A machine learning surrogate solver for dynamic response of submerged structures under shock loads

The complex physics of underwater explosion (UNDEX) phenomena poses significant challenges for obtaining accurate analytical solutions. This study presents a novel neural network-based surrogate model (NNSM) for predicting the dynamic response equation of submerged structures subjected to shock loading from UNDEX events. As a proof of concept, the NNSM is evaluated against the physics-informed neural network (PINN) framework. The structural model consists of two rigid parallel plates connected by a linear spring and dashpot, representing stiffness and damping. The explosion is assumed to occur at a sufficient distance such that the pressure loading can be approximated as a planar shock wave. The coupled governing ordinary differential equations (ODEs) are derived and solved analytically and numerically–using the classical fourth-order Runge–Kutta method–to generate reference data for training both the NNSM and the PINN. The PINN framework embeds the governing physics into the loss function, enabling predictions without external simulation data. In contrast, the proposed NNSM learns the time-dependent interaction term ϕ(t) between the plates using a neural network. This reduces the second-order ODE to a first-order formulation, significantly simplifying the model. The NNSM effectively captures critical response features–including shock attenuation, cavitation onset time, and peak momentum transfer time–under varying stiffness and damping conditions. Comparative analysis shows that the NNSM closely matches numerical solutions and outperforms the PINN in both accuracy and computational efficiency. Key contributions of this work include: (1) a novel order-reduction strategy that reformulates the second-order system by learning ϕ(t); (2) quantitative validation demonstrating relative prediction errors below 2.5% across all metrics; and (3) a systematic evaluation of the model's sensitivity and generalizability to varying shock profiles.