论文标题
部分可观测时空混沌系统的无模型预测
Generalization to translation shifts: a study in architectures and augmentations
论文作者
论文摘要
储层计算是预测湍流的有力工具,其简单的架构具有处理大型系统的计算效率。然而,其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间,然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用,该系统模拟了湍流的若干特征。我们表明,使用径向基函数作为非线性投影器,即使只有部分观测并且不知道控制方程,也能稳健地捕捉复杂的系统非线性。最后,我们表明,当测量稀疏、不完整且带有噪声,甚至控制方程变得不准确时,我们的网络仍然可以产生相当准确的预测,从而为实际湍流系统的无模型预测铺平了道路。
We study how effective data augmentation is at capturing the inductive bias of carefully designed network architectures for spatial translation invariance. We evaluate various image classification architectures (antialiased, convolutional, vision transformer, and fully connected MLP networks) and data augmentation techniques towards generalization to large translation shifts. We observe that: (a) without data augmentation, all architectures, including convolutional networks with antialiased modification suffer some degradation in performance when evaluated on translated test distributions. Understandably, both the in-distribution accuracy and degradation to shifts is significantly worse for non-convolutional models. (b) The robustness of performance is improved by even a minimal augmentation of $4$ pixel random crop across all architectures. In some instances, even $1-2$ pixel random crop is sufficient. This suggests that there is a form of meta generalization from augmentation. For non-convolutional architectures, while the absolute accuracy is still low with this basic augmentation, we see substantial improvements in robustness to translation shifts. (c) With a sufficiently advanced augmentation pipeline ($4$ pixel crop+RandAugmentation+Erasing+MixUp), all architectures can be trained to have competitive performance in terms of in-distribution accuracy as well as generalization to large translation shifts.