Neural Conservation Laws: A Divergence-Free Perspective. (arXiv:2210.01741v1 [cs.LG])

We investigate the parameterization of deep neural networks that by design
satisfy the continuity equation, a fundamental conservation law. This is
enabled by the observation that solutions of the continuity equation can be
represented as a divergence-free vector field. We hence propose building
divergence-free neural networks through the concept of differential forms, and
with the aid of automatic differentiation, realize two practical constructions.
As a result, we can parameterize pairs of densities and vector fields that
always satisfy the continuity …

arxiv conservation divergence free laws perspective