Scientific Machine Learning for Elastic and Acoustic Wave Propagation: Neural Operator and Physics-Guided Neural Network

Abstract

Scientific machine learning (SciML) offers an emerging alternative to the traditional modeling approaches for wave propagation. These physics-based models rely on computationally demanding numerical techniques. However, SciML extends artificial neural network-based wave models with the capability of learning wave physics. Contrary to the physics-intensive methods, particularly physics-informed neural networks (PINNs) presented earlier, this study presents data-driven frameworks of physics-guided neural networks (PgNNs) and neural operators (NOs). Unlike PINNs and PgNNs, which focus on specific PDEs with respective boundary conditions, NOs solve a family of PDEs and hold the potential to easily solve different boundary conditions. Hence, NOs provide a more generalized SciML approach. NOs extend neural networks to map between functions rather than vectors, enhancing their applicability. This review highlights the potential of NOs in wave propagation modeling, aiming to advance wave-based structural health monitoring (SHM). Through comparative analysis of existing NO algorithms applied across different engineering fields, this study demonstrates how NOs improve generalization, accelerate inference, and enhance scalability for practical wave modeling scenarios. Lastly, this article identifies current limitations and suggests promising directions for future research on NO-based methods within computational wave mechanics.

Keywords

• scientific machine learning
• wave propagation
• physics-guided neural network
• neural operator
• deep operator network
• Fourier neural operator