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EikoNet: Solving the Eikonal equation with Deep Neural Networks

Smith, Jonathan D. and Azizzadenesheli, Kamyar and Ross, Zachary E. (2020) EikoNet: Solving the Eikonal equation with Deep Neural Networks. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20200526-084219717

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Abstract

The recent deep learning revolution has created an enormous opportunity for accelerating compute capabilities in the context of physics-based simulations. Here, we propose EikoNet, a deep learning approach to solving the Eikonal equation, which characterizes the first-arrival-time field in heterogeneous 3D velocity structures. Our grid-free approach allows for rapid determination of the travel time between any two points within a continuous 3D domain. These travel time solutions are allowed to violate the differential equation - which casts the problem as one of optimization - with the goal of finding network parameters that minimize the degree to which the equation is violated. In doing so, the method exploits the differentiability of neural networks to calculate the spatial gradients analytically, meaning the network can be trained on its own without ever needing solutions from a finite difference algorithm. EikoNet is rigorously tested on several velocity models and sampling methods to demonstrate robustness and versatility. Training and inference are highly parallelized, making the approach well-suited for GPUs. EikoNet has low memory overhead, and further avoids the need for travel-time lookup tables. The developed approach has important applications to earthquake hypocenter inversion, ray multi-pathing, and tomographic modeling, as well as to other fields beyond seismology where ray tracing is essential.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2004.00361arXivDiscussion Paper
https://github.com/Ulvetanna/EikoNetRelated ItemCode
ORCID:
AuthorORCID
Smith, Jonathan D.0000-0002-1684-1344
Azizzadenesheli, Kamyar0000-0001-8507-1868
Ross, Zachary E.0000-0002-6343-8400
Additional Information:This project was partly supported by a grant from the USGS. K. Azizzadenesheli gratefully acknowledge the financial support of Raytheon and Amazon Web Services. An outline for the code used throughout this article can be found at https://github.com/Ulvetanna/EikoNet.
Group:Seismological Laboratory
Funders:
Funding AgencyGrant Number
USGSUNSPECIFIED
Raytheon CompanyUNSPECIFIED
Amazon Web ServicesUNSPECIFIED
Record Number:CaltechAUTHORS:20200526-084219717
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200526-084219717
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:103439
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:26 May 2020 16:01
Last Modified:26 May 2020 16:01

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