Dembélé, M Alex (2024) Using an operator framework to represent fully/partially-observable nonlinear dynamics in a linearly-parametrized network. PFE - Project Graduation, ENSTA.
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Abstract
Most real-world systems exhibit nonlinear dynamics. However, through Koopman operator theory, it is possible to map the state and control variables of a nonlinear dynamical system to those of a linear system, albeit in a higher-dimensional space. In this project, we aim to learn such transformations using Machine Learning techniques based on an operator-theoretic framework, relying solely on data to model the underlying dynamics. We combine this approach with the Neural Engineering Framework (NEF) to represent these dynamics as a network. Additionally, we focus on reconstructing a full-state system from partial observations using these methods, Takens’s theorem and delay embeddings. These transformed systems can then be employed to analyze and control the original nonlinear or partially observed systems using methods that are either analytically tractable or more efficient for linear systems. A primary goal of this work is using Spiking Neural Networks (SNNs) to model and linearize the dynamics.
Item Type: | Thesis (PFE - Project Graduation) |
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Uncontrolled Keywords: | Dynamical system, Koopman Operator Theory, Machine Learning, Neural Engineering Framework, Takens’s Theorem |
Subjects: | Information and Communication Sciences and Technologies Mathematics and Applications |
ID Code: | 10428 |
Deposited By: | Alex DEMBÉLÉ |
Deposited On: | 09 oct. 2024 19:23 |
Dernière modification: | 09 oct. 2024 19:23 |
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