We utilize extreme-learning machines for the prediction of partial differential equations (PDEs). Our method splits the state space into multiple windows that are predicted individually using a single model. Despite requiring only few data points (in some cases, our method can learn from a single full-state snapshot), it still achieves high accuracy and can predict the flow of PDEs over long time horizons. Moreover, we show how additional symmetries can be exploited to increase sample efficiency and to enforce equivariance.

翻译：我们采用极限学习机进行偏微分方程（PDE）的预测。该方法将状态空间分割为多个窗口，并使用单一模型对各窗口进行独立预测。尽管仅需少量数据点（在某些情况下，本方法仅需单个全状态快照即可完成学习），其仍能实现高精度预测，并能对偏微分方程的流进行长期预测。此外，我们展示了如何利用附加对称性提升样本效率并强制等变性。