Fine-Tuning DeepONets to Enhance Physics-informed Neural Networks for solving Partial Differential Equations

2024/10/18 by Sidi Wu, Wu, Sidi
Computer Science · Physics and Astronomy · #FOS: Mathematics #Model Reduction and Neural Networks #Neural Networks and Applications #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2410.14134

openalex publication_date 2024/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Physics-Informed Neural Networks (PINNs) have emerged as powerful tools for solving partial differential equations (PDEs). However, training PINNs from scratch is often computationally intensive and time-consuming. To address this problem, we propose a parameter-efficient approach that fine-tunes pre-trained DeepONet models within the PINN framework (FTO-PINN), enabling more efficient meshless PDE solving. Specifically, we freeze the weights of the pre-trained DeepONet model and fine-tune the output of the branch net by incorporating a small number of new trainable parameters, which can be quickly determined using least-squares techniques. Additionally, we introduce trunk net expansions and low-rank adaptation strategies to further enhance the performance of FTO-PINN. The effectiveness of our proposed method is demonstrated through a series of numerical experiments across various types of PDEs. FTO-PINN significantly reduces the training time of vanilla PINNs while maintaining comparable accuracy, and outperforms DeepONet, which is pre-trained on general function data, in both fidelity and generalization capabilities.

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