论文标题

部分可观测时空混沌系统的无模型预测

UltraMNIST Classification: A Benchmark to Train CNNs for Very Large Images

论文作者

Gupta, Deepak K., Bamba, Udbhav, Thakur, Abhishek, Gupta, Akash, Sharan, Suraj, Demir, Ertugrul, Prasad, Dilip K.

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。

Convolutional neural network (CNN) approaches available in the current literature are designed to work primarily with low-resolution images. When applied on very large images, challenges related to GPU memory, smaller receptive field than needed for semantic correspondence and the need to incorporate multi-scale features arise. The resolution of input images can be reduced, however, with significant loss of critical information. Based on the outlined issues, we introduce a novel research problem of training CNN models for very large images, and present 'UltraMNIST dataset', a simple yet representative benchmark dataset for this task. UltraMNIST has been designed using the popular MNIST digits with additional levels of complexity added to replicate well the challenges of real-world problems. We present two variants of the problem: 'UltraMNIST classification' and 'Budget-aware UltraMNIST classification'. The standard UltraMNIST classification benchmark is intended to facilitate the development of novel CNN training methods that make the effective use of the best available GPU resources. The budget-aware variant is intended to promote development of methods that work under constrained GPU memory. For the development of competitive solutions, we present several baseline models for the standard benchmark and its budget-aware variant. We study the effect of reducing resolution on the performance and present results for baseline models involving pretrained backbones from among the popular state-of-the-art models. Finally, with the presented benchmark dataset and the baselines, we hope to pave the ground for a new generation of CNN methods suitable for handling large images in an efficient and resource-light manner.

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