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

TL;DR

This paper addresses real-time prediction of a small USV's heave near a wall by building a physics-informed surrogate. It combines sparse regression (SINDy) to identify a low-order nonlinear ODE capturing hydrostatic, radiation, and simple excitation terms from CFD data, with a neural operator that maps wall distance and drop height to the identified ODE coefficients for rapid, continuous surrogacy across input space. The main contributions are a validated nonlinear ROM anchored in physical mechanisms and a SINDy-informed neural operator that delivers real-time predictions with interpretable coefficient pathways. The work advances practical launch-and-recovery analysis by offering a real-time, data-driven, physics-consistent surrogate that can be extended to more complex motion and forcing regimes.

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.

Figures (19)

• Figure 1: Schematic of the heaving sphere near a vertical wall, representing a simplified LARS configuration.
• Figure 2: Freeze frame from CFD simulation.
• Figure 3: Raw dataset; train-test split
• Figure 4: Validation of drop test from drop height of (a) $0.1$ and (b) $0.5$ of the spheres diameter. Comparison between our CFD simulation, experimental data Kramer2021 and linear model.
• Figure 5: Validation of RAO for our CFD by comparing our results for the spheres heaving RAO with a linear model