1. HDNet: Physics-Inspired Neural Network for Flow Estimation based on Helmholtz Decomposition
- Author
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Qi, Miao, Idoughi, Ramzi, and Heidrich, Wolfgang
- Subjects
Computer Science - Machine Learning ,Computer Science - Artificial Intelligence - Abstract
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.
- Published
- 2024