Disentangling Generative Factors of Physical Fields Using Variational Autoencoders

The ability to extract generative parameters from high-dimensional fields of data in an unsupervised manner is a highly desirable yet unrealized goal computational physics. This work explores the use variational autoencoders for non-linear dimension reduction with specific aim disentangling low-dimensional latent variables identify independent physical that generated data. A disentangled decomposition interpretable, and can be transferred variety tasks including modeling, design optimization, probabilistic reduced order modelling. major emphasis this characterize disentanglement using VAEs while minimally modifying classic VAE loss function (i.e., Evidence Lower Bound) maintain high reconstruction accuracy. landscape characterized by over-regularized local minima which surround solutions. We illustrate comparisons between entangled representations juxtaposing learned distributions true factors model porous flow problem. Hierarchical priors are shown facilitate learning representations. regularization unaffected rotation when training rotationally-invariant priors, thus non-rotationally-invariant aids capturing properties factors, improving disentanglement. Finally, it semi-supervised - accomplished labeling small number samples ( O (1%))–results accurate consistently learned.