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Efficient Solutions to the Acoustic Wave Equation Using Extreme Learning Machines With Domain Decomposition

Description: 

In this study, we propose a novel approach for solving the acoustic wave equation to model seismic wavefield by leveraging Extreme Learning Machines (ELM) in combination with domain decomposition techniques. Traditional numerical methods, such as finite difference and finite element methods, face computational limitations when handling large-scale data and complex boundary conditions. Physics-Informed Neural Networks (PINNs) have shown promise in addressing these limitations, yet they often struggle with computational cost and scalability. This research seeks to address these challenges by integrating ELM, a neural network model with fixed hidden layer weights and optimized output weights, with local neural networks across subdomains (locELM). This combination allows for efficient and parallelizable solutions, significantly enhancing computational speed and accuracy in seismic wave modeling.
Initial results indicate that our method not only rivals PINNs in accuracy but also reduces computational overhead, making it suitable for large-scale seismic problems. Additionally, the locELM framework incorporates physical continuity constraints across subdomain boundaries, achieving high accuracy in both forward and inverse seismic problems. This approach advances computational geophysics by enabling scalable and rapid seismic simulations, fostering better subsurface imaging and resource exploration. This work contributes to the scientific machine learning community by extending ELM applications to the seismic acoustic equation, an area largely unexplored, thereby highlighting the potential of ELMs in PDE modeling across geophysical and engineering fields.

Keywords: Extreme Learning Machine, Acoustic Wave Equation, Domain Decomposition, Seismic Modeling, Physics-Informed Neural Networks, Computational Geophysics

Session: Scientific Machine Learning for Forward and Inverse Wave Equation Problems - I

Type: Oral

Date: 4/15/2025

Presentation Time: 05:00 PM (local time)

Presenting Author: Emuobosa

Student Presenter: Yes

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