Transfer Learning on Multi-Dimensional Data: A Novel Approach to Neural Network-Based Surrogate Modeling

• URL: http://arxiv.org/abs/2410.12241v1
• Date: Wed, 16 Oct 2024 05:07:48 GMT
• Title: Transfer Learning on Multi-Dimensional Data: A Novel Approach to Neural Network-Based Surrogate Modeling
• Authors: Adrienne M. Propp, Daniel M. Tartakovsky,
• Abstract summary: Convolutional neural networks (CNNs) have gained popularity as the basis for such surrogate models. 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. 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.
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• Abstract: The development of efficient surrogates of 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.

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