D-PINNs: A diffusion physics-informed neural networks framework for DSMV near-bottom plume velocity prediction

Near-bottom tailings discharge from deep-sea mining vehicles (DSMVs) generates a complex coupled wake–plume flow that governs environmental impact assessment and discharge-strategy optimization. High-fidelity CFD can resolve this composite disturbance, but its computational cost hinders rapid multi-scenario evaluation. This study proposes a Diffusion physics-informed neural network (D-PINN) for efficient reconstruction of near-bottom velocity fields under DSMV discharge conditions. The governing momentum equations are augmented with structured source terms representing jet-induced momentum injection, wake-induced momentum deficit, and their coupling, which are embedded directly into the partial differential equation (PDE) residual. This residual formulation enables the network to distinguish localized forcing from wake-driven redistribution. A diffusion training strategy is introduced to reconstruct the velocity field from sparsely sampled or low-resolution grids. Local subdomains are trained sequentially to recover velocity gradients without mesh refinement. The reconstructed fields are then used to train a parametric PINN model that generalizes across unseen held-out operating conditions within the studied parameter range. Numerical results show accurate flow-field reconstruction, stable convergence, and good generalization across the tested operating conditions. The proposed framework significantly reduces the reliance on repeated CFD simulations and provides an efficient approach for physics-consistent near-wake flow prediction. The proposed framework provides a practical tool for fast plume prediction, discharge optimization, and preliminary environmental risk screening in ocean engineering.