Input parametrized physics-informed neural networks for super-resolution of hemodynamic flow images

Physics-informed neural networks (PINNs) have successfully been used for super-resolution of low resolution, artifact prone, and noisy blood flow images. PINNs do not require the labeled data sets (ground truth) for training. Furthermore, automatic differentiation (AD) enables accurate calculation of velocity and pressure gradients. However, the main drawback of PINNs is the lack of its ability to institute any kind of transfer learning. Consequently, PINNs take significant amount of time for processing new data sets. In this talk we present a scheme to parametrize the PINN solution with respect to the input data. Wavelet transform of the input followed by selection of k coefficients is used to reduce the input data cube to a latent parameter vector. The latent parameter vector is then appended to the spatio-temporal coordinate input of a fully connected network. The common loss function imposes data fidelity with the input data set as well as flow physics through regularization. Synthetic data from computational fluid dynamics (CFD) simulations as well as actual image data can be used to pre-train the network. The proposed scheme retains useful properties of PINNs, namely, computation of pressure and velocity gradients through AD and eliminates the need for expensive ab-initio training required for new data sets.