The ability to extract generative parameters from high-dimensional fields of data in an unsupervised manner is a highly desirable yet unrealized goal in computational physics. This work explores the use of variational autoencoders (VAEs) for non-linear dimension reduction with the aim of disentangling the low-dimensional latent variables to identify independent physical parameters that generated the data. A disentangled decomposition is interpretable and can be transferred to a variety of tasks including generative modeling, design optimization, and probabilistic reduced order modelling. A major emphasis of this work is to characterize disentanglement using VAEs while minimally modifying the classic VAE loss function (i.e. the ELBO) to maintain high reconstruction accuracy. Disentanglement is shown to be highly sensitive to rotations of the latent space, hyperparameters, random initializations and the learning schedule. The loss landscape is characterized by over-regularized local minima which surrounds desirable solutions. We illustrate comparisons between disentangled and entangled representations by juxtaposing learned latent distributions and the 'true' generative factors in a model porous flow problem. Implementing hierarchical priors (HP) is shown to better facilitate the learning of disentangled representations over the classic VAE. The choice of the prior distribution is shown to have a dramatic effect on disentanglement. In particular, the regularization loss is unaffected by latent rotation when training with rotationally-invariant priors, and thus learning non-rotationally-invariant priors aids greatly in capturing the properties of generative factors, improving disentanglement. Some issues inherent to training VAEs, such as the convergence to over-regularized local minima are illustrated and investigated, and potential techniques for mitigation are presented.

翻译：以不受监督的方式从高维数据领域提取变异参数的能力是计算物理中一个非常可取但却没有实现的目标。 这项工作探索使用变异自动电解器( VAE) 来降低非线性维度, 目的是分解低维潜变量, 以辨别生成数据的独立物理参数。 分解是可以解释的, 并可以转移到各种任务中, 包括变异模型、 设计优化和概率递减顺序建模。 这项工作的主要重点是, 使用 VAEs 来描述变异的解动, 同时对传统的 VAE 损失函数( 即 ELBO ) 进行最小化, 以保持较高的重建精度。 变异性对生成数据的隐性空间、 超光度、 随机初始化和学习时间表的旋转非常敏感。 损失环境的特征是过于常规化的本地变异性缩缩缩缩图, 我们通过对一些变异性变动的变异性变异性变异性变性变异性变异性演算, 在前变变性变变异性变变的变变变变变变变变变性变性变变变变变变的变变变变变变变变变的变变变变变变变变变变变变的变变变变变变变变变变的变变变变变变变变变变变变变变变变变变变变变变变变变变的变的变变变变变变变变变的变的变变变变变的变的变变变变变变变变变变变变变变变变变变变变变变变变变变变变变的变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变中, 变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变变