提出可处理任意网格的生成型算子模型，突破传统方法对规则网格的依赖。
Mesh-Informed Neural Operator : A Transformer Generative Approach
- 基于图神经网络与交叉注意力机制，构建域无关、离散化无关的生成框架
- 在非规则网格上实现稳定生成，适用于复杂几何场景的函数空间建模
- 提供统一接口，适配各类深度学习架构，适合科学计算与逆问题研究者
函数空间中的生成模型作为生成建模与算子学习的交叉领域，因在众多科学与工程应用中的巨大潜力而受到越来越多关注。尽管函数生成模型理论上具有域无关和离散化无关的特性，但现有实现严重依赖傅里叶神经算子（FNO），限制了其在规则网格和矩形域之外的应用。为克服这一关键局限，本文提出网格感知神经算子（MINO）。通过引入图神经算子与交叉注意力机制，MINO提供了一个原则性、域无关且离散化无关的函数空间生成建模范式。该方法显著拓展了此类模型在生成、反演及回归任务中的适用范围。此外，MINO为神经算子与通用先进深度学习架构的融合提供了统一视角。最后，本文设计了一套标准化评估指标，实现了对函数生成模型的客观比较，弥补了该领域的另一关键空白。
原文摘要 · Abstract (English)
Generative models in function spaces, situated at the intersection of generative modeling and operator learning, are attracting increasing attention due to their immense potential in diverse scientific and engineering applications. While functional generative models are theoretically domain- and discretization-agnostic, current implementations heavily rely on the Fourier Neural Operator (FNO), limiting their applicability to regular grids and rectangular domains. To overcome these critical limitations, we introduce the Mesh-Informed Neural Operator (MINO). By leveraging graph neural operators and cross-attention mechanisms, MINO offers a principled, domain- and discretization-agnostic backbone for generative modeling in function spaces. This advancement significantly expands the scope of such models to more diverse applications in generative, inverse, and regression tasks. Furthermore, MINO provides a unified perspective on integrating neural operators with general advanced deep learning architectures. Finally, we introduce a suite of standardized evaluation metrics that enable objective comparison of functional generative models, addressing another critical gap in the field.
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