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.

该论文介绍了一种用于模拟弹性基础上横梁动力学的新方法。通过在因果关系尊重的物理信息神经网络（PINN）框架内采用迁移学习方法来模拟Winkler基础上的Euler-Bernoulli和Timoshenko梁模型，有效地捕捉了潜在的物理特征，以加快收敛并确保在不同情境下获得准确结果。该方法在Euler-Bernoulli梁的数值实验中表现出了显著的效果，并展示了在较大时空范围内应用于Timoshenko梁的潜力，在标准$L^2$-norm度量和加速收敛方面优于最先进的物理信息方法。

用于光束模拟的因果物理信息神经网络的迁移学习，以提高推广能力