We propose a variational autoencoder (VAE)-based model for building forward
and inverse structure-property linkages, a problem of paramount importance in
computational materials science. Our model systematically combines VAE with
regression, linking the two models through a two-level prior conditioned on the
regression variables. The regression loss is optimized jointly with the
reconstruction loss of the variational autoencoder, learning microstructure
features relevant for property prediction and reconstruction. The resultant
model can be used for both forward and inverse prediction i.e., for predicting
the properties of a given microstructure as well as for predicting the
microstructure required to obtain given properties. Since the inverse problem
is ill-posed (one-to-many), we derive the objective function using a
multi-modal Gaussian mixture prior enabling the model to infer multiple
microstructures for a target set of properties. We show that for forward
prediction, our model is as accurate as state-of-the-art forward-only models.
Additionally, our method enables direct inverse inference. We show that the
microstructures inferred using our model achieve desired properties reasonably
accurately, avoiding the need for expensive optimization loops.

我们提出了一种基于变分自编码器 (VAE) 的模型，用于构建前向和逆向的结构 - 性质联系，这是计算材料科学中至关重要的问题。我们的模型通过一个双层先验条件于回归变量来系统地结合 VAE 和回归模型。回归损失与变分自编码器的重构损失一起进行优化，学习与属性预测和重构相关的微观结构特征。该模型可以用于前向和逆向预测，即预测给定微观结构的属性以及预测获取给定属性所需的微观结构。由于逆向问题存在不适定性（多对一关系），我们使用多模态高斯混合先验导出了目标函数，使模型能够推断出多个适用于一组目标属性的微观结构。我们显示，在前向预测方面，我们的模型与最先进的仅前向模型一样准确。此外，我们的方法实现了直接逆向推断。我们表明，使用我们的模型推断的微观结构能够相当准确地实现所需的属性，避免了昂贵的优化过程。