物理变压器：为一般偏微分方程预测定制变压器
Physics Transformer: Tailoring Transformer for General PDE Prediction
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中文总结 AI 辅助
研究如何将Transformer应用于偏微分方程预测，提出基于函数投影的物理变压器架构，它能将物理场离散化并投影得到紧凑物理令牌，在多样基准实验中准确捕捉物理结构，取得先进预测性能，为PDE求解的Transformer架构设计奠定基础。
中文摘要 AI 辅助
变压器架构因其在处理不规则离散化方面的灵活性和捕捉长程物理依赖性的能力，在求解偏微分方程（PDE）方面受到越来越多关注。但物理场是无限维函数的有限样本，与离散语言令牌或固定分辨率图像块不同。为此，我们提出物理变压器，一种基于函数投影的用于物理场预测的变压器架构。它将物理场视为连续函数，划分为保留局部性的空间块，在每个块内动态学习自适应局部基函数并投影采样场以获得紧凑物理令牌。实验表明其能准确捕捉细粒度物理结构并实现先进预测性能，为设计用于PDE求解的变压器架构奠定了基础。
英文摘要
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 \methodname{Physics 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.
发表机构
- Gaoling School of Artificial Intelligence, Renmin University of China（中国人民大学高瓴人工智能学院）
- School of Mechanics and Engineering Science, Peking University（北京大学力学与工程科学学院）
机构由 AI 辅助整理，请以论文原文为准。
