Related papers: Sparse identification of nonlinear dynamics with l…
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…
This work proposes an iterative sparse-regularized regression method to recover governing equations of nonlinear dynamical systems from noisy state measurements. The method is inspired by the Sparse Identification of Nonlinear Dynamics…
We present a novel extension of the SINDy framework to delay differential equations with {\it distributed delays} and {\it renewal equations}, where typically the dependence from the past manifests via integrals in which the history is…
Vortex-induced vibrations (VIV) remain a canonical yet complex manifestation of fluid-structure interactions, where coupled nonlinear dynamics govern the motion of bluff bodies. For several years, we have relied on traditional reduced-order…
Decision formation in perceptual decision-making involves sensory evidence accumulation instantiated by the temporal integration of an internal decision variable towards some decision criterion or threshold, as described by sequential…
The SINDy algorithm has been successfully used to identify the governing equations of dynamical systems from time series data. In this paper, we argue that this makes SINDy a potentially useful tool for causal discovery and that existing…
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…
Rheology plays a pivotal role in understanding the flow behavior of fluids by discovering governing equations that relate deformation and stress, known as constitutive equations. Despite the importance of these equations, current methods…
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)…
The moment quantities associated with the nonlinear Schrodinger equation offer important insights towards the evolution dynamics of such dispersive wave partial differential equation (PDE) models. The effective dynamics of the moment…
Research on dynamics of robotic manipulators provides promising support for model-based control. In general, rigorous first-principles-based dynamics modeling and accurate identification of mechanism parameters are critical to achieving…
Research in modern data-driven dynamical systems is typically focused on the three key challenges of high dimensionality, unknown dynamics, and nonlinearity. The dynamic mode decomposition (DMD) has emerged as a cornerstone for modeling…
In recent years there has been a push to discover the governing equations dynamical systems directly from measurements of the state, often motivated by systems that are too complex to directly model. Although there has been substantial work…
A key task in the field of modeling and analyzing nonlinear dynamical systems is the recovery of unknown governing equations from measurement data only. There is a wide range of application areas for this important instance of system…
We extend the data-driven method of Sparse Identification of Nonlinear Dynamics (SINDy) developed by Brunton et al, Proc. Natl. Acad. Sci USA 113 (2016) to the case of delay differential equations (DDEs). This is achieved in a bilevel…
We draw on the latest advancements in the physics community to propose a novel method for discovering the governing non-linear dynamics of physical systems in reinforcement learning (RL). We establish that this method is capable of…
Forced oscillations may jeopardize the secure operation of power systems. To mitigate forced oscillations, locating the sources is critical. In this paper, leveraging on Sparse Identification of Nonlinear Dynamics (SINDy), an online purely…
We demonstrate the synthesis of sparse sampling and machine learning to characterize and model complex, nonlinear dynamical systems over a range of bifurcation parameters. First, we construct modal libraries using the classical proper…
Inferring physical laws from data is a central challenge in science and engineering, including but not limited to healthcare, physical sciences, biosciences, social sciences, sustainability, climate, and robotics. Deep networks offer…
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…