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Identifying from observation data the governing differential equations of a physical dynamics is a key challenge in machine learning. Although approaches based on SINDy have shown great promise in this area, they still fail to address a…
In many problems of data-driven modeling for dynamical systems, the governing equations are not known a priori and must be selected phenomenologically from a large set of candidate interactions and basis functions. In such situations, point…
Collective response of the plasma medium is well known and has been explored extensively in several contexts. The single particle response is typically treated as collisional interactions leading to dissipative effects. In this manuscript a…
Interacting particle system (IPS) models have proven to be highly successful for describing the spatial movement of organisms. However, it has proven challenging to infer the interaction rules directly from data. In the field of equation…
The discovery of governing differential equations from data is an open frontier in machine learning. The sparse identification of nonlinear dynamics (SINDy) \citep{brunton_discovering_2016} framework enables data-driven discovery of…
We present a pragmatic approach to the sparse identification of nonlinear dynamics for systems with discrete delays. It relies on approximating the underlying delay model with a system of ordinary differential equations via pseudospectral…
This paper presents a comprehensive approach to nonlinear dynamics identification for UAVs using a combination of data-driven techniques and theoretical modeling. Two key methodologies are explored: Proportional-Derivative (PD)…
Identifying Ordinary Differential Equations (ODEs) from measurement data requires both fitting the dynamics and assimilating, either implicitly or explicitly, the measurement data. The Sparse Identification of Nonlinear Dynamics (SINDy)…
Symbolic Regression (SR) is a widely studied field of research that aims to infer symbolic expressions from data. A popular approach for SR is the Sparse Identification of Nonlinear Dynamical Systems (SINDy) framework, which uses sparse…
Hysteresis-controlled devices are widely used in industrial applications. For example, cooling devices usually contain a two-point controller, resulting in a nonlinear hybrid system with two discrete states. Dynamic models of systems are…
Distilling physical laws autonomously from data has been of great interest in many scientific areas. The sparse identification of nonlinear dynamics (SINDy) and its variations have been developed to extract the underlying governing…
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…
Dusty plasma can exist in a wide range, from the laboratory to Saturn's rings. The coupling parameter plays a very important role in diagnosing dusty plasma. There are two ways to deal analytically with the effect of coupling in plasma.…
Plasma supports collective modes and particle-wave interactions that leads to complex behavior in inertial fusion energy applications. While plasma can sometimes be modeled as a charged fluid, a kinetic description is useful towards the…
The particle-in-cell numerical method of plasma physics balances a trade-off between computational cost and intrinsic noise. Inference on data produced by these simulations generally consists of binning the data to recover the particle…
In order to give a basis for the structure and correlation analysis of fine particle (dusty) plasma and colloidal suspensions, thermodynamic treatment of mixtures of macroscopic and microscopic charged particles within the adiabatic…
Two-dimensional classical cluster of particles interacting through a screened Coulomb potential is studied. This system can be used as a model for "dusty particles" in high-frequency discharge plasma. For systems consisting of N = 2 - 40…
One-dimensional and quasi-one-dimensional strongly-coupled dusty plasma rings have been created experimentally. Longitudinal (acoustic) and transverse (optical) dispersion relations for the 1-ring were measured and found to be in very good…
Modeling real-world spatio-temporal data is exceptionally difficult due to inherent high dimensionality, measurement noise, partial observations, and often expensive data collection procedures. In this paper, we present Sparse…
Identifying network dynamics is a critical yet challenging task to to understand the mechanism of real-world social systems. There are two types of algorithms, and one requires the knowledge of self-dynamics function, interactive function,…