Reduced-Order Hydrodynamic Modelling of a Sphere Near a Wall Using Sparse Regression and Neural Networks

Abstract

This work presents an interpretable parametric surrogate model motivated by the need to identify a hydrodynamic model for resolving the trajectory of an object in real-time. The surrogate is formulated as a reduced-order model for a canonical configuration in which a one-degree-of-freedom heaving sphere operates near a vertical wall. High-fidelity CFD simulations are used to generate a parametric dataset of heave-decay responses over varying wall distances (WD) and drop heights (DH). Sparse Identification of Nonlinear Dynamics (SINDy) is then applied to each CFD trajectory to identify a low-order nonlinear ordinary differential equation (ODE) with polynomial terms representing effective hydrostatic restoring and radiation damping, and the harmonic terms representing the wave-induced excitation forces. The SINDy identified coefficients are then used as a prior constraint in a neural operator network (ONet) that learns a smooth mapping from wall distance and drop height to the ODE coefficients, yielding a surrogate capable of predicting dynamics at arbitrary points in the input space without rerunning expensive CFD calculations. The resulting surrogate reproduces CFD heave-decay responses with near-optimal accuracy given the limiting assumptions while being capable of running in real time. The approach provides a practical pathway toward real-time, physics-informed surrogate modelling for launch-and-recovery operations.