Transfer Operator Learning with Fusion Frame
This addresses the challenge of making operator learning models more adaptable for scientific and engineering applications, though it appears incremental as it builds on existing methods like DeepONet.
The paper tackled the problem of transfer learning for operator learning models in solving PDEs, which often struggle with generalization across tasks and datasets, by introducing a framework that integrates fusion frame theory with POD-DeepONet, demonstrating superior performance in experiments.
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.