  Autoencoder-based reduced-order modeling (ROM) has recently attracted
significant attention, owing to its ability to capture underlying nonlinear
features. However, two critical drawbacks severely undermine its scalability to
various physical applications: entangled and therefore uninterpretable latent
variables (LVs) and the blindfold determination of latent space dimension. In
this regard, this study proposes the physics-aware ROM using only interpretable
and information-intensive LVs extracted by $\beta$-variational autoencoder,
which are referred to as physics-aware LVs throughout this paper. To extract
these LVs, their independence and information intensity are quantitatively
scrutinized in a two-dimensional transonic flow benchmark problem. Then, the
physical meanings of the physics-aware LVs are thoroughly investigated and we
confirmed that with appropriate hyperparameter $\beta$, they actually
correspond to the generating factors of the training dataset, Mach number and
angle of attack. To the best of the authors' knowledge, our work is the first
to practically confirm that $\beta$-variational autoencoder can automatically
extract the physical generating factors in the field of applied physics.
Finally, physics-aware ROM, which utilizes only physics-aware LVs, is compared
with conventional ROMs, and its validity and efficiency are successfully
verified.
