HDNet: Physics-Inspired Neural Network for Flow Estimation based on Helmholtz Decomposition
<|reference_start|>HDNet: Physics-Inspired Neural Network for Flow Estimation based on Helmholtz Decomposition: 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.<|reference_end|>
@article{qi2024hdnet:,
    title={HDNet: Physics-Inspired Neural Network for Flow Estimation based on
  Helmholtz Decomposition},
    author={Miao Qi, Ramzi Idoughi and Wolfgang Heidrich},
    journal={arXiv preprint arXiv:2406.08570},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.08570},
    primaryClass={cs.LG cs.AI}
}