Transfer Learning on Multi-Dimensional Data: A Novel Approach to Neural Network-Based Surrogate Modeling
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arXiv
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| Format: | Preprint |
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2024
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| author | Propp, Adrienne M. Tartakovsky, Daniel M. |
| author_facet | Propp, Adrienne M. Tartakovsky, Daniel M. |
| contents | The development of efficient surrogates for partial differential equations (PDEs) is a critical step towards scalable modeling of complex, multiscale systems-of-systems. Convolutional neural networks (CNNs) have gained popularity as the basis for such surrogate models due to their success in capturing high-dimensional input-output mappings and the negligible cost of a forward pass. However, the high cost of generating training data -- typically via classical numerical solvers -- raises the question of whether these models are worth pursuing over more straightforward alternatives with well-established theoretical foundations, such as Monte Carlo methods. To reduce the cost of data generation, we propose training a CNN surrogate model on a mixture of numerical solutions to both the $d$-dimensional problem and its ($d-1$)-dimensional approximation, taking advantage of the efficiency savings guaranteed by the curse of dimensionality. We demonstrate our approach on a multiphase flow test problem, using transfer learning to train a dense fully-convolutional encoder-decoder CNN on the two classes of data. Numerical results from a sample uncertainty quantification task demonstrate that our surrogate model outperforms Monte Carlo with several times the data generation budget. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_12241 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Transfer Learning on Multi-Dimensional Data: A Novel Approach to Neural Network-Based Surrogate Modeling Propp, Adrienne M. Tartakovsky, Daniel M. Machine Learning Numerical Analysis Mathematical Physics The development of efficient surrogates for partial differential equations (PDEs) is a critical step towards scalable modeling of complex, multiscale systems-of-systems. Convolutional neural networks (CNNs) have gained popularity as the basis for such surrogate models due to their success in capturing high-dimensional input-output mappings and the negligible cost of a forward pass. However, the high cost of generating training data -- typically via classical numerical solvers -- raises the question of whether these models are worth pursuing over more straightforward alternatives with well-established theoretical foundations, such as Monte Carlo methods. To reduce the cost of data generation, we propose training a CNN surrogate model on a mixture of numerical solutions to both the $d$-dimensional problem and its ($d-1$)-dimensional approximation, taking advantage of the efficiency savings guaranteed by the curse of dimensionality. We demonstrate our approach on a multiphase flow test problem, using transfer learning to train a dense fully-convolutional encoder-decoder CNN on the two classes of data. Numerical results from a sample uncertainty quantification task demonstrate that our surrogate model outperforms Monte Carlo with several times the data generation budget. |
| title | Transfer Learning on Multi-Dimensional Data: A Novel Approach to Neural Network-Based Surrogate Modeling |
| topic | Machine Learning Numerical Analysis Mathematical Physics |
| url | https://arxiv.org/abs/2410.12241 |