用改进的物理信息神经网络分析梁结构振动，精度提升超40%。
A-PINN: Auxiliary Physics-informed Neural Networks for Structural Vibration Analysis in Continuous Euler-Bernoulli Beam
- 引入辅助物理约束优化器，增强模型对梁振动方程的拟合能力。
- 在多种工况下数值模拟显示，预测精度和稳定性均优于基线模型40%以上。
- 适合从事结构动力学与科学机器学习交叉研究的读者参考。
近年来，物理信息神经网络（PINNs）及其变体因其在求解微分方程主导的正问题与逆问题中的有效性而受到广泛关注。本文提出一种改进的辅助物理信息神经网络（A-PINN）框架，采用平衡自适应优化器，用于连续欧拉-伯努利梁的结构振动分析。为准确表征结构系统，捕捉振动现象并确保可靠预测至关重要。为此，我们通过多种数值模拟评估了A-PINN在不同场景下对欧拉-伯努利梁方程的逼近性能。结果表明，该模型在数值稳定性和预测精度方面均有显著提升，相较基线模型至少提高40%。
原文摘要 · Abstract (English)
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.
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