A hybrid Decoder-DeepONet operator regression framework for unaligned observation data

TL;DR

This paper introduces a hybrid Decoder-DeepONet framework and a Multi-Decoder-DeepONet for efficient operator regression with unaligned observation data, validated through numerical experiments showing improved accuracy and handling of data alignment issues.

Contribution

The paper presents a novel hybrid Decoder-DeepONet framework and a Multi-Decoder-DeepONet that effectively handle unaligned data and improve prediction accuracy in operator regression.

Findings

Decoder-DeepONet handles unaligned data effectively.

Multi-Decoder-DeepONet improves prediction accuracy.

Frameworks are validated on Darcy and airfoil flow problems.

Abstract

Deep neural operators (DNOs) have been utilized to approximate nonlinear mappings between function spaces. However, DNOs face the challenge of increased dimensionality and computational cost associated with unaligned observation data. In this study, we propose a hybrid Decoder-DeepONet operator regression framework to handle unaligned data effectively. Additionally, we introduce a Multi-Decoder-DeepONet, which utilizes an average field of training data as input augmentation. The consistencies of the frameworks with the operator approximation theory are provided, on the basis of the universal approximation theorem. Two numerical experiments, Darcy problem and flow-field around an airfoil, are conducted to validate the efficiency and accuracy of the proposed methods. Results illustrate the advantages of Decoder-DeepONet and Multi-Decoder-DeepONet in handling unaligned observation data and showcase their potentials in improving prediction accuracy.