Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2410.14134 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917808264183808 |
|---|---|
| author | Wu, Sidi |
| author_facet | Wu, Sidi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_14134 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fine-Tuning DeepONets to Enhance Physics-informed Neural Networks for solving Partial Differential Equations Wu, Sidi Numerical Analysis 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. |
| title | Fine-Tuning DeepONets to Enhance Physics-informed Neural Networks for solving Partial Differential Equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2410.14134 |