The primary research objective of the study is to explore the application of physics-informed neural networks (PINNs) in predicting the displacement and rotations of a double beam based on Euler-Bernoulli and Timoshenko theories under various load conditions. The research aims to demonstrate the accuracy and efficiency of PINNs in handling forward and inverse problems involving partial differential equations (PDEs), even with a limited number of training points and the presence of noise in the data. This objective is to introduce physics informed machine learning techniques in structural engineering contexts specifically beam dynamics.
The research focuses on the practical implementation of theoretical concepts in machine learning and structural engineering. It leverages computational methods to solve real-world engineering problems, demonstrating the utility of PINNs in predicting structural behaviors accurately and efficiently. The study combines elements of machine learning and structural engineering by leveraging the physical knowledge of beam dynamics.
Data collection in this study involves the generation of synthetic data through forward PINNs simulations. This data includes displacement and rotation measurements of a double Timoshenko beam subjected to different loading conditions. The study also introduces Gaussian noise into the data to test the robustness of the PINN model. Additionally, the researchers compare their results with those obtained from traditional numerical methods and other machine learning approaches to validate their findings.
For the forward problem, a well-posed physical equation is needed, while for the inverse problem, data from the forward problem is utilized. For validating the forward and inverse problems, we have an analytic closed-form solution which is explicitly mentioned in the Python notebooks. All implementations of the proposed methodology are on Jupyter Python notebooks. To run the notebooks, only need to execute the cells with Shift+Enter.
" authors: - family-names: Kapoor given-names: Taniya orcid: "https://orcid.org/0000-0002-6361-446X" title: "Data and code underlying the publication: Physics-Informed Neural Networks for Solving Forward and Inverse Problems in Complex Beam Systems." keywords: version: 1 identifiers: - type: doi value: 10.4121/2bdddf05-f883-48a5-89bf-268f5595342f.v1 license: CC BY 4.0 date-released: 2024-06-05