标题： 从量子材料的无序图像数据中学习深度学习哈密顿量 显示英文标题

标题： Deep Learning Hamiltonians from Disordered Image Data in Quantum Materials

摘要： 图像探测实验的能力正在迅速扩展，为量子材料在前所未有的长度和时间尺度上提供了新的信息。 许多这样的材料在可观察表面上表现出不均匀的电子特性，并形成复杂的图案。 这种丰富的空间结构包含了关于相互作用、维度和无序的信息——这是驱动图案形成的哈密顿量的空间编码。 机器学习中的图像识别技术是解读此类图像中空间关系所编码信息的优秀工具。 在此，我们开发了一个深度学习框架，利用这些空间相关性中可用的丰富信息，以发现驱动图案形成的底层哈密顿量。 我们首先在一个已知案例上验证了该方法，即对VO2薄膜进行近场扫描光学显微镜实验。 然后，我们将训练好的卷积神经网络架构应用于另一种VO2薄膜在金属-绝缘体转变过程中的新光学显微镜图像。 我们发现，在转变过程中，金属和绝缘体区域的复杂分形交织需要一个包含相互作用和随机场无序的二维哈密顿量来解释。 关于底层哈密顿量的详细知识为使用该模型通过定制的滞后协议来控制图案形成铺平了道路。 我们还引入了一种基于分布的多标签分类器结果的置信度度量，该度量不依赖于对抗训练。 此外，我们提出了一种基于机器学习的新标准，用于诊断物理系统接近临界性的程度。 显示英文摘要

摘要： The capabilities of image probe experiments are rapidly expanding, providing new information about quantum materials on unprecedented length and time scales. Many such materials feature inhomogeneous electronic properties with intricate pattern formation on the observable surface. This rich spatial structure contains information about interactions, dimensionality, and disorder -- a spatial encoding of the Hamiltonian driving the pattern formation. Image recognition techniques from machine learning are an excellent tool for interpreting information encoded in the spatial relationships in such images. Here, we develop a deep learning framework for using the rich information available in these spatial correlations in order to discover the underlying Hamiltonian driving the patterns. We first vet the method on a known case, scanning near-field optical microscopy on a thin film of VO2. We then apply our trained convolutional neural network architecture to new optical microscope images of a different VO2 film as it goes through the metal-insulator transition. We find that a two-dimensional Hamiltonian with both interactions and random field disorder is required to explain the intricate, fractal intertwining of metal and insulator domains during the transition. This detailed knowledge about the underlying Hamiltonian paves the way to using the model to control the pattern formation via, e.g., tailored hysteresis protocols. We also introduce a distribution-based confidence measure on the results of a multi-label classifier, which does not rely on adversarial training. In addition, we propose a new machine learning based criterion for diagnosing a physical system's proximity to criticality.