  We propose a self-supervised approach for learning physics-based subspaces
for real-time simulation. Existing learning-based methods construct subspaces
by approximating pre-defined simulation data in a purely geometric way.
However, this approach tends to produce high-energy configurations, leads to
entangled latent space dimensions, and generalizes poorly beyond the training
set. To overcome these limitations, we propose a self-supervised approach that
directly minimizes the system's mechanical energy during training. We show that
our method leads to learned subspaces that reflect physical equilibrium
constraints, resolve overfitting issues of previous methods, and offer
interpretable latent space parameters.
