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Reducing Frequency Bias of Fourier Neural Operators in 3D Seismic Wavefield Simulations Through Multistage Training

Journal Article · · Seismological Research Letters
DOI:https://doi.org/10.1785/0220250085· OSTI ID:2585316
 [1];  [2];  [1];  [1];  [3];  [2];  [1];  [2]
  1. Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
  2. California Institute of Technology (CalTech), Pasadena, CA (United States)
  3. NVIDIA Corporation, Santa Clara, CA (United States)
+ Show Author Affiliations
The recent development of neural operator (NeurOp) learning for solutions to the elastic wave equation shows promising results and provides the basis for fast large-scale simulations for different seismological applications. In this article, we use the Fourier neural operator (FNO) model to directly solve the 3D Helmholtz wave equation for fast seismic ground-motion simulations on different frequencies and show the frequency bias of the FNO model, that is, it learns the lower frequencies better comparing to the higher frequencies. To reduce the frequency bias, we adopt the multistage FNO training, that is, after training a stage 1 FNO model for estimating the ground motion, we use a second FNO model as the stage 2 to learn from the residual, which greatly reduced the errors on the higher frequencies. By adopting this multistage training, the FNO models show reduced biases on higher frequencies, which enhanced the overall results of the ground-motion simulations. Thus the multistage training FNO improves the accuracy and realism of the ground-motion simulations.
Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
AC52-07NA27344
OSTI ID:
2585316
Report Number(s):
LLNL--JRNL-2002877
Journal Information:
Seismological Research Letters, Journal Name: Seismological Research Letters; ISSN 0895-0695; ISSN 1938-2057
Publisher:
Seismological Society of America (SSA)Copyright Statement
Country of Publication:
United States
Language:
English

References (19)

Three ways to solve partial differential equations with neural networks — A review journal May 2021
Overview Frequency Principle/Spectral Bias in Deep Learning journal September 2024
3D elastic wave propagation with a Factorized Fourier Neural Operator (F-FNO) journal February 2024
Physics informed machine learning: Seismic wave equation journal November 2020
Multi-fidelity Fourier neural operator for fast modeling of large-scale geological carbon storage journal February 2024
Neural operators for accelerating scientific simulations and design journal April 2024
Real-time high-resolution CO2 geological storage prediction using nested Fourier neural operators journal January 2023
Building high accuracy emulators for scientific simulations with deep neural architecture search journal December 2021
Deep neural Helmholtz operators for 3-D elastic wave propagation and inversion journal September 2024
Modular and flexible spectral-element waveform modelling in two and three dimensions journal November 2018
High-frequency wavefield extrapolation using the Fourier neural operator journal April 2022
FourCastNet: Accelerating Global High-Resolution Weather Forecasting Using Adaptive Fourier Neural Operators conference June 2023
On the Partial Difference Equations of Mathematical Physics journal March 1967
Small-data-driven fast seismic simulations for complex media using physics-informed Fourier neural operators journal November 2022
Conditioned Simulation of Ground-Motion Time Series at Uninstrumented Sites Using Gaussian Process Regression journal September 2021
Broadband Ground-Motion Synthesis via Generative Adversarial Neural Operators: Development and Validation journal March 2024
Seismic Wave Propagation and Inversion with Neural Operators journal October 2021
Adam: A Method for Stochastic Optimization preprint January 2014
Deep learning for fast simulation of seismic waves in complex media journal January 2020

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Related Subjects

earthquakes
ground motion
mathematical equation
neural networks