# Physics Transformer: Tailoring Transformer for General PDE Prediction

arXiv: https://arxiv.org/abs/2607.24513 · HTML: https://mlsanity.com/paper/2607.24513/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 29 references that are in the map.
- First posted on arXiv 27 Jul 2026.

## Builds on (most cited first, 25 of 25)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Point Transformer V3: Simpler, Faster, Stronger](https://mlsanity.com/paper/2312.10035/) (2023)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [Choose a Transformer: Fourier or Galerkin](https://mlsanity.com/paper/2105.14995/) (2021)
- [GNOT: A General Neural Operator Transformer for Operator Learning](https://mlsanity.com/paper/2302.14376/) (2023)
- [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)
- [Transformer for Partial Differential Equations' Operator Learning](https://mlsanity.com/paper/2205.13671/) (2022)
- [Factorized Fourier Neural Operators](https://mlsanity.com/paper/2111.13802/) (2021)
- [The Well: a Large-Scale Collection of Diverse Physics Simulations for Machine Learning](https://mlsanity.com/paper/2412.00568/) (2024)
- [Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries](https://mlsanity.com/paper/2502.02414/) (2025)
- [Geometry Aware Operator Transformer as an Efficient and Accurate Neural Surrogate for PDEs on Arbitrary Domains](https://mlsanity.com/paper/2505.18781/) (2025)
- [AB-UPT: Scaling Neural CFD Surrogates for High-Fidelity Automotive Aerodynamics Simulations via Anchored-Branched Universal Physics Transformers](https://mlsanity.com/paper/2502.09692/) (2025)
- [DrivAerML: High-Fidelity Computational Fluid Dynamics Dataset for Road-Car External Aerodynamics](https://mlsanity.com/paper/2408.11969/) (2024)
- [GeoTransolver: Learning Physics on Irregular Domains Using Multi-scale Geometry Aware Physics Attention Transformer](https://mlsanity.com/paper/2512.20399/) (2025)
- [Erwin: A Tree-based Hierarchical Transformer for Large-scale Physical Systems](https://mlsanity.com/paper/2502.17019/) (2025)
- [Transolver-3: Scaling Up Transformer Solvers to Industrial-Scale Geometries](https://mlsanity.com/paper/2602.04940/) (2026)
- [Transolver is a Linear Transformer: Revisiting Physics-Attention through the Lens of Linear Attention](https://mlsanity.com/paper/2511.06294/) (2025)
- [Towards scalable surrogate models based on Neural Fields for large scale aerodynamic simulations](https://mlsanity.com/paper/2505.14704/) (2025)
- [Benchmarking neural surrogates on realistic spatiotemporal multiphysics flows](https://mlsanity.com/paper/2512.18595/) (2025)

## Abstract (arXiv)

Transformer architectures have attracted increasing attention for solving partial differential equations (PDEs), owing to their flexibility in handling irregular discretizations and their ability to capture long-range physical dependencies. However, unlike discrete language tokens or fixed-resolution image patches, observed physical fields are finite samples of underlying infinite-dimensional functions. Consequently, effectively applying Transformers to PDEs requires a tokenizer that respects the functional nature of physical fields and constructs physically expressive tokens from arbitrary discretizations.To this end, we propose methodnamePhysics Transformer, a function-projection-based Transformer architecture for physical field prediction. Physics Transformer treats a physical field as a continuous function and partitions its discretization into locality-preserving spatial patches. Within each patch, it dynamically learns a set of adaptive local basis functions and projects the sampled field onto these bases to obtain compact physics tokens. The resulting tokens capture diverse latent physical states while preserving fine-scale spatial structures, enabling efficient global interaction through factorized attention across space and physical states. The projected representation further supports efficient decoding at arbitrary query locations. Extensive experiments on diverse benchmarks, ranging from two-dimensional PDE dynamics to industrial-scale three-dimensional CFD simulations, demonstrate that Physics Transformer accurately captures fine-grained physical structures and achieves state-of-the-art predictive performance. These results establish function projection as a practical and effective foundation for designing Transformer architectures for PDE solving.