Equivariant Neural Operator Learning with Graphon Convolution
Chaoran Cheng Jian Peng
We propose a general architecture that combines the coefficient learning
scheme with a residual operator layer for learning mappings between continuous
functions in the 3D Euclidean space. Our proposed model is guaranteed to
achieve SE(3)-equivariance by design. From the graph spectrum view, our method
can be interpreted as convolution on graphons (dense graphs with infinitely
many nodes), which we term InfGCN. By leveraging both the continuous graphon
structure and the discrete graph structure of the input data, our model can
effectively capture the geometric information while preserving equivariance.
Through extensive experiments on large-scale electron density datasets, we
observed that our model significantly outperformed the current state-of-the-art
architectures. Multiple ablation studies were also carried out to demonstrate
the effectiveness of the proposed architecture.