论文标题
部分可观测时空混沌系统的无模型预测
Dataset Condensation with Latent Space Knowledge Factorization and Sharing
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。
In this paper, we introduce a novel approach for systematically solving dataset condensation problem in an efficient manner by exploiting the regularity in a given dataset. Instead of condensing the dataset directly in the original input space, we assume a generative process of the dataset with a set of learnable codes defined in a compact latent space followed by a set of tiny decoders which maps them differently to the original input space. By combining different codes and decoders interchangeably, we can dramatically increase the number of synthetic examples with essentially the same parameter count, because the latent space is much lower dimensional and since we can assume as many decoders as necessary to capture different styles represented in the dataset with negligible cost. Such knowledge factorization allows efficient sharing of information between synthetic examples in a systematic way, providing far better trade-off between compression ratio and quality of the generated examples. We experimentally show that our method achieves new state-of-the-art records by significant margins on various benchmark datasets such as SVHN, CIFAR10, CIFAR100, and TinyImageNet.
