论文标题
自旋玻璃实验
Spin glass experiments
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。
A spin glass is a diluted magnetic material in which the magnetic moments are randomly interacting, with a huge number of metastable states which prevent reaching equilibrium. Spin-glass models are conceptually simple, but require very sophisticated treatments. These models have become a paradigm for the understanding of glassy materials and also for the solution of complex optimization problems. After cooling from the paramagnetic phase, the spin glass remains out of equilibrium, and slowly evolves. This aging phenomenon corresponds to the growth of a mysterious "spin-glass order", whose correlation length can be measured. A cooling temperature step during aging causes a partial "rejuvenation", while the "memory" of previous aging is stored and can be retrieved. Many glassy materials present aging, and rejuvenation and memory effects can be found in some cases, but they are usually less pronounced. Numerical simulations of these phenomena are presently under active development using custom-built supercomputers. A general understanding of the glassy systems, for which spin glasses bring a prominent insight, is still under construction.
