Open Access

REVIEW

Physics-Informed Neural Networks: Current Progress and Challenges in Computational Solid and Structural Mechanics

Itthidet Thawon^1,2, Duy Vo^3,4, Tinh Quoc Bui^3,4, Kanya Rattanamongkhonkun¹, Chakkapong Chamroon¹, Nakorn Tippayawong¹, Yuttana Mona¹, Ramnarong Wanison¹, Pana Suttakul^1,*

1 Department of Mechanical Engineering, Faculty of Engineering, Chiang Mai University, Chiang Mai, Thailand
2 Office of Research Administration, Chiang Mai University, Chiang Mai, Thailand
3 Duy Tan Research Institute for Computational Engineering (DTRICE), Duy Tan University, Ho Chi Minh City, Vietnam
4 Faculty of Civil Engineering, Duy Tan University, Da Nang, Vietnam

* Corresponding Author: Pana Suttakul. Email:

(This article belongs to the Special Issue: Data-Driven Artificial Intelligence and Machine Learning in Computational Modelling for Engineering and Applied Sciences)

Computer Modeling in Engineering & Sciences 2026, 146(2), 2 https://doi.org/10.32604/cmes.2026.077044

Received 01 December 2025; Accepted 30 January 2026; Issue published 26 February 2026

Abstract

Physics-informed neural networks (PINNs) have emerged as a promising class of scientific machine learning techniques that integrate governing physical laws into neural network training. Their ability to enforce differential equations, constitutive relations, and boundary conditions within the loss function provides a physically grounded alternative to traditional data-driven models, particularly for solid and structural mechanics, where data are often limited or noisy. This review offers a comprehensive assessment of recent developments in PINNs, combining bibliometric analysis, theoretical foundations, application-oriented insights, and methodological innovations. A bibliometric survey indicates a rapid increase in publications on PINNs since 2018, with prominent research clusters focused on numerical methods, structural analysis, and forecasting. Building upon this trend, the review consolidates advancements across five principal application domains, including forward structural analysis, inverse modeling and parameter identification, structural and topology optimization, assessment of structural integrity, and manufacturing processes. These applications are propelled by substantial methodological advancements, encompassing rigorous enforcement of boundary conditions, modified loss functions, adaptive training, domain decomposition strategies, multi-fidelity and transfer learning approaches, as well as hybrid finite element–PINN integration. These advances address recurring challenges in solid mechanics, such as high-order governing equations, material heterogeneity, complex geometries, localized phenomena, and limited experimental data. Despite remaining challenges in computational cost, scalability, and experimental validation, PINNs are increasingly evolving into specialized, physics-aware tools for practical solid and structural mechanics applications.

---

Keywords

---