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Sparse identification of nonlinear dynamical systems is a topic of continuously increasing significance in the dynamical systems community. Here we explore it at the level of lattice nonlinear dynamical systems of many degrees of freedom.…
This paper presents a new learning based Stochastic Hybrid System (LSHS) framework designed for the detection and classification of contingencies in modern power systems. Unlike conventional monitoring schemes, the proposed approach is…
Extracting governing equations from dynamic data is an essential task in model selection and parameter estimation. The form of the governing equation is rarely known a priori; however, based on the sparsity-of-effect principle one may…
With an increasing share of renewable energy sources, accurate and efficient modeling of grid-forming inverters is becoming crucial for system stability. Linear methods are a powerful tool for understanding dynamics close to an operating…
One way to understand time-series data is to identify the underlying dynamical system which generates it. This task can be done by selecting an appropriate model and a set of parameters which best fits the dynamics while providing the…
In applications of nonlinear and complex dynamical systems, a common situation is that the system can be measured but its structure and the detailed rules of dynamical evolution are unknown. The inverse problem is to determine the system…
Sparse regression on a library of candidate features has developed as the prime method to discover the partial differential equation underlying a spatio-temporal data-set. These features consist of higher order derivatives, limiting model…
Unprecedented dynamic phenomena may appear in power grids due to higher and higher penetration of inverter-based resources (IBR), e.g., wind and solar photovoltaic (PV). A major challenge in dynamic modeling and analysis is that unlike…
The recent focus on the efficiency of deep neural networks (DNNs) has led to significant work on model compression approaches, of which weight pruning is one of the most popular. At the same time, there is rapidly-growing computational…
This paper presents a practical and scalable grid-based state estimation method for high-dimensional models with invertible linear dynamics and with highly non-linear measurements, such as the nearly constant velocity model with…
Finding interpretable biomechanical models can provide insight into the functionality of organs with regard to physiology and disease. However, identifying broadly applicable dynamical models for in vivo tissue remains challenging. In this…
This article introduces a novel methodology that integrates singular value decomposition (SVD) with a shallow linear neural network for forecasting high resolution fluid mechanics data. The method, termed LC-SVD-DLinear, combines a low-cost…
Pattern-forming systems can exhibit a diverse array of complex behaviors as external parameters are varied, enabling a variety of useful functions in biological and engineered systems. First-principles derivations of the underlying…
Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…
The multiscale and turbulent nature of Earth's atmosphere has historically rendered accurate weather modeling a hard problem. Recently, there has been an explosion of interest surrounding data-driven approaches to weather modeling, which in…
We investigate the problem of recovering a structured sparse signal from a linear observation model with an uncertain dynamic grid in the sensing matrix. The state-of-the-art expectation maximization based compressed sensing (EM-CS)…
Estimation of sensitivity matrices in electrical transmission systems allows grid operators to evaluate in real-time how changes in power injections reflect into changes in power flows. In this paper, we propose a robust low-rank…
Many studies on acoustic radiation forces focus on characterizing the behavior of acoustic fields. However, the dynamic response of objects, particularly those larger than the wavelength, remains underexplored. Here we bridge this gap by…
The estimation of static parameters in dynamical systems and control theory has been extensively studied, with significant progress made in estimating varying parameters in specific system types. Suppose, in the general case, we have data…
Periodic orbits are among the simplest non-equilibrium solutions to dynamical systems, and they play a significant role in our modern understanding of the rich structures observed in many systems. For example, it is known that embedded…