# GLOBE: Accurate and Generalizable PDE Surrogates using Domain-Inspired Architectures and Equivariances

arXiv: https://arxiv.org/abs/2511.15856 · HTML: https://mlsanity.com/paper/2511.15856/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 40 references that are in the map.
- First posted on arXiv 19 Nov 2025.

## Builds on (most cited first, 16 of 16)

- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [On the Variance of the Adaptive Learning Rate and Beyond](https://mlsanity.com/paper/1908.03265/) (2019)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Transolver: A Fast Transformer Solver for PDEs on General Geometries](https://mlsanity.com/paper/2402.02366/) (2024)
- [Geometry-Informed Neural Operator for Large-Scale 3D PDEs](https://mlsanity.com/paper/2309.00583/) (2023)
- [e3nn: Euclidean Neural Networks](https://mlsanity.com/paper/2207.09453/) (2022)
- [Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations](https://mlsanity.com/paper/2407.07218/) (2024)
- [Operator Learning with Neural Fields: Tackling PDEs on General Geometries](https://mlsanity.com/paper/2306.07266/) (2023)
- [AirfRANS: High Fidelity Computational Fluid Dynamics Dataset for Approximating Reynolds-Averaged Navier-Stokes Solutions](https://mlsanity.com/paper/2212.07564/) (2022)
- [DrivAerML: High-Fidelity Computational Fluid Dynamics Dataset for Road-Car External Aerodynamics](https://mlsanity.com/paper/2408.11969/) (2024)
- [NeuralFoil: An Airfoil Aerodynamics Analysis Tool Using Physics-Informed Machine Learning](https://mlsanity.com/paper/2503.16323/) (2025)
- [Towards scalable surrogate models based on Neural Fields for large scale aerodynamic simulations](https://mlsanity.com/paper/2505.14704/) (2025)
- [Geometry aware inference of steady state PDEs using Equivariant Neural Fields representations](https://mlsanity.com/paper/2504.18591/) (2025)
- [Accelerating Transient CFD through Machine Learning-Based Flow Initialization](https://mlsanity.com/paper/2503.15766/) (2025)

## Abstract (arXiv)

We introduce GLOBE, a new neural surrogate for homogeneous PDEs that draws inductive bias from boundary-element methods and equivariant ML. GLOBE represents solutions as superpositions of learnable Green's-function-like kernels evaluated from boundary faces to targets, composed across multiscale branches and communication hyperlayers. The architecture is translation-, rotation-, and parity-equivariant; discretization-invariant in the fine-mesh limit; and units-invariant via rigorous nondimensionalization. An explicit far-field decay envelope stabilizes extrapolation, boundary-to-boundary hyperlayer communication mediates long-range coupling, and the all-to-all boundary-to-target evaluation yields a global receptive field that respects PDE information flow, even for elliptic PDEs. On AirFRANS (steady incompressible RANS over NACA airfoils), GLOBE achieves substantial accuracy improvements. On the "Full" split, it reduces mean-squared error by roughly 200x on all fields relative to the dataset's reference baselines, and roughly 50x relative to the next-best-performing model. In the "Scarce" split, it achieves over 100x lower error on velocity and pressure fields and over 600x lower error on surface pressure than Transolver. Qualitative results show sharp near-wall gradients, coherent wakes, and limited errors under modest extrapolation in Reynolds number and angle of attack. In addition to this accuracy, the model is quite compact (117k parameters), and fields can be evaluated at arbitrary points during inference. We also demonstrate the ability to train and predict with non-watertight meshes, which has strong practical implications. These results show that rigorous physics- and domain-inspired inductive biases can achieve large gains in accuracy, generalizability, and practicality for ML-based PDE surrogates for industrial computer-aided engineering (CAE).