AutoBasisEncoder: Pre-trained Neural Field Basis via Autoencoding for Operator Learning

Thomas X Wang, Nicolas Baskiotis, patrick gallinari

Keywords: operator learning, auto-encoding, neural fields, pre-training, basis

TL;DR: We introduce AutoBasisEncoder, a novel framework designed for operator learning This approach autonomously discovers a basis of functions optimized for the target function space and utilizes this pre-trained basis for efficient operator learning.

Abstract:

We introduce AutoBasisEncoder, a novel framework designed for operator learn-
ing – the task of learning to map from one function to another. This approach au-
tonomously discovers a basis of functions optimized for the target function space
and utilizes this pre-trained basis for efficient operator learning. By introducing
an intermediary auto-encoding task to the popular DeepONet framework, AutoBa-
sisEncoder disentangles the learning of the basis functions and of the coefficients,
simplifying the operator learning process. Initially, the framework learns basis
functions through auto-encoding, followed by leveraging this basis to predict the
coefficients of the target function. Preliminary experiments indicate that Auto-
BasisEncoder’s basis functions exhibit superior suitability for operator learning
and function reconstruction compared to DeepONet. These findings underscore
the potential of AutoBasisEncoder to enhance the landscape of operator learning
frameworks

Submission Number: 102