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.
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