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Continuous-time state-space models (SSMs) are flexible tools for analysing irregularly sampled sequential observations that are driven by an underlying state process. Corresponding applications typically involve restrictive assumptions…
Koopman analysis of a general dynamics system provides a linear Koopman operator and an embedded eigenfunction space, enabling the application of standard techniques from linear analysis. However, in practice, deriving exact operators and…
The goal of this paper is to provide a system identification-friendly introduction to the Structured State-space Models (SSMs). These models have become recently popular in the machine learning community since, owing to their…
Estimating the state of a dynamical system from a series of noise-corrupted observations is fundamental in many areas of science and engineering. The most well-known method, the Kalman smoother (and the related Kalman filter), relies on…
This work focuses on developing a data-driven framework using Koopman operator theory for system identification and linearization of nonlinear systems for control. Our proposed method presents a deep learning framework with recursive…
Spectral decomposition of the Koopman operator is attracting attention as a tool for the analysis of nonlinear dynamical systems. Dynamic mode decomposition is a popular numerical algorithm for Koopman spectral analysis; however, we often…
Detecting anomalies and discovering driving signals is an essential component of scientific research and industrial practice. Often the underlying mechanism is highly complex, involving hidden evolving nonlinear dynamics and noise…
Providing efficient and accurate parametrizations for model reduction is a key goal in many areas of science and technology. Here we present a strong link between data-driven and theoretical approaches to achieving this goal. Formal…
This paper presents a sequence of two approaches for the data-driven control-oriented modeling of networked systems, i.e., the systems that involve many interacting dynamical components. First, a novel deep learning approach named the weak…
Koopman operator theory has emerged as a leading data-driven approach that relies on a judicious choice of observable functions to realize global linear representations of nonlinear systems in the lifted observable space. However,…
Recent selective state space models (SSMs), such as Mamba and Mamba-2, have demonstrated strong performance in sequence modeling owing to input-dependent selection mechanisms. However, these mechanisms lack theoretical grounding and cannot…
The accurate simulation of complex dynamics in fluid flows demands a substantial number of degrees of freedom, i.e. a high-dimensional state space. Nevertheless, the swift attenuation of small-scale perturbations due to viscous diffusion…
Recent deep learning extensions in Koopman theory have enabled compact, interpretable representations of nonlinear dynamical systems which are amenable to linear analysis. Deep Koopman networks attempt to learn the Koopman eigenfunctions…
In data-driven modelling of complex dynamic processes, it is often desirable to combine different classes of models to enhance performance. Examples include coupled models of different fidelities, or hybrid models based on physical…
We develop a data-driven, model-free approach for the optimal control of the dynamical system. The proposed approach relies on the Deep Neural Network (DNN) based learning of Koopman operator for the purpose of control. In particular, DNN…
System representations inspired by the infinite-dimensional Koopman operator (generator) are increasingly considered for predictive modeling. Due to the operator's linearity, a range of nonlinear systems admit linear predictor…
This work explores the in-context learning capabilities of State Space Models (SSMs) and presents, to the best of our knowledge, the first theoretical explanation of a possible underlying mechanism. We introduce a novel weight construction…
Koopman operator theory has served as the basis to extract dynamics for nonlinear system modeling and control across settings, including non-holonomic mobile robot control. There is a growing interest in research to derive robustness…
We present an approach to construct approximate Koopman-type decompositions for dynamical systems depending on static or time-varying parameters. Our method simultaneously constructs an invariant subspace and a parametric family of…
In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace. The Koopman operator is an infinite-dimensional linear operator that evolves…