In Materials Science, material development involves evaluating and optimizing
the internal structures of the material, generically referred to as
microstructures. Microstructures structure is stochastic, analogously to image
textures. A particular microstructure can be well characterized by its spatial
statistics, analogously to image texture being characterized by the response to
a Fourier-like filter bank. Material design would benefit from low-dimensional
representation of microstructures Paulson et al. (2017).
In this work, we train a Variational Autoencoders (VAE) to produce
reconstructions of textures that preserve the spatial statistics of the
original texture, while not necessarily reconstructing the same image in data
space. We accomplish this by adding a differentiable term to the cost function
in order to minimize the distance between the original and the reconstruction
in spatial statistics space.
Our experiments indicate that it is possible to train a VAE that minimizes
the distance in spatial statistics space between the original and the
reconstruction of synthetic images. In future work, we will apply the same
techniques to microstructures, with the goal of obtaining low-dimensional
representations of material microstructures.

在材料科学中，通过训练变分自动编码器 (VAE) 来重建材料的空间统计特征，从而获得材料的低维表示。

优化空间统计学空间中学习微结构的潜变量表示

Toward Learning Latent-Variable Representations of Microstructures by  Optimizing in Spatial Statistics Space

In supervised learning, acquiring labeled training data for a predictive
model can be very costly, but acquiring a large amount of unlabeled data is
often quite easy. Active learning is a method of obtaining predictive models
with high precision at a limited cost through the adaptive selection of samples
for labeling. This paper explains the basic problem settings of active learning
and recent research trends. In particular, research on learning acquisition
functions to select samples from the data for labeling, theoretical work on
active learning algorithms, and stopping criteria for sequential data
acquisition are highlighted. Application examples for material development and
measurement are introduced.

本文介绍了有监督学习中获取标记数据的高成本和获取大量未标记数据的轻松方法，以及通过自适应选择标记样本来获得高精度预测模型的主要问题设置和最近的研究趋势。重点介绍了选择从数据中进行标记的学习获取函数的研究、关于主动学习算法的理论工作和顺序数据获取的停止标准。介绍了材料开发和测量的应用示例。