用随机特征映射精准预测高维混沌系统，仅调一个超参数。
Learning dynamical systems with hit-and-run random feature maps
- 通过数据驱动选择权重，让特征聚焦激活函数的非线性区域。
- 在512维混沌系统上实现单轨迹与长期统计量的优秀预测性能。
- 结构简化、只需调一个超参数，适合追求高效建模的研究者。
我们展示了如何利用随机特征映射对动力系统进行高精度预测。采用tanh激活函数，并以数据驱动方式精心选择内部权重，使生成的特征充分探索激活函数的非线性且未饱和区域。引入跳跃连接，构建了由多个单元组合而成的深度随机特征映射。为缓解维度诅咒，提出局部化策略，学习局部映射并利用条件独立性。改进后的随机特征映射在多种高达512维的混沌动力系统上，实现了优异的单轨迹预测及长期统计特性估计能力。相较于需大量超参数调优的储备池计算等方法，本方法仅需调节单一超参数，即可在更小网络规模下达到当前最优预测性能。
原文摘要 · Abstract (English)
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.
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