Small-data Reduced Order Modeling of Chaotic Dynamics through SyCo-AE:
  Synthetically Constrained Autoencoders
Andrey A. Popov Renato Zanetti
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.