论文标题
部分可观测时空混沌系统的无模型预测
Toward deep-learning-assisted spectrally-resolved imaging of magnetic noise
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。
Recent progress in the application of color centers to nanoscale spin sensing makes the combined use of noise spectroscopy and scanning probe imaging an attractive route for the characterization of arbitrary material systems. Unfortunately, the traditional approach to characterizing the environmental magnetic field fluctuations from the measured probe signal typically requires the experimenter's input, thus complicating the implementation of automated imaging protocols based on spectrally resolved noise. Here, we probe the response of color centers in diamond in the presence of externally engineered random magnetic signals, and implement a deep neural network to methodically extract information on their associated spectral densities. Building on a long sequence of successive measurements under different types of stimuli, we show that our network manages to efficiently reconstruct the spectral density of the underlying fluctuating magnetic field with good fidelity under a broad set of conditions and with only a minimal measured data set, even in the presence of substantial experimental noise. These proof-of-principle results create opportunities for the application of machine-learning methods to color-center-based nanoscale sensing and imaging.