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arXiv · 2306.04096

An enrichment approach for enhancing the expressivity of neural operators with applications to seismology

Ehsan Haghighat·Umair bin Waheed·George Karniadakis
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Abstract

The Eikonal equation plays a central role in seismic wave propagation and hypocenter localization, a crucial aspect of efficient earthquake early warning systems. Despite recent progress, real-time earthquake localization remains challenging due to the need to learn a generalizable Eikonal operator. We introduce a novel deep learning architecture, Enriched-DeepONet (En-DeepONet), addressing the limitations of current operator learning models in dealing with moving-solution operators. Leveraging addition and subtraction operations and a novel `root' network, En-DeepONet is particularly suitable for learning such operators and achieves up to four orders of magnitude improved accuracy without increased training cost. We demonstrate the effectiveness of En-DeepONet in earthquake localization under variable velocity and arrival time conditions. Our results indicate that En-DeepONet paves the way for real-time hypocenter localization for velocity models of practical interest. The proposed method represents a significant advancement in operator learning that is applicable to a gamut of scientific problems, including those in seismology, fracture mechanics, and phase-field problems.

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Ehsan Haghighat, Umair bin Waheed, George Karniadakis. 2023-06-07. An enrichment approach for enhancing the expressivity of neural operators with applications to seismology. https://arxiv.org/abs/2306.04096

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