Physics-Informed Neural Networks for Structural Mechanics and Construction: Modeling the Deflection of a Single-Span Beam Physics-Informed Neural Networks

Abstract

This article presents the development and analysis of a Physics-Informed Neural Network (PINN) model for calculating the deflection of a simply supported beam under uniformly distributed load. The training dataset was synthesized based on analytical principles of structural mechanics and included the following parameters: relative length of the measurement section l, number of measurement points N, and noise level R. The training dataset consisted of 1,296 rows describing random points within the beam span. In this study, 480 PINN models were trained to evaluate the impact of the weight of the physics-informed loss function, the number of measurements, and the noise level on prediction accuracy. The results demonstrated that PINN models achieve high accuracy (R² ≥ 0.88) even with high noise levels (R > 20 %) and exhibit robustness to low and moderate noise levels. The study identified that adjusting the weight of the physics-informed loss function is a key parameter for achieving an optimal balance between the loss functions of physical laws and experimental data. Increasing the number of measurement points positively influences accuracy at low noise levels. However, an increase in the number of measurement points under high noise levels reduces the prediction accuracy of the model. The scientific novelty of the study lies in proposing an approach for structural analysis using PINN, which integrates physical laws into the training process. The findings confirm the potential of using PINN for engineering calculations, particularly under limited data conditions.