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

arXiv: https://arxiv.org/abs/2608.29355 · HTML: https://mlsanity.com/paper/2608.29355/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 32 references that are in the map.
- First posted on arXiv 29 Aug 2026.

## Builds on (most cited first, 17 of 17)

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- [Predicting Physics in Mesh-reduced Space with Temporal Attention](https://mlsanity.com/paper/2201.09113/) (2022)
- [CFDBench: A Large-Scale Benchmark for Machine Learning Methods in Fluid Dynamics](https://mlsanity.com/paper/2310.05963/) (2023)
- [Recent Advances on Machine Learning for Computational Fluid Dynamics: A Survey](https://mlsanity.com/paper/2408.12171/) (2024)
- [DeepCFD: Efficient Steady-State Laminar Flow Approximation with Deep Convolutional Neural Networks](https://mlsanity.com/paper/2004.08826/) (2020)
- [Fusion-DeepONet: A Data-Efficient Neural Operator for Geometry-Dependent Hypersonic and Supersonic Flows](https://mlsanity.com/paper/2501.01934/) (2025)
- [Comparison of CNN-based deep learning architectures for unsteady CFD acceleration on small datasets](https://mlsanity.com/paper/2502.06837/) (2025)
- [Ship Performance Monitoring using Machine-learning](https://mlsanity.com/paper/2110.03594/) (2021)

## Abstract (arXiv)

Large non-uniform point sets make direct attention-based surrogate modeling costly for ship hydrodynamics. We introduce APPSolver, a point-wise flow-prediction framework built around Adaptive Patch Partitioning (APP), a deterministic quadtree representation for fixed two-dimensional horizontal slices extracted from ship CFD simulations. APP assigns finer patches near the hull and coarser patches farther away, downsamples patch contents, and recovers predictions to the full reference point set. Under a corrected protocol that constructs natural (t,t+1) pairs before splitting, reuses training-set normalization statistics, and reports three model seeds, learned tokenizers are more accurate than APP-Transformer, and a persistence baseline has lower one-step MAE on all three ShipBench hulls. The supported benefit of APP is therefore computational rather than universal predictive superiority: on a representative DTC input, APP-Transformer requires 1.815 GFLOPs and 1.309 ms per model forward, while a matched ablation shows that adaptive partitioning reduces MAE by 16.4-24.9% relative to a uniform partition augmented with learned slicing. Condition encoders provide setting-dependent gains in leave-one-hull-out evaluation, but the current absolute next-state objective does not establish accurate long-horizon dynamics. These results characterize APP as a compact spatial representation with an explicit accuracy--efficiency trade-off. Code is available at https://github.com/wenhuahuo/APPSolver .