  Flow estimation problems are ubiquitous in scientific imaging. Often, the
underlying flows are subject to physical constraints that can be exploited in
the flow estimation; for example, incompressible (divergence-free) flows are
expected for many fluid experiments, while irrotational (curl-free) flows arise
in the analysis of optical distortions and wavefront sensing. In this work, we
propose a Physics- Inspired Neural Network (PINN) named HDNet, which performs a
Helmholtz decomposition of an arbitrary flow field, i.e., it decomposes the
input flow into a divergence-only and a curl-only component. HDNet can be
trained exclusively on synthetic data generated by reverse Helmholtz
decomposition, which we call Helmholtz synthesis. As a PINN, HDNet is fully
differentiable and can easily be integrated into arbitrary flow estimation
problems.
