Data-driven Analysis of T-Product-based Dynamical Systems
A wide variety of data can be represented using third-order tensors, spanning applications in chemometrics, psychometrics, and image processing. However, traditional data-driven frameworks are not naturally equipped to process tensors without first unfolding or flattening the data, which can result in a loss of crucial higher-order structural information. In this article, we introduce a novel framework for the data-driven analysis of T-product-based dynamical systems (TPDSs), where the system evolution is governed by the T-product between a third-order dynamic tensor and a third-order state tensor. In particular, we examine the data informativity of TPDSs concerning system identification, stability, controllability, and stabilizability and illustrate significant computational improvements over traditional approaches by leveraging the unique properties of the T-product. The effectiveness of our framework is demonstrated through numerical examples.
Code (1)
Similar Papers 제목 키워드 기반
Data-driven Control of T-Product-based Dynamical Systems
Data-driven control is a powerful tool that enables the design and implementation of control strategies directly from data without explicitly identifying the underlying system dynamics. While various data-driven control …
Model Predictive ControlData-driven model order reduction for T-Product-Based dynamical systems
Model order reduction plays a crucial role in simplifying complex systems while preserving their essential dynamic characteristics, making it an invaluable tool in a wide range of applications, including robotic systems,…
Comparing Dynamical Models Through Diffeomorphic Vector Field Alignment
Dynamical systems models such as recurrent neural networks (RNNs) are increasingly popular in theoretical neuroscience for hypothesis-generation and data analysis. Evaluating the dynamics in such models is key to underst…
Deriving dynamical systems for language based on the Tolerance Principle
In this research note, I derive explicit dynamical systems for language within an acquisition-driven framework (Niyogi \& Berwick, 1997; Niyogi, 2006) assuming that children/learners follow the Tolerance Principle (Yang,…
Language AcquisitionA Low-complexity Structured Neural Network to Realize States of Dynamical Systems
Data-driven learning is rapidly evolving and places a new perspective on realizing state-space dynamical systems. However, dynamical systems derived from nonlinear ordinary differential equations (ODEs) suffer from limit…
Computational Efficiency