Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport

• URL: http://arxiv.org/abs/2204.06684v1
• Date: Thu, 14 Apr 2022 01:01:24 GMT
• Title: Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport
• Authors: Lu Lu, Raphael Pestourie, Steven G. Johnson, Giuseppe Romano
• Abstract summary: We develop a multifidelity neural operator based on a deep operator network (DeepONet) A multifidelity DeepONet significantly reduces the required amount of high-fidelity data and achieves one order of magnitude smaller error when using the same amount of high-fidelity data. We apply a multifidelity DeepONet to learn the phonon Boltzmann transport equation (BTE), a framework to compute nanoscale heat transport.
• Score: 2.512625172084287
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Deep neural operators can learn operators mapping between infinite-dimensional function spaces via deep neural networks and have become an emerging paradigm of scientific machine learning. However, training neural operators usually requires a large amount of high-fidelity data, which is often difficult to obtain in real engineering problems. Here, we address this challenge by using multifidelity learning, i.e., learning from multifidelity datasets. We develop a multifidelity neural operator based on a deep operator network (DeepONet). A multifidelity DeepONet includes two standard DeepONets coupled by residual learning and input augmentation. Multifidelity DeepONet significantly reduces the required amount of high-fidelity data and achieves one order of magnitude smaller error when using the same amount of high-fidelity data. We apply a multifidelity DeepONet to learn the phonon Boltzmann transport equation (BTE), a framework to compute nanoscale heat transport. By combining a trained multifidelity DeepONet with genetic algorithm or topology optimization, we demonstrate a fast solver for the inverse design of BTE problems.

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