Hybrid Least Squares/Gradient Descent Methods for DeepONets
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| author | Choi, Jun Lee, Chang-Ock Moon, Minam |
| author_facet | Choi, Jun Lee, Chang-Ock Moon, Minam |
| contents | We propose an efficient hybrid least squares/gradient descent method to accelerate DeepONet training. Since the output of DeepONet can be viewed as linear with respect to the last layer parameters of the branch network, these parameters can be optimized using a least squares (LS) solve, and the remaining hidden layer parameters are updated by means of gradient descent form. However, building the LS system for all possible combinations of branch and trunk inputs yields a prohibitively large linear problem that is infeasible to solve directly. To address this issue, our method decomposes the large LS system into two smaller, more manageable subproblems $\unicode{x2014}$ one for the branch network and one for the trunk network $\unicode{x2014}$ and solves them separately. This method is generalized to a broader type of $L^2$ loss with a regularization term for the last layer parameters, including the case of unsupervised learning with physics-informed loss. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_15394 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hybrid Least Squares/Gradient Descent Methods for DeepONets Choi, Jun Lee, Chang-Ock Moon, Minam Machine Learning Artificial Intelligence Numerical Analysis 47-08, 65F45, 65Y10, 68T07, 68T20 We propose an efficient hybrid least squares/gradient descent method to accelerate DeepONet training. Since the output of DeepONet can be viewed as linear with respect to the last layer parameters of the branch network, these parameters can be optimized using a least squares (LS) solve, and the remaining hidden layer parameters are updated by means of gradient descent form. However, building the LS system for all possible combinations of branch and trunk inputs yields a prohibitively large linear problem that is infeasible to solve directly. To address this issue, our method decomposes the large LS system into two smaller, more manageable subproblems $\unicode{x2014}$ one for the branch network and one for the trunk network $\unicode{x2014}$ and solves them separately. This method is generalized to a broader type of $L^2$ loss with a regularization term for the last layer parameters, including the case of unsupervised learning with physics-informed loss. |
| title | Hybrid Least Squares/Gradient Descent Methods for DeepONets |
| topic | Machine Learning Artificial Intelligence Numerical Analysis 47-08, 65F45, 65Y10, 68T07, 68T20 |
| url | https://arxiv.org/abs/2508.15394 |