论文标题
物理信息的回声状态网络
Physics-Informed Echo State Networks
论文作者
论文摘要
我们提出了一个具有物理信息的回声状态网络（ESN），以预测混乱系统的演变。与传统的ESN相比，对物理知识的ESN进行了培训，可以解决监督的学习任务，同时确保其预测不会违反物理定律。这是通过在培训期间引入额外的损失功能来实现的，该功能基于系统的管理方程。额外的损失函数会惩罚非物理预测，而无需任何其他培训数据。这种方法在混乱的洛伦兹系统和Charney-Devore系统的截断上得到了证明。与常规的ESN相比，物理信息的ESN提高了约两个Lyapunov时的可预测性范围。这种方法也证明在噪声方面是强大的。提出的框架显示了使用机器学习与先前的物理知识相结合的潜力，以改善混乱动力学系统的时间准确性预测。
We propose a physics-informed Echo State Network (ESN) to predict the evolution of chaotic systems. Compared to conventional ESNs, the physics-informed ESNs are trained to solve supervised learning tasks while ensuring that their predictions do not violate physical laws. This is achieved by introducing an additional loss function during the training, which is based on the system's governing equations. The additional loss function penalizes non-physical predictions without the need of any additional training data. This approach is demonstrated on a chaotic Lorenz system and a truncation of the Charney-DeVore system. Compared to the conventional ESNs, the physics-informed ESNs improve the predictability horizon by about two Lyapunov times. This approach is also shown to be robust with regard to noise. The proposed framework shows the potential of using machine learning combined with prior physical knowledge to improve the time-accurate prediction of chaotic dynamical systems.
