Neural Inference of Fluid–Structure Interactions from Lagrangian Particle Tracks

Fluid–structure interactions (FSI) involve flexible structures that couple to internal or external flow. We report a novel configuration of physics-informed neural networks (PINNs) to reconstruct FSI from a sparse set of Lagrangian particle trajectories, called tracks. To do this, we use a "fluid network" to represent the liquid or gas phase; a "solid network" models the surface response via coefficients of a parameterized surface. Data are included in the algorithm via a "kinematics-constrained track" model that embeds the advection equation as a hard constraint and can handle noise and inertial transport effects. We specify data and physics losses for the fluid, as well as a no-slip boundary loss for inter-phase coupling. Minimizing the aggregate loss yields spatiotemporally resolved flow states that are consistent with observed data and governing equations for the fluid and a surface response that complies with the boundary condition. Crucially, the approach does not require a constitutive model for the solid phase. We demonstrate our method synthetically using 2D flow over a flapping plate and 3D flow inside a flexible pipe. Accurate reconstructions of both phases are obtained from the sparse, noisy tracks.