Sparse particle tracks are enough to map a whole flow: one network predicts long-range paths and full fields

Where a particle travels in a complex flow can now come directly from a network trained on a few trajectory measurements, without first solving the whole velocity field and then integrating particle paths. The established route solves the Navier–Stokes equations, and numerical and experimental methods require deep physical insight and incur high computational cost; existing machine-learning alternatives fail to generalize long-range particle trajectory prediction in sparse data regimes. Across two numerical examples, lid-driven cavity flow and complex cylinder flow, and two experimental test cases, aortic blood flow and left-ventricle blood flow, the model predicts full-field flows and long-range particle trajectories.

The network learns two descriptions at once: velocity and pressure on a spatial grid, and the position over time of individual particles, tied together by the same physical constraints. This is a physics-informed neural network, meaning fluid-equation constraints enter the training objective so outputs stay physically consistent rather than merely fitting observations. Training uses only scarce measurements of flow trajectories, yet the model handles complex flow patterns with irregular boundaries and images long-range trajectories of any arbitrary particle.

The scope is full-field flow and long-range particle trajectory prediction from sparse trajectory measurements, demonstrated on two numerical examples, lid-driven cavity flow and complex cylinder flow, and two experimental test cases, aortic blood flow and left-ventricle blood flow. Intended readers are fluid mechanicians, experimental flow-measurement specialists and biomedical flow analysts who need to reconstruct flows and track particles from limited trajectory observations. The source states no next experiment or deployment plan.

Effectiveness is demonstrated on numerical and experimental cases, and the source gives no pooled quantitative error summary across cases or systematic comparison conclusion against other methods. A probabilistic variant reports mean and standard deviation of pressure prediction using 100 Stein particles, and this uncertainty quantification appears only for experimental blood-flow pressure. The range of long-range extrapolation under sparse data is described as scarce measurement, without a transferable data-volume threshold.