Small-data Reduced Order Modeling of Chaotic Dynamics through SyCo-AE: Synthetically Constrained Autoencoders

• URL: http://arxiv.org/abs/2305.08036v1
• Date: Sun, 14 May 2023 00:42:24 GMT
• Title: Small-data Reduced Order Modeling of Chaotic Dynamics through SyCo-AE: Synthetically Constrained Autoencoders
• Authors: Andrey A. Popov, Renato Zanetti
• Abstract summary: Data-driven reduced order modeling of chaotic dynamics can result in systems that either dissipate or diverge catastrophically. We aim to solve this problem by imposing a synthetic constraint in the reduced order space. The synthetic constraint allows our reduced order model both the freedom to remain fully non-linear and highly unstable while preventing divergence.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Data-driven reduced order modeling of chaotic dynamics can result in systems that either dissipate or diverge catastrophically. Leveraging non-linear dimensionality reduction of autoencoders and the freedom of non-linear operator inference with neural-networks, we aim to solve this problem by imposing a synthetic constraint in the reduced order space. The synthetic constraint allows our reduced order model both the freedom to remain fully non-linear and highly unstable while preventing divergence. We illustrate the methodology with the classical 40-variable Lorenz '96 equations, showing that our methodology is capable of producing medium-to-long range forecasts with lower error using less data.

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