Related papers: Universal structural estimator and dynamics approx…

Many consequential real-world systems, like wind fields and ocean currents, are dynamic and hard to model. Learning their governing dynamics remains a central challenge in scientific machine learning. Dynamic Mode Decomposition (DMD)…

We have developed an adaptive structural Deep Belief Network (Adaptive DBN) that finds an optimal network structure in a self-organizing manner during learning. The Adaptive DBN is the hierarchical architecture where each layer employs…

The restricted Boltzmann machine (RBM) is one of the fundamental building blocks of deep learning. RBM finds wide applications in dimensional reduction, feature extraction, and recommender systems via modeling the probability distributions…

The field of world modeling is fragmented, with researchers developing bespoke architectures that rarely build upon each other. We propose a framework that specifies the natural building blocks for structured world models based on the…

A numerical framework is proposed for identifying partial differential equations (PDEs) governing dynamical systems directly from their observation data using Chebyshev polynomial approximation. In contrast to data-driven approaches such as…

We demonstrate that a number of sociology models for social network dynamics can be viewed as continuous time Bayesian networks (CTBNs). A sampling-based approximate inference method for CTBNs can be used as the basis of an…

We propose a dynamic network sampling scheme to optimize block recovery for stochastic blockmodel (SBM) in the case where it is prohibitively expensive to observe the entire graph. Theoretically, we provide justification of our proposed…

Extracting automatically the complex set of features composing real high-dimensional data is crucial for achieving high performance in machine--learning tasks. Restricted Boltzmann Machines (RBM) are empirically known to be efficient for…

Modern distributed cyber-physical systems (CPSs) encounter a large variety of physical faults and cyber anomalies and in many cases, they are vulnerable to catastrophic fault propagation scenarios due to strong connectivity among the…

The long-timescale behavior of complex dynamical systems can be described by linear Markov or Koopman models in a suitable latent space. Recent variational approaches allow the latent space representation and the linear dynamical model to…

Unsupervised neural nets such as Restricted Boltzmann Machines(RBMs) and Deep Belif Networks(DBNs), are powerful in automatic feature extraction,unsupervised weight initialization and density estimation. In this paper,we demonstrate that…

We introduce Thurstonian Boltzmann Machines (TBM), a unified architecture that can naturally incorporate a wide range of data inputs at the same time. Our motivation rests in the Thurstonian view that many discrete data types can be…

This paper presents a physics-informed neural network approach for dynamic modeling of saturable synchronous machines, including cases with spatial harmonics. We introduce an architecture that incorporates gradient networks directly into…

The stochastic block model (SBM) is a popular framework for studying community detection in networks. This model is limited by the assumption that all nodes in the same community are statistically equivalent and have equal expected degrees.…

Deep Learning has a hierarchical network architecture to represent the complicated feature of input patterns. The adaptive structural learning method of Deep Belief Network (DBN) has been developed. The method can discover an optimal number…

Network reconstruction is fundamental to understanding the dynamical behaviors of the networked systems. Many systems, modeled by multiplex networks with various types of interactions, display an entirely different dynamical behavior…

Community detection approaches resolve complex networks into smaller groups (communities) that are expected to be relatively edge-dense and well-connected. The stochastic block model (SBM) is one of several approaches used to uncover…

Dynamic mode decomposition (DMD) is a data-driven technique used for capturing the dynamics of complex systems. DMD has been connected to spectral analysis of the Koopman operator, and essentially extracts spatial-temporal modes of the…

Complex systems are ubiquitous in nature and engineering, but their analysis and control are hampered by their high dimensionality and the influence of various factors on their dynamics. Dimensionality reduction aims to find a…

In our research, an adaptive structural learning method of Restricted Boltzmann Machine (RBM) and Deep Belief Network (DBN) has been developed as one of prominent deep learning models. The neuron generation-annihilation in RBM and layer…