# Full-field prediction for engineering-scale three-dimensional aircraft with multigrid-hierarchical learning

arXiv: https://arxiv.org/abs/2605.30375 · HTML: https://mlsanity.com/paper/2605.30375/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 45 references that are in the map.
- First posted on arXiv 26 May 2026.

## Builds on (most cited first, 3 of 3)

- [Rethinking Network Design and Local Geometry in Point Cloud: A Simple Residual MLP Framework](https://mlsanity.com/paper/2202.07123/) (2022)
- [Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks](https://mlsanity.com/paper/1901.06523/) (2019)
- [DeepCFD: Efficient Steady-State Laminar Flow Approximation with Deep Convolutional Neural Networks](https://mlsanity.com/paper/2004.08826/) (2020)

## Abstract (arXiv)

High-fidelity computational fluid dynamics is essential for aerospace design, but engineering-scale simulations of practical three-dimensional aircraft remain computationally expensive. Learning-based flow-field initialization can improve efficiency by reducing the numerical distance between the initial and converged solutions, yet existing deep learning approaches remain difficult to scale to large three-dimensional aircraft flows with multiscale regional heterogeneity. Most prior studies therefore focus on two-dimensional problems, surface quantities, integral aerodynamic coefficients, or simplified three-dimensional cases with limited grid resolution.Here we propose MHLF, a multigrid-hierarchical learning framework for accelerating engineering-scale aircraft flow simulations while preserving high-fidelity numerical accuracy. MHLF combines a topologically consistent geometric multigrid representation with a hierarchical strategy that captures regional flow heterogeneity during both prediction and subsequent CFD correction. Across three engineering-scale aircraft cases spanning Mach 0.15 to 6.0 and covering subsonic, transonic and supersonic regimes, MHLF accelerates convergence without sacrificing flow-field accuracy, achieving a 3 to 8 times efficiency improvement over conventional initialization. These results demonstrate practical full-flow-field prediction for large three-dimensional aircraft within the CFD domain and provide a foundation for data-driven acceleration of high-fidelity aircraft flow simulation.