Related papers: BINDy -- Bayesian identification of nonlinear dyna…
The discovery of governing equations from data has been an active field of research for decades. One widely used methodology for this purpose is sparse regression for nonlinear dynamics, known as SINDy. Despite several attempts, noisy and…
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…
Recent advances in the field of data-driven dynamics allow for the discovery of ODE systems using state measurements. One approach, known as Sparse Identification of Nonlinear Dynamics (SINDy), assumes the dynamics are sparse within a…
Data-driven methodologies are nowadays ubiquitous. Their rapid development and spread have led to applications even beyond the traditional fields of science. As far as dynamical systems and differential equations are concerned, neural…
This work designs a scalable, parameter-aware sparse regression framework for discovering interpretable partial differential equations and subgrid-scale closures from multi-parameter simulation data. Building on SINDy (Sparse Identification…
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)…
Dynamical systems provide a mathematical framework for understanding complex physical phenomena. The mathematical formulation of these systems plays a crucial role in numerous applications; however, it often proves to be quite intricate.…
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 recent years, identification of nonlinear dynamical systems from data has become increasingly popular. Sparse regression approaches, such as Sparse Identification of Nonlinear Dynamics (SINDy), fostered the development of novel governing…
This paper proposes a sparse Bayesian treatment of deep neural networks (DNNs) for system identification. Although DNNs show impressive approximation ability in various fields, several challenges still exist for system identification…
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…
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…
In this paper we consider sparse and identifiable linear latent variable (factor) and linear Bayesian network models for parsimonious analysis of multivariate data. We propose a computationally efficient method for joint parameter and model…
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…
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)…
This study presents a Bayesian maximum \textit{a~posteriori} (MAP) framework for dynamical system identification from time-series data. This is shown to be equivalent to a generalized Tikhonov regularization, providing a rational…
Robust physics discovery is of great interest for many scientific and engineering fields. Inspired by the principle that a representative model is the one simplest possible, a new model selection criteria considering both model's Parsimony…
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…
Deriving constitutive models (CMs) from numerical data has been an attractive approach as a systematic CM building method. One recent study is Rheo-SINDy, which extended the sparse identification of nonlinear dynamics (SINDy) method to…
The growing integration of renewable energy sources has significantly reduced grid inertia, making modern power systems more vulnerable to instabilities. Accurate estimation of dynamic parameters such as inertia constants and damping…