论文标题
部分可观测时空混沌系统的无模型预测
Compressed Matrix Computations
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。
Frugal computing is becoming an important topic for environmental reasons. In this context, several techniques have been proposed to reduce the storage of scientific data by dedicated compression methods specially tailored for arrays of floating-point numbers. While these techniques are quite efficient to save memory, they introduce additional computations to compress and decompress the data before processing them. In this article, we introduce a new lossy, fixed-rate compression technique for 2D-arrays of floating-point numbers which allows one to compute directly on the compressed data, without decompressing them. We obtain important speedups since less operations are needed to compute among the compressed data and since no decompression and re-compression is needed. More precisely, our technique makes it possible to perform basic linear algebra operations such as addition, multiplication by a constant among compressed matrices and dot product and matrix multiplication among partly uncompressed matrices. This work has been implemented into a tool named blaz and a comparison with the well-known compressor zfp in terms of execution-time and accuracy is presented.