论文标题
在混沌系统中学习奇异的平均值
Learning ergodic averages in chaotic systems
论文作者
论文摘要
我们提出了一种具有物理信息的机器学习方法，以预测混乱吸引子的时间平均水平。该方法基于混合回波状态网络（HESN）。我们假设系统是千古的，因此时间的平均值等于梯形平均水平。与传统的回声状态网络（ESN）（纯粹是数据驱动）相比，HESN使用了来自不完整或不完美的物理模型中的其他信息。我们评估HES的性能，并将其与ESN的性能进行比较。这种方法在混乱的时间延迟的热声系统上证明，其中包含物理模型可显着提高预测的准确性，从而将相对误差从48％降低到7％。该改进是以较低的额外成本来解决两个普通微分方程的成本。该框架显示了使用机器学习技术与先前的物理知识相结合的潜力，以改善混乱系统中时间平均数量的预测。
We propose a physics-informed machine learning method to predict the time average of a chaotic attractor. The method is based on the hybrid echo state network (hESN). We assume that the system is ergodic, so the time average is equal to the ergodic average. Compared to conventional echo state networks (ESN) (purely data-driven), the hESN uses additional information from an incomplete, or imperfect, physical model. We evaluate the performance of the hESN and compare it to that of an ESN. This approach is demonstrated on a chaotic time-delayed thermoacoustic system, where the inclusion of a physical model significantly improves the accuracy of the prediction, reducing the relative error from 48% to 7%. This improvement is obtained at the low extra cost of solving two ordinary differential equations. This framework shows the potential of using machine learning techniques combined with prior physical knowledge to improve the prediction of time-averaged quantities in chaotic systems.
