Related papers: PowerSINDy: Identifying Nonlinear Time-Dependent D…
We study the performance of sparse regression methods and propose new techniques to distill the governing equations of dynamical systems from data. We first look at the generic methodology of learning interpretable equation forms from data,…
We develop data-driven dynamical models of the nonlinear aeroelastic effects on a long-span suspension bridge from sparse, noisy sensor measurements which monitor the bridge. Using the {\em sparse identification of nonlinear dynamics}…
This study explores data-driven modeling techniques to capture the dynamics of a grid-forming converter-based infinite bus system, critical for renewable-integrated power grids. Using sparse identification of nonlinear dynamics and deep…
This paper addresses identification of sparse linear and noise-driven continuous-time state-space systems, i.e., the right-hand sides in the dynamical equations depend only on a subset of the states. The key assumption in this study, is…
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…
We model and study the problem of localizing a set of sparse forcing inputs for linear dynamical systems from noisy measurements when the initial state is unknown. This problem is of particular relevance to detecting forced oscillations in…
This paper focuses on the system identification of an important class of nonlinear systems: linearly parameterized nonlinear systems, which enjoys wide applications in robotics and other mechanical systems. We consider two system…
Data-driven discovery of governing equations from data remains a fundamental challenge in nonlinear dynamics. Although sparse regression techniques have advanced system identification, they struggle with rational functions and noise…
Spatiotemporal dynamics pervade the natural sciences, from the morphogen dynamics underlying patterning in animal pigmentation to the protein waves controlling cell division. A central challenge lies in understanding how controllable…
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…
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…
Nonlinear dynamics are ubiquitous in science and engineering applications, but the physics of most complex systems is far from being fully understood. Discovering interpretable governing equations from measurement data can help us…
Temporal variations in biological systems and more generally in natural sciences are typically modelled as a set of Ordinary, Partial, or Stochastic Differential or Difference Equations. Algorithms for learning the structure and the…
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 study of complex dynamical systems, understanding and accurately modeling the underlying physical processes is crucial for predicting system behavior and designing effective interventions. Yet real-world systems exhibit pronounced…
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…
Learning governing equations from data is central to understanding the behavior of physical systems across diverse scientific disciplines, including physics, biology, and engineering. The Sindy algorithm has proven effective in leveraging…
We compare the efficiency and ease-of-use of the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm and Sparse Physics-Informed Discovery of Empirical Relations (SPIDER) framework in recovering the relevant governing equations…
Nonlinear system identification often involves a fundamental trade-off between interpretability and flexibility, often requiring the incorporation of physical constraints. We propose a unified data-driven framework that combines the…
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…