How to Use a PINN for a Navier-Stokes Inverse Problem

Physics-Informed Neural Networks (PINNs) can reconstruct a complete blood flow field within a narrowed artery using only a handful of scattered, noisy velocity measurements. A PyTorch model built from scratch successfully determined the velocity and pressure fields and even solved for the fluid's unknown viscosity as a learnable parameter. The network accurately captured complex flow features like the jet stream and the reversed flow zone behind the blockage without any direct measurements at the artery wall. This method also allows for the calculation of wall shear stress, a clinically important value linked to plaque buildup that is otherwise very difficult to measure directly. Crucially, the model's success in inferring physical properties depended heavily on the amount of data, requiring at least 40 sensor readings to converge on the correct viscosity.