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We introduce a fully spectral learning framework that eliminates traditional neural layers by operating entirely in the wavelet domain. The model applies learnable nonlinear transformations, including soft-thresholding and gain-phase…
In this paper, we study the nonlinear inverse problem of estimating the spectrum of a system matrix, that drives a finite-dimensional affine dynamical system, from partial observations of a single trajectory data. In the noiseless case, we…
We study the Kaczmarz methods for solving systems of quadratic equations, i.e., the generalized phase retrieval problem. The methods extend the Kaczmarz methods for solving systems of linear equations by integrating a phase selection…
Modeling an unknown dynamical system is crucial in order to predict the future behavior of the system. A standard approach is training recurrent models on measurement data. While these models typically provide exact short-term predictions,…
Methods from learning theory are used in the state space of linear dynamical and control systems in order to estimate the system matrices. An application to stabilization via algebraic Riccati equations is included. The approach is…
We present that, instead of establishing the equations of motion, one can model-freely reveal the dynamical properties of a black-box system using a learning machine. Trained only by a segment of time series of a state variable recorded at…
We present a complexity reduction algorithm for a family of parameter-dependent linear systems when the system parameters belong to a compact semi-algebraic set. This algorithm potentially describes the underlying dynamical system with…
Phase retrieval in dynamical sampling is a novel research direction, where an unknown signal has to be recovered from the phaseless measurements with respect to a dynamical frame, i.e. a sequence of sampling vectors constructed by the…
In a traditional convolutional layer, the learned filters stay fixed after training. In contrast, we introduce a new framework, the Dynamic Filter Network, where filters are generated dynamically conditioned on an input. We show that this…
In the application of the Expectation Maximization algorithm to identification of dynamical systems, internal states are typically chosen as latent variables, for simplicity. In this work, we propose a different choice of latent variables,…
In this document, some general results in approximation theory and matrix analysis with applications to sparse identification of time series models and nonlinear discrete-time dynamical systems are presented. The aforementioned theoretical…
State-space models are a popular statistical framework for analysing sequential data. Within this framework, particle filters are often used to perform inference on non-linear state-space models. We introduce a new method, StateMixNN, that…
System identification is a fundamental problem in reinforcement learning, control theory and signal processing, and the non-asymptotic analysis of the corresponding sample complexity is challenging and elusive, even for linear time-varying…
This paper investigates a subgradient-based algorithm to solve the system identification problem for linear time-invariant systems with non-smooth objectives. This is essential for robust system identification in safety-critical…
This note addresses identification of the $A$-matrix in continuous time linear dynamical systems on state-space form. If this matrix is partially known or known to have a sparse structure, such knowledge can be used to simplify the…
We consider the problem of finite-time identification of linear dynamical systems from $T$ samples of a single trajectory. Recent results have predominantly focused on the setup where either no structural assumption is made on the system…
An external description for aperiodically sampled MIMO linear systems has been developed. Emphasis is on the sampling period sequence, included among the variables to be handled. The computational procedure is simple and no use of…
Understanding the learning dynamics of neural networks is one of the key issues for the improvement of optimization algorithms as well as for the theoretical comprehension of why deep neural nets work so well today. In this paper, we…
This paper proposes a novel parametric identification approach for linear systems using Deep Learning (DL) and the Modified Relay Feedback Test (MRFT). The proposed methodology utilizes MRFT to reveal distinguishing frequencies about an…
Estimating and detecting faults is crucial in ensuring safe and efficient automated systems. In the presence of disturbances, noise or varying system dynamics, such estimation is even more challenging. To address this challenge, this…