APPSolver: Adaptive Patch Partitioning for Point-Wise Ship Flow Prediction on Unstructured Meshes

Accurate prediction of hydrodynamic performance is central to ship design, yet high-fidelity computational fluid dynamics remains prohibitively expensive for large-scale parametric exploration. This motivates the development of data-driven surrogate models that provide rapid approximations to hydrodynamic predictions at substantially reduced cost. We present ShipNet, a geometric deep-learning surrogate that predicts both hull-surface pressure distributions and far-field free-surface wave patterns directly from hull geometry and speed. The network employs a regularized dynamic graph convolutional backbone on hull point clouds, with a multi-head decoder for simultaneous near-body pressure and free-surface elevation outputs. Training data consist of 420 inviscid free-surface simulations generated using a potential-flow panel method for two parent yacht hulls, each parameterized into 70 variants and evaluated at three speeds. ShipNet predicts per-point pressure coefficient and two-dimensional wave elevation map using a composite loss that combines point-wise regression and image-structure terms. On a geometry-held-out test set, ShipNet achieves R^2=0.98 for hull pressure and R^2=0.91 for wave fields. Inference requires approximately 0.15s per case, yielding over a 550x speedup relative to the potential-flow solver on conventional hardware. Limitations include the restricted geometry and speed ranges and the inviscid training data, while future work will extend the model to high-fidelity viscous simulations with physics-informed regularization.

Computational fluid dynamics (CFD) provides high-fidelity simulations of fluid flows but remains computationally expensive for many-query applications. In recent years deep learning (DL) has been used to construct data-driven fluid-dynamic surrogate models. In this work we consider a different learning paradigm and embrace generative modelling as a framework for constructing scalable fluid-dynamics surrogate models. We introduce FluidFlow, a generative model based on conditional flow-matching, a recent alternative to diffusion models that learns deterministic transport maps between noise and data distributions. FluidFlow is specifically designed to operate directly on CFD data defined on both structured and unstructured meshes alike, without the needs to perform any mesh interpolation pre-processing and preserving geometric fidelity. We assess the capabilities of FluidFlow using two different core neural network architectures, a U-Net and diffusion transformer (DiT), and condition their learning on physically meaningful parameters. The methodology is validated on two benchmark problems of increasing complexity: prediction of pressure coefficients along an airfoil boundary across different operating conditions, and prediction of pressure and friction coefficients over a full three-dimensional aircraft geometry discretized on a large unstructured mesh. In both cases, FluidFlow outperform strong multilayer perceptron baselines, achieving significantly lower error metrics and improved generalisation across operating conditions. Notably, the transformer-based architecture enables scalable learning on large unstructured datasets while maintaining high predictive accuracy. These results demonstrate that flow-matching generative models provide an effective and flexible framework for surrogate modelling in fluid dynamics, with potential for realistic engineering and scientific applications.

Deep learning surrogates can produce high-resolution coastal flood maps orders of magnitude faster than physics-based hydrodynamic simulators, yet transferring them to new coastal regions remains costly, since generating target-region data for fine-tuning typically requires numerous time-consuming simulations. To tackle this bottleneck, we introduce the Physics Adapter (PA), a compact, architecture-agnostic adaptation interface that enables efficient few-shot transfer of flood prediction models across diverse coastal regions. PA predicts peak water level through a differentiable wet/dry response that compares terrain elevation against a learned water level, and blends this physics-structured prediction with a data-driven branch through a learned gate. Unlike physics-informed formulations, PA imposes no PDE-residual or conservation losses and instead exploits elevation as an architectural inductive bias, adding a negligible number of trainable parameters. We integrate PA into 12 heterogeneous models, and evaluate them on two coastal regions with markedly distinct geometries, topographies, and shoreline protection configurations. The performance of PA is benchmarked against a no-physics baseline, full fine-tuning, and standard parameter-efficient fine-tuning (PEFT) methods, considering both within-region generalization to unseen sea level rise values and between-region transfer. In low-shot regime (K=3), and averaged over all backbones and transfer settings, adding PA reduces root mean square error by 11.5% when only the output head is adapted on a frozen backbone, by 15.4% when combined with PEFT methods, and by 22.9% under full fine-tuning, compared to matched configurations without PA. Taken together, the findings of this work offer practitioners a concrete recipe for extending DL-based coastal flood predictors to new, data-scarce regions.