{
  "id": "2410.14134",
  "version": "v1",
  "published": "2024-10-18T03:02:19.000Z",
  "updated": "2024-10-18T03:02:19.000Z",
  "title": "Fine-Tuning DeepONets to Enhance Physics-informed Neural Networks for solving Partial Differential Equations",
  "authors": [
    "Sidi Wu"
  ],
  "comment": "24 pages, 8 figures,6 tables",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-18T03:02:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "solving partial differential equations",
      "enhance physics-informed neural networks",
      "fine-tuning deeponets",
      "pre-trained deeponet model",
      "low-rank adaptation strategies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}