalized machine learning framework to probabilistically parameterize upper-scale models in the form of nonlinear PDEs consistent with a continuum theory, based on coarse-grained atomistic simulation data of mechanical…
We use an "equation-free", coarse-grained computational approach to accelerate molecular dynamics-based computations of demixing (segregation) of dissimilar particles subject to an upward gas flow (gas-fluidized beds). We explore the…
State-space graphical models and the variational autoencoder framework provide a principled apparatus for learning dynamical systems from data. State-of-the-art probabilistic approaches are often able to scale to large problems at the cost…
We propose NonStGM, a general nonparametric graphical modeling framework for studying dynamic associations among the components of a nonstationary multivariate time series. It builds on the framework of Gaussian Graphical Models (GGM) and…
This paper proposes a web-based visual graph analytics platform for interactive graph mining, visualization, and real-time exploration of networks. GraphVis is fast, intuitive, and flexible, combining interactive visualizations with…
We propose a general approach for change-point detection in dynamic networks. The proposed method is model-free and covers a wide range of dynamic networks. The key idea behind our approach is to effectively utilize the network structure in…
In this paper, we propose a simple, versatile model for learning the structure and parameters of multivariate distributions from a data set. Learning a Markov network from a given data set is not a simple problem, because Markov networks…
Methods connecting dynamical systems and graph theory have attracted increasing interest in the past few years, with applications ranging from a detailed comparison of different kinds of dynamics to the characterisation of empirical data.…
We review some recent coarse-graining and multi-scale methods, but also put forward some new ideas for addressing such issues. We find that, if one is guided by nonequilibrium statistical mechanics and thermodynamics, it is possible to…
Engineering components must meet increasing technological demands in ever shorter development cycles. To face these challenges, a holistic approach is essential that allows for the concurrent development of part design, material system and…
Many different classification tasks need to manage structured data, which are usually modeled as graphs. Moreover, these graphs can be dynamic, meaning that the vertices/edges of each graph may change during time. Our goal is to jointly…
With the birth of quantum information science, many tools have been developed to deal with many-body quantum systems. Although a complete description of such systems is desirable, it will not always be possible to achieve this goal, as the…
The modeling of complicated time-evolving physical dynamics from partial observations is a long-standing challenge. Particularly, observations can be sparsely distributed in a seemingly random or unstructured manner, making it difficult to…
Graphical Gaussian models have proven to be useful tools for exploring network structures based on multivariate data. Applications to studies of gene expression have generated substantial interest in these models, and resulting recent…