Abstract
Physics-informed neural networks (PINNs) offer a promising framework by embedding partial differential equations (PDEs) into the loss function together with measurement data, making them well-suited for inverse problems. However, plain PINNs face challenges with time-dependent PDEs due to the high computational cost of space-time training and the risk of convergence to local minima. These limitations are particularly pronounced in hemodynamic analysis, where 4D-flow magnetic resonance imaging (4D-flow MRI) yields temporally sparse velocity snapshots over the cardiac cycle. To address this challenge, we propose a PINN framework that reconstructs instantaneous flow fields from transient velocity snapshots by inferring the acceleration term in the incompressible Navier-Stokes equations. By designing the network without explicit time as an input, the proposed approach enables physics enforcement using spatial evaluations alone, improving training efficiency while maintaining physical consistency with transient flow characteristics. In addition, we introduce an acceleration-mismatch loss that penalizes discrepancies between predicted and measured accelerations, which improves prediction accuracy through regularization. Numerical examples on pulsatile flow behind a stenosis using temporally and spatially downsampled synthetic data generated from time-resolved CFD demonstrate that the proposed framework reliably reconstructs velocity fields even under sparse temporal sampling, and appropriate regularization for acceleration improves predictions of pressure-gradient and acceleration fields.
