This paper introduces a novel methodology for simulating the dynamics of beams on elastic foundations. Specifically, Euler-Bernoulli and Timoshenko beam models on the Winkler foundation are simulated using a transfer learning approach within a causality-respecting physics-informed neural network (PINN) framework. Conventional PINNs encounter challenges in handling large space-time domains, even for problems with closed-form analytical solutions. A causality-respecting PINN loss function is employed to overcome this limitation, effectively capturing the underlying physics. However, it is observed that the causality-respecting PINN lacks generalizability. We propose using solutions to similar problems instead of training from scratch by employing transfer learning while adhering to causality to accelerate convergence and ensure accurate results across diverse scenarios. Numerical experiments on the Euler-Bernoulli beam highlight the efficacy of the proposed approach for various initial conditions, including those with noise in the initial data. Furthermore, the potential of the proposed method is demonstrated for the Timoshenko beam in an extended spatial and temporal domain. Several comparisons suggest that the proposed method accurately captures the inherent dynamics, outperforming the state-of-the-art physics-informed methods under standard $L^2$-norm metric and accelerating convergence.

翻译：本文提出了一种模拟弹性地基上梁动力学特性的新方法。具体而言，在遵循因果关系的物理信息神经网络（PINN）框架内，采用迁移学习方法对Winkler地基上的Euler-Bernoulli梁和Timoshenko梁模型进行仿真。传统PINN在处理大时空域问题时（即使存在闭式解析解）仍面临挑战。为克服这一局限性，本文采用遵循因果关系的PINN损失函数，有效捕获底层物理规律。然而研究发现，遵循因果关系的PINN缺乏泛化能力。我们建议利用相似问题的先验解替代从头训练，通过遵循因果关系的迁移学习策略，在保证加速收敛的同时实现多场景下的精确结果。针对Euler-Bernoulli梁的数值实验验证了该方法在不同初始条件（含噪声初始数据）下的有效性。此外，在扩展时空域中针对Timoshenko梁的仿真展示了所提方法的潜力。多项对比结果表明，该方法的动力学特性捕获精度优于现有基于物理的先进方法（以标准$L^2$范数为度量指标），且显著加速了收敛过程。