Mehtaj Nafisa, Banerjee Sourav
Integrated Material Assessment and Predictive Simulation Laboratory (iMAPS), Department of Mechanical Engineering, Molinaroli College of Engineering and Computing, University of South Carolina, Columbia, SC 29201, USA.
Sensors (Basel). 2025 Jun 6;25(12):3588. doi: 10.3390/s25123588.
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.
科学机器学习（SciML）为波传播的传统建模方法提供了一种新兴的替代方案。这些基于物理的模型依赖于计算量较大的数值技术。然而，SciML扩展了基于人工神经网络的波动模型，使其具有学习波动物理的能力。与物理密集型方法，特别是早期提出的物理信息神经网络（PINNs）不同，本研究提出了物理引导神经网络（PgNNs）和神经算子（NOs）的数据驱动框架。与专注于具有各自边界条件的特定偏微分方程（PDEs）的PINNs和PgNNs不同，NOs可以求解一类PDEs，并且有潜力轻松求解不同的边界条件。因此，NOs提供了一种更通用的SciML方法。NOs将神经网络扩展为在函数之间进行映射，而不是在向量之间进行映射，从而增强了它们的适用性。本综述强调了NOs在波传播建模中的潜力，旨在推进基于波的结构健康监测（SHM）。通过对应用于不同工程领域的现有NO算法的比较分析，本研究展示了NOs如何提高泛化能力、加速推理并增强实际波动建模场景的可扩展性。最后，本文指出了当前的局限性，并为计算波动力学中基于NO的方法的未来研究提出了有前景的方向。
