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 Feb 25;25(5):1401. doi: 10.3390/s25051401.
The governing Partial Differential Equation (PDE) for wave propagation or the wave equation involves multi-scale and multi-dimensional oscillatory phenomena. Wave PDE challenges traditional computational methods due to high computational costs with rigid assumptions. The advent of scientific machine learning (SciML) presents a novel paradigm by embedding physical laws within neural network architectures, enabling efficient and accurate solutions. This study explores the evolution of SciML approaches, focusing on PINNs, and evaluates their application in modeling acoustic, elastic, and guided wave propagation. PINN is a gray-box predictive model that offers the strong predictive capabilities of data-driven models but also adheres to the physical laws. Through theoretical analysis and problem-driven examples, the findings demonstrate that PINNs address key limitations of traditional methods, including discretization errors and computational inefficiencies, while offering robust predictive capabilities. Despite current challenges, such as optimization difficulties and scalability constraints, PINNs hold transformative potential for advancing wave propagation modeling. This comprehensive study underscores the transformative potential of PINN, followed by recommendations on why and how it could advance elastic, acoustic, and guided wave propagation modeling and sets the stage for future research in the field of Structural Health Monitoring (SHM)/Nondestructive Evaluation (NDE).
用于波传播的支配偏微分方程（PDE）或波动方程涉及多尺度和多维度的振荡现象。波动PDE由于严格假设带来的高计算成本而对传统计算方法提出了挑战。科学机器学习（SciML）的出现通过将物理定律嵌入神经网络架构提出了一种新范式，能够实现高效且准确的解决方案。本研究探索了SciML方法的发展，重点关注物理信息神经网络（PINNs），并评估了它们在声学、弹性和导波传播建模中的应用。PINN是一种灰箱预测模型，它既具有数据驱动模型强大的预测能力，又遵循物理定律。通过理论分析和问题驱动的示例，研究结果表明，PINN解决了传统方法的关键局限性，包括离散化误差和计算效率低下问题，同时具有强大的预测能力。尽管目前存在诸如优化困难和可扩展性限制等挑战，但PINN在推进波传播建模方面具有变革潜力。这项全面的研究强调了PINN的变革潜力，随后给出了关于它为何以及如何能够推进弹性、声学和导波传播建模的建议，并为结构健康监测（SHM）/无损检测（NDE）领域的未来研究奠定了基础。
