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

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 spaceand utilizes this pre-trained basis for efficient operator learning. By introducingan 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 basisfunctions through auto-encoding, followed by leveraging this basis to predict thecoefficients of the target function. Preliminary experiments indicate that Auto-BasisEncoder’s basis functions exhibit superior suitability for operator learningand function reconstruction compared to DeepONet. These findings underscorethe potential of AutoBasisEncoder to enhance the landscape of operator learningframeworks