Lagrangian-Eulerian learning of flow field and trajectories with TrajectoryFlowNet
Predicting particle transport in complex flows is traditionally achieved by solving the Navier-Stokes equations. While various numerical and experimental methods exist, they typically require deep physical insights and incur high computational costs. Machine learning offers an alternative by learning predictive patterns directly from data, avoiding explicit physical modeling. However, purely data-driven approaches often lack interpretability, physical consistency, and generalizability in sparse data regimes. To this end, we propose TrajectoryFlowNet, a Lagrangian-Eulerian physics-informed neural network architecture, for fluid flow velocimetry and imaging via learning to predict spatiotemporal flow fields and long-range particle trajectories. The salient features of our model include its ability to handle complex flow patterns with irregular boundaries, predict the full-field flows, image the long-range flow trajectory of any arbitrary particle, and ensure physical consistency in predictions based only on very scarce measurement of flow trajectories. We validate TrajectoryFlowNet via both numerical examples (e.g., lid-driven cavity flow and complex cylinder flow) and experimental test cases (e.g., aortic and ventricle blood flows) across diverse flow scenarios. The results demonstrate our model's effectiveness in capturing intricate particle-laden flow dynamics, enabling long-range tracking of particles and accurate construction of flow fields in real-world applications.