We show how random feature maps can be used to forecast dynamical systems with excellent forecasting skill. We consider the tanh activation function and judiciously choose the internal weights in a data-driven manner such that the resulting features explore the nonlinear, non-saturated regions of the activation function. We introduce skip connections and construct a deep variant of random feature maps by combining several units. To mitigate the curse of dimensionality, we introduce localization where we learn local maps, employing conditional independence. Our modified random feature maps provide excellent forecasting skill for both single trajectory forecasts as well as long-time estimates of statistical properties, for a range of chaotic dynamical systems with dimensions up to 512. In contrast to other methods such as reservoir computers which require extensive hyperparameter tuning, we effectively need to tune only a single hyperparameter, and are able to achieve state-of-the-art forecast skill with much smaller networks.

翻译：本文展示了如何利用随机特征映射来预测动力系统，并实现卓越的预测性能。我们采用双曲正切激活函数，并以数据驱动的方式审慎选择内部权重，使得生成的特征能够探索激活函数的非线性、非饱和区域。通过引入跳跃连接并组合多个单元，我们构建了随机特征映射的深度变体。为缓解维度灾难，我们引入局部化方法，在条件独立的框架下学习局部映射。改进后的随机特征映射在维度高达512的一系列混沌动力系统中，无论是单轨迹预测还是统计特性的长期估计，均展现出优异的预测能力。与储层计算机等其他需要大量超参数调优的方法相比，本方法仅需有效调优单个超参数，即可用更小的网络实现最先进的预测性能。