Date of Award
Spring 2026
Document Type
Open Access Thesis
Department
Mechanical Engineering
First Advisor
Sourav Banerjee
Abstract
Wave propagation, governed by partial differential equations (PDEs), plays a critical role in structural health monitoring (SHM). However, traditional numerical solvers suffer from discretization errors, heavy meshing requirements, and prohibitive computational costs in large or high-frequency domains. Scientific Machine Learning (SciML) offers an alternative by embedding physics into neural architectures, reducing reliance on dense data and ensuring physically consistent solutions. Physics-Informed Neural Networks (PINNs) exemplify this approach but often fail to capture the discontinuities and sharp gradients of hyperbolic wave equations owing to spectral bias and optimization instability. This thesis introduces SciNoNet, a multi-head PINN that predicts the wavefield by decomposing it into three outputs: wave potential, coefficient, and exponent of the wavefield displacement. This design improves training stability and enables accurate learning of high-frequency guided wave patterns beyond the capability of classical PINNs. In this study, both soft constraints (PDE terms in the loss) and hard constraints (PDE terms embedded in neural network architecture) are explored along with different task typologies (regression or classification). SciNoNet successfully reconstructed the wavefield with high fidelity, even when trained on just 0.25% of labeled data. A custom empirical loss function further improved accuracy, outperforming existing baseline loss formulations. Overall, SciNoNet with the custom adaptive loss function demonstrates a significant advancement in guided wave modeling, combining physics-informed learning with multi-task neural networks to achieve efficient, interpretable wavefield predictions.
Rights
© 2026, Nafisa Mehtaj
Recommended Citation
Mehtaj, N.(2026). Scientific Machine Learning for Wave PDEs: An Application of Physics Informed Neural Network (PINN). (Master's thesis). Retrieved from https://scholarcommons.sc.edu/etd/8949