Related papers: SINDy-BVP: Sparse Identification of Nonlinear Dyna…
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…
Despite the recent proliferation of machine learning methods like SINDy that promise automatic discovery of governing equations from time-series data, there remain significant challenges to discovering models from noisy datasets. One reason…
This paper presents an online algorithm for identification of partial differential equations (PDEs) based on the weak-form sparse identification of nonlinear dynamics algorithm (WSINDy). The algorithm is online in a sense that if performs…
This work leverages laser vibrometry and the weak form of the sparse identification of nonlinear dynamics (WSINDy) for partial differential equations to learn macroscale governing equations from full-field experimental data. In the…
In the present paper, two existing nonlinear system identification methodologies are used to identify data-driven models. The first methodology focuses on identifying the system using steady-state excitations. To accomplish this, a…
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…
In future power systems, the detailed structure and dynamics may not always be fully known. This is due to an increasing number of distributed energy resources, such as photovoltaic generators, battery storage systems, heat pumps and…
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…
The Linear Parameter-Varying (LPV) framework provides a modeling and control design toolchain to address nonlinear (NL) system behavior via linear surrogate models. Despite major research effort on LPV data-driven modeling, a key…
dentifying accurate and yet interpretable low-order models from data has gained a renewed interest over the past decade. In the present work, we illustrate how the combined use of dimensionality reduction and sparse system identification…
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…
We introduce a novel procedure that, given sparse data generated from a stationary deterministic nonlinear dynamical system, can characterize specific local and/or global dynamic behavior with rigorous probability guarantees. More…
To comprehend complex systems with multiple states, it is imperative to reveal the identity of these states by system outputs. Nevertheless, the mathematical models describing these systems often exhibit nonlinearity so that render the…
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…
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…
Modeling realistic fluid and plasma flows is computationally intensive, motivating the use of reduced-order models for a variety of scientific and engineering tasks. However, it is challenging to characterize, much less guarantee, the…
Lithium-ion batteries (LIBs) are utilized as a major energy source in various fields because of their high energy density and long lifespan. During repeated charging and discharging, the degradation of LIBs, which reduces their maximum…
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…
Poincar\'e maps are an integral aspect to our understanding and analysis of nonlinear dynamical systems. Despite this fact, the construction of these maps remains elusive and is primarily left to simple motivating examples. In this…
In this paper, we study the system identification problem for sparse linear time-invariant systems. We propose a sparsity promoting block-regularized estimator to identify the dynamics of the system with only a limited number of input-state…