小数据混沌动力学降阶建模：通过SyCo-AE（合成约束自编码器）
Small-data Reduced Order Modeling of Chaotic Dynamics through SyCo-AE: Synthetically Constrained Autoencoders
AI总结：
针对混沌动力学数据驱动降阶建模易发散或耗散的问题，提出SyCo-AE方法，在降阶空间施加合成约束，兼顾非线性与稳定性，在Lorenz '96方程上以更少数据实现更低误差的中长期预测。
摘要：
数据驱动的混沌动力学降阶建模可能导致系统要么耗散，要么灾难性发散。利用自编码器的非线性降维和神经网络非线性算子推断的自由度，我们旨在通过在降阶空间中施加合成约束来解决这个问题。合成约束使我们的降阶模型既保持完全非线性和高度不稳定的自由度，同时防止发散。我们用经典的40变量Lorenz '96方程说明了该方法，表明我们的方法能够使用更少的数据，以更低的误差产生中到长期预测。
英文摘要：
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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