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Title: | DATA-DRIVEN DISCOVERY OF STATE VARIABLES FROM DYNAMICAL SYSTEM OBSERVATIONS | Authors: | CHAVELLI FELIX THEO ANAEL | ORCID iD: | orcid.org/0000-0002-5439-7467 | Keywords: | Physics-Informed Neural Networks, Dynamical Systems, Machine Learning | Issue Date: | 19-Jan-2024 | Citation: | CHAVELLI FELIX THEO ANAEL (2024-01-19). DATA-DRIVEN DISCOVERY OF STATE VARIABLES FROM DYNAMICAL SYSTEM OBSERVATIONS. ScholarBank@NUS Repository. | Abstract: | Creating a model of a dynamical system based on raw observational data necessitates a comprehensive understanding of its phase space, encompassing the identification of its dimension and state variables. Recently introduced by Chen et al., a state-of-the-art method employs encoder-decoders and geometric manifold learning to unearth hidden variables within experimental data. This method harnesses intrinsic dimension estimators on the manifold of observations to gauge the system's state space dimension. In this thesis, we extend the repertoire of intrinsic dimension estimators proposed by the authors. Our focus then shifts to second-order dynamical systems. We leverage on Chen et al's work to present an innovative approach for extracting a minimal set of governing variables from raw observational data. Our methodology combines the an encoder-decoder for extracting a compact representation from consecutive pairs of data frames with a physics-informed variational autoencoder. The latent space of this autoencoder is constrained to represent a second-order system ensuring that our model effectively retains the inherent relationships between consecutive observations. The system's phase space dimension is discovered during the training, eliminating the need for an intrinsic dimension estimation step. The outcome is a minimal set of disentangled and explainable latent variables modeling the systems dynamics. | URI: | https://scholarbank.nus.edu.sg/handle/10635/248148 |
Appears in Collections: | Master's Theses (Open) |
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