  Aquatic locomotion is a classic fluid-structure interaction (FSI) problem of
interest to biologists and engineers. Solving the fully coupled FSI equations
for incompressible Navier-Stokes and finite elasticity is computationally
expensive. Optimizing robotic swimmer design within such a system generally
involves cumbersome, gradient-free procedures on top of the already costly
simulation. To address this challenge we present a novel, fully differentiable
hybrid approach to FSI that combines a 2D direct numerical simulation for the
deformable solid structure of the swimmer and a physics-constrained neural
network surrogate to capture hydrodynamic effects of the fluid. For the
deformable solid simulation of the swimmer's body, we use state-of-the-art
techniques from the field of computer graphics to speed up the finite-element
method (FEM). For the fluid simulation, we use a U-Net architecture trained
with a physics-based loss function to predict the flow field at each time step.
The pressure and velocity field outputs from the neural network are sampled
around the boundary of our swimmer using an immersed boundary method (IBM) to
compute its swimming motion accurately and efficiently. We demonstrate the
computational efficiency and differentiability of our hybrid simulator on a 2D
carangiform swimmer. Due to differentiability, the simulator can be used for
computational design of controls for soft bodies immersed in fluids via direct
gradient-based optimization.
