Capturing functional relations in fluid-structure interaction via machine learning

While fluid-structure interaction (FSI) problems are ubiquitous in various applications from cell-biology to aerodynamics, they involve huge computational overhead. In this paper, we adopt a machine learning (ML)-based strategy to bypass the detailed FSI analysis that requires cumbersome simulations in solving the Navier-Stokes (N-S) equations. To mimic the effect of fluid on an immersed beam, we have introduced dissipation into the beam model with time-varying forces acting on it. The forces in a discretized setup have been decoupled via an appropriate linear algebraic operation, which generates the ground truth force/moment data for the ML analysis. The adopted ML technique, symbolic regression, generates computationally tractable functional forms to represent the force/moment with respect to space and time. These estimates are fed into the dissipative beam model to generate the immersed beam's deflections over time, which are in conformity with the detailed FSI solutions. Numerical results demonstrate that the ML-estimated continuous force and moment functions are able to accurately predict the beam deflections under different discretizations.