Bridging Autoencoders and Dynamic Mode Decomposition for Reduced-order Modeling and Control of PDEs

• URL: http://arxiv.org/abs/2409.06101v1
• Date: Mon, 9 Sep 2024 22:56:40 GMT
• Title: Bridging Autoencoders and Dynamic Mode Decomposition for Reduced-order Modeling and Control of PDEs
• Authors: Priyabrata Saha, Saibal Mukhopadhyay,
• Abstract summary: This paper explores a deep autocodingen learning method for reduced-order modeling and control of dynamical systems governed by Ptemporals. We first show that an objective for learning a linear autoen reduced-order model can be formulated to yield a solution closely resembling the result obtained through the dynamic mode decomposition with control algorithm. We then extend this linear autoencoding architecture to a deep autocoding framework, enabling the development of a nonlinear reduced-order model.
• Score: 12.204795159651589
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Modeling and controlling complex spatiotemporal dynamical systems driven by partial differential equations (PDEs) often necessitate dimensionality reduction techniques to construct lower-order models for computational efficiency. This paper explores a deep autoencoding learning method for reduced-order modeling and control of dynamical systems governed by spatiotemporal PDEs. We first analytically show that an optimization objective for learning a linear autoencoding reduced-order model can be formulated to yield a solution closely resembling the result obtained through the dynamic mode decomposition with control algorithm. We then extend this linear autoencoding architecture to a deep autoencoding framework, enabling the development of a nonlinear reduced-order model. Furthermore, we leverage the learned reduced-order model to design controllers using stability-constrained deep neural networks. Numerical experiments are presented to validate the efficacy of our approach in both modeling and control using the example of a reaction-diffusion system.

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