Mesh-Informed Neural Operator : A Transformer Generative Approach

TL;DR

The paper introduces MINO, a mesh-informed neural operator that overcomes limitations of previous models by being domain- and discretization-agnostic, enabling broader applications in generative modeling for scientific and engineering problems.

Contribution

MINO combines graph neural operators and cross-attention to create a flexible, domain-agnostic backbone for functional generative models, expanding their applicability and providing standardized evaluation metrics.

Findings

MINO outperforms Fourier Neural Operator on diverse domains.

The model enables generative, inverse, and regression tasks across irregular meshes.

Standardized metrics facilitate objective comparison of models.

Abstract

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.