A-PINN: Auxiliary Physics-informed Neural Networks for Structural Vibration Analysis in Continuous Euler-Bernoulli Beam

TL;DR

This paper introduces A-PINN, an improved physics-informed neural network framework with adaptive optimizers, for more accurate and stable structural vibration analysis of Euler-Bernoulli beams, demonstrating significant performance gains.

Contribution

The paper proposes a modified A-PINN framework with balanced adaptive optimizers specifically designed for structural vibration problems, enhancing stability and accuracy.

Findings

At least 40% improvement over baseline models.

Enhanced numerical stability and predictive accuracy.

Effective in various vibration scenarios.

Abstract

Recent advancements in physics-informed neural networks (PINNs) and their variants have garnered substantial focus from researchers due to their effectiveness in solving both forward and inverse problems governed by differential equations. In this research, a modified Auxiliary physics-informed neural network (A-PINN) framework with balanced adaptive optimizers is proposed for the analysis of structural vibration problems. In order to accurately represent structural systems, it is critical for capturing vibration phenomena and ensuring reliable predictive analysis. So, our investigations are crucial for gaining deeper insight into the robustness of scientific machine learning models for solving vibration problems. Further, to rigorously evaluate the performance of A-PINN, we conducted different numerical simulations to approximate the Euler-Bernoulli beam equations under the various scenarios. The numerical results substantiate the enhanced performance of our model in terms of both numerical stability and predictive accuracy. Our model shows improvement of at least 40% over the baselines.