Related papers: Data-Driven Reduced Modeling of Delayed Dynamical …
The manifold hypothesis suggests that high-dimensional neural time series lie on a low-dimensional manifold shaped by simpler underlying dynamics. To uncover this structure, latent dynamical variable models such as state-space models,…
Delay embeddings of time series data have emerged as a promising coordinate basis for data-driven estimation of the Koopman operator, which seeks a linear representation for observed nonlinear dynamics. Recent work has demonstrated the…
This paper develops a data-driven safe control framework for linear systems possessing a known strict-feedback structure, but with most plant parameters, external disturbances, and input delay being unknown. By leveraging Koopman operator…
Stochastic differential equations (SDEs) are a ubiquitous modeling framework that finds applications in physics, biology, engineering, social science, and finance. Due to the availability of large-scale data sets, there is growing interest…
This paper develops an explicit spectral representation for solutions of a one-dimensional linear wave equation with a constant time delay. The model is considered on a bounded interval with non-homogeneous Dirichlet boundary data and a…
Boolean Delay Equations (BDEs) are semi-discrete dynamical models with Boolean-valued variables that evolve in continuous time. Systems of BDEs can be classified into conservative or dissipative, in a manner that parallels the…
Data-driven modeling of dynamical systems is a crucial area of machine learning. In many scenarios, a thorough understanding of the model's behavior becomes essential for practical applications. For instance, understanding the behavior of a…
In this paper, we consider a surrogate modeling approach using a data-driven nonparametric likelihood function constructed on a manifold on which the data lie (or to which they are close). The proposed method represents the likelihood…
Invariant manifolds are important constructs for the quantitative and qualitative understanding of nonlinear phenomena in dynamical systems. In nonlinear damped mechanical systems, for instance, spectral submanifolds have emerged as useful…
Computing reduced-order models using non-intrusive methods is particularly attractive for systems that are simulated using black-box solvers. However, obtaining accurate data-driven models can be challenging, especially if the underlying…
The increasing integration of Distributed Energy Resources (DERs) into power systems necessitates the accurate representation of their dynamic behavior at the transmission level. Traditional electromagnetic transient models (EMT), while…
Learning interpretable representations of neural dynamics at a population level is a crucial first step to understanding how observed neural activity relates to perception and behavior. Models of neural dynamics often focus on either…
Presence of model uncertainties creates challenges for model-based control design, and complexity of the control design is further exacerbated when coping with nonlinear systems. This paper presents a sliding mode control (SMC) design…
Stochastic differential equations (SDEs) describe dynamical systems where deterministic flows, governed by a drift function, are superimposed with random fluctuations, dictated by a diffusion function. The accurate estimation (or discovery)…
Data-driven inference of the generative dynamics underlying a set of observed time series is of growing interest in machine learning and the natural sciences. In neuroscience, such methods promise to alleviate the need to handcraft models…
This paper proposes the use of spectral element methods \citep{canuto_spectral_1988} for fast and accurate training of Neural Ordinary Differential Equations (ODE-Nets; \citealp{Chen2018NeuralOD}) for system identification. This is achieved…
Delay embedding---a method for reconstructing dynamical systems by delay coordinates---is widely used to forecast nonlinear time series as a model-free approach. When multivariate time series are observed, several existing frameworks can be…
Deep state space models (SSMs) are an actively researched model class for temporal models developed in the deep learning community which have a close connection to classic SSMs. The use of deep SSMs as a black-box identification model can…
This survey presents recent research on determining control-theoretic properties and designing controllers with rigorous guarantees using semidefinite programming and for nonlinear systems for which no mathematical models but measured…
A novel way of using neural networks to learn the dynamics of time delay systems from sequential data is proposed. A neural network with trainable delays is used to approximate the right hand side of a delay differential equation. We relate…