HDNet: Physics-Inspired Neural Network for Flow Estimation based on Helmholtz Decomposition
This work addresses flow estimation for scientific imaging applications, such as fluid experiments and optical analysis, by incorporating physical constraints, but it is incremental as it builds on existing physics-inspired neural network methods.
The authors tackled the problem of flow estimation in scientific imaging by proposing HDNet, a physics-inspired neural network that decomposes arbitrary flow fields into divergence-only and curl-only components using Helmholtz decomposition, enabling training on synthetic data and integration into various flow estimation tasks.
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.