Fully differentiable boundary element solver for hydrodynamic sensitivity analysis of wave-structure interactions

Accurately predicting wave-structure interactions is critical for the effective design and analysis of marine structures. This is typically achieved using solvers that employ the boundary element method (BEM), which relies on linear potential flow theory. Precise estimation of the sensitivity of these interactions is equally important for system-level applications such as design optimization. Current BEM solvers are unable to provide these sensitivities as they do not support automatic differentiation (AD). To address these challenges, we have developed a fully differentiable BEM solver, MarineHydro.jl, for marine hydrodynamics, capable of calculating diffraction and radiation coefficients, and their derivatives with high accuracy. MarineHydro.jl implements both direct and indirect BEM formulations and incorporates two Green’s function expressions, offering a trade-off between accuracy and computational speed. Gradients are computed using reverse-mode AD within the Julia programming language. As a first case study, we analyze two identical floating spheres, evaluating gradients with respect to physical dimensions, inter-sphere distance, and wave frequency. Verification studies demonstrate excellent agreement between AD-computed gradients and finite-difference results. In a second case study, we leverage AD-computed gradients to optimize the mechanical power production of a pair of wave energy converters (WECs). This represents the first application of exact gradients obtained from BEM solver in WEC power optimization. Both studies offer valuable insights into hydrodynamic interactions and advance the understanding of layout optimization. Beyond power optimization, the differentiable BEM solver highlights the potential of AD for offshore design studies. It paves the way for broader applications in machine learning integration, optimal control, and uncertainty quantification of hydrodynamic coefficients, offering new directions for advancing wave-structure interaction analysis and system-level optimization.