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Data-driven reduced order modeling of chaotic dynamics can result in systemsthat either dissipate or diverge catastrophically. Leveraging non-lineardimensionality reduction of autoencoders and the freedom of non-linear operatorinference with neural-networks, we aim to solve this problem by imposing asynthetic constraint in the reduced order space. The synthetic constraintallows our reduced order model both the freedom to remain fully non-linear andhighly unstable while preventing divergence. We illustrate the methodology withthe classical 40-variable Lorenz '96 equations, showing that our methodology iscapable of producing medium-to-long range forecasts with lower error using lessdata.

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