Machine Learning Assisted Resistive Force Theory for Helical Structures at Low Reynolds Number

The hydrodynamic forces on a slender rod in a fluid medium at low Reynolds number can be modeled using resistive force theories (RFTs) or slender body theories (SBTs). The former represent the forces by local drag coefficients and are computationally cheap; however, they are physically inaccurate when long-range hydrodynamic interaction is involved. The later are physically accurate but require solving integral equations and, therefore, are computationally expensive. This paper investigates RFTs in comparison with state-of-the art SBT methods. During the process, a neural network-based hydrodynamic model that -- similar to RFTs -- relies on local drag coefficients for computational efficiency was developed. However, the network is trained using data from an SBT (regularized stokeslet segments method). The $R^2$ value of the trained coefficients were $\sim 0.99$ with mean absolute error of $1.6\times10^{-2}$. The machine learning resistive force theory (MLRFT) accounts for local hydrodynamic forces distribution, the dependence on rotational and translational speeds and directions, and geometric parameters of the slender object. We show that, when classical RFT fails to accurately predict the forces, torques, and drags on slender rods under low Reynolds number flows, MLRFT exhibits good agreement with physically accurate SBT simulations. In terms of computational speed, MLRFT forgoes the need of solving an inverse problem and, therefore, requires negligible computation time in comparison with SBT. MLRFT presents a computationally inexpensive hydrodynamic model for flagellar propulsion can be used in the design and optimization of biomimetic flagellated robots and analysis of bacterial locomotion.