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Most recent advances in machine learning and analytics for process control pose the question of how to naturally integrate new data-driven methods with classical process models and control. We propose a process modeling framework enabling…
This manuscript presents novel techniques for identifying the switch states, phase identification, and estimation of equipment parameters in multi-phase low voltage electrical grids, which is a major challenge in long-standing German low…
This paper presents an intertemporal bimodal network to analyze the evolution of the semantic content of a scientific field within the framework of topic modeling, namely using the Latent Dirichlet Allocation (LDA). The main contribution is…
Topology learning of networked dynamical systems is an important problem with implications to optimal control, decision-making over networks, cybersecurity and safety. The majority of prior work in consistent topology estimation relies on…
Topological order in a 2d quantum matter can be determined by the topological contribution to the entanglement R\'enyi entropies. However, when close to a quantum phase transition, its calculation becomes cumbersome. Here we show how…
Discovering the governing equations of evolving systems from available observations is essential and challenging. In this paper, we consider a new scenario: discovering governing equations from streaming data. Current methods struggle to…
Dynamic Mode Decomposition (DMD) and its variants, such as extended DMD (EDMD), are broadly used to fit simple linear models to dynamical systems known from observable data. As DMD methods work well in several situations but perform poorly…
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…
Topological Data Analysis (TDA) is a modern approach to Data Analysis focusing on the topological features of data; it has been widely studied in recent years and used extensively in Biology, Physics, and many other areas. However,…
Simultaneous recordings from many neurons hide important information and the connections characterizing the network remain generally undiscovered despite the progresses of statistical and machine learning techniques. Discerning the presence…
The single, double, and triple pendulum has served as an illustrative experimental benchmark system for scientists to study dynamical behavior for more than four centuries. The pendulum system exhibits a wide range of interesting behaviors,…
There is a broad need in the neuroscience community to understand and visualize large-scale recordings of neural activity, big data acquired by tens or hundreds of electrodes simultaneously recording dynamic brain activity over minutes to…
A new probabilistic network construction system, DYNASTY, is proposed for diagnostic reasoning given variables whose probabilities change over time. Diagnostic reasoning is formulated as a sequential stochastic process, and is modeled using…
Given sensor readings over time from a power grid, how can we accurately detect when an anomaly occurs? A key part of achieving this goal is to use the network of power grid sensors to quickly detect, in real-time, when any unusual events,…
Topological data analysis (TDA) approaches are becoming increasingly popular for studying the dependence patterns in multivariate time series data. In particular, various dependence patterns in brain networks may be linked to specific tasks…
The precise knowledge regarding the state of the power grid is important in order to ensure optimal and reliable grid operation. Specifically, knowing the state of the distribution grid becomes increasingly important as more renewable…
We propose to construct cross and joint ordinal pattern transition networks from multivariate time series for two coupled systems, where synchronizations are often present. In particular, we focus on phase synchronization, which is one of…
Topological Data Analysis (TDA) is increasingly crucial in investigating the shape of complex data structures across scientific fields, particularly in neuroscience and finance. This study delves into persistent homology, a TDA component…
In this paper we present an analytical study of dynamic membership (aka churn) in structured peer-to-peer networks. We use a fluid model approach to describe steady-state or transient phenomena, and apply it to the Chord system. For any…
We demonstrate the identification and classification of topological phase transitions from experimental data using Diffusion Maps: a nonlocal unsupervised machine learning method. We analyze experimental data from an optical system…