Papers › Physics Informed Token Transformer for Solving Partial Differential Equations

Physics Informed Token Transformer for Solving Partial Differential Equations

15 May 2023arXiv:2305.08757archive 2025-07-28

Cooper Lorsung, Zijie Li, Amir Barati Farimani

Solving Partial Differential Equations (PDEs) is the core of many fields of science and engineering. While classical approaches are often prohibitively slow, machine learning models often fail to incorporate complete system information. Over the past few years, transformers have had a significant impact on the field of Artificial Intelligence and have seen increased usage in PDE applications. However, despite their success, transformers currently lack integration with physics and reasoning. This study aims to address this issue by introducing PITT: Physics Informed Token Transformer. The purpose of PITT is to incorporate the knowledge of physics by embedding partial differential equations (PDEs) into the learning process. PITT uses an equation tokenization method to learn an analytically-driven numerical update operator. By tokenizing PDEs and embedding partial derivatives, the transformer models become aware of the underlying knowledge behind physical processes. To demonstrate this, PITT is tested on challenging 1D and 2D PDE neural operator prediction tasks. The results show that PITT outperforms popular neural operator models and has the ability to extract physically relevant information from governing equations.

PaperPDFCode

In Syntology Open this paper in Syntology's Atlas, the map of the papers in Syntology's graph and their citations.

Code

baratilab/physicsinformedtokentransformer officialmentioned in papermentioned on GitHubpytorch report

Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.

Code Syntology ran Syntology

Not run by Syntology. Nothing on this page verifies that the listed code works.

Results from the paper archive 2025-07-28

No leaderboard rows for this paper in the archive.

Methods

AWAREAbsolute Position EncodingsAdamAttentionBPEDense ConnectionsDropoutLabel SmoothingLayer NormalizationLinear LayerMulti-Head AttentionPosition-Wise Feed-Forward LayerResidual ConnectionSoftmaxTransformerfail

Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections