Small-data Reduced Order Modeling of Chaotic Dynamics through SyCo-AE: Synthetically Constrained Autoencoders
This addresses the challenge of stable and accurate reduced order modeling for chaotic systems, which is incremental as it builds on existing autoencoder and neural-network methods with a new constraint.
The paper tackled the problem of data-driven reduced order modeling of chaotic dynamics, which often leads to dissipative or divergent systems, by imposing a synthetic constraint in the reduced order space to prevent divergence while allowing non-linear freedom. The result was medium-to-long range forecasts with lower error using less data, as demonstrated on the 40-variable Lorenz '96 equations.
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.