HDNet: Physics-Inspired Neural Network for Flow Estimation based on Helmholtz Decomposition

TL;DR

HDNet is a physics-inspired neural network that performs Helmholtz decomposition of flow fields, enabling accurate flow estimation by leveraging physical constraints like incompressibility and irrotationality, trained solely on synthetic Helmholtz synthesis data.

Contribution

The paper introduces HDNet, a novel neural network that decomposes flow fields into divergence and curl components using Helmholtz decomposition, trained exclusively on synthetic data.

Findings

HDNet effectively decomposes flow fields into physical components.

HDNet can be integrated into various flow estimation tasks.

Training on synthetic Helmholtz synthesis data suffices for accurate decomposition.

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.