A Physics-Informed Neural Network for Fluid-Structure Coupled Simulation of A Euler-Bernouli Beam Under Steady Flow

Despite the significant progress in the last few years in numerical simulations with physics-informed neural network (PINN), it is still a challenge to utilize PINN to solve coupled fluid-structure interaction problems. This work adopts PINN to approximate two-dimensional fluid-structure interaction for both forward and inverse problems. For the forward problem, we select data from the fluid domain randomly and combine the data with certain physics laws, including Robin boundary condition and Euler-Bernoulli Equation, to infer the displacement of beam.  For the inverse problem, in which the parameter in the Euler-Bernoulli equation is unknown, we solve the fluid problem with data and physics laws to infer the fluid pressure and pressure gradient on the interface, and compute the pressure and acceleration of the beam through the Robin boundary condition.  Finally, with the data we acquire from the last step, the displacement of the beam, as well as the unknown parameter, can be calculated. The results demonstrate that PINN can solve fluid-structure coupled problems accurately by composing conservation laws at some random points with less than 1% relative L2 error, especially in the inverse problem, where conventional techniques are difficult to handle.