Transfer Operator Learning with Fusion Frame

TL;DR

This paper introduces a novel framework combining fusion frame theory with POD-DeepONet to improve transfer learning in operator models for PDEs, enabling better generalization across diverse scientific and engineering problems.

Contribution

The work presents an innovative architecture that integrates fusion frames with POD-DeepONet, significantly enhancing transfer learning capabilities for PDE operator models.

Findings

Demonstrates superior performance across various PDEs

Addresses transfer learning challenges in operator models

Paves the way for adaptable solutions in scientific applications

Abstract

The challenge of applying learned knowledge from one domain to solve problems in another related but distinct domain, known as transfer learning, is fundamental in operator learning models that solve Partial Differential Equations (PDEs). These current models often struggle with generalization across different tasks and datasets, limiting their applicability in diverse scientific and engineering disciplines. This work presents a novel framework that enhances the transfer learning capabilities of operator learning models for solving Partial Differential Equations (PDEs) through the integration of fusion frame theory with the Proper Orthogonal Decomposition (POD)-enhanced Deep Operator Network (DeepONet). We introduce an innovative architecture that combines fusion frames with POD-DeepONet, demonstrating superior performance across various PDEs in our experimental analysis. Our framework addresses the critical challenge of transfer learning in operator learning models, paving the way for adaptable and efficient solutions across a wide range of scientific and engineering applications.