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.

使用自编码器的非线性降维和神经网络的非线性操作推断，通过在降维空间中引入合成约束，解决了混沌动力学的降阶建模问题，使模型既能够保持完全非线性和高度不稳定，又能防止发散，在经典的 Lorenz 方程中进行了演示，并表明我们的方法可以使用更少的数据产生较低误差的中长程预测。