Data and code underlying the publication: Transfer learning for improved generalizability in causal physics-informed neural networks for beam simulations

### Research Objective<br>The main objective of the research is to improve the generalizability of causal physics-informed neural networks (PINNs) for simulating the dynamics of beams on elastic foundations. This is achieved by integrating transfer learning into the PINN framework to address the limitations of conventional PINNs, particularly in simulation for large space-time domains and varying initial conditions.<br>### Type of Research<br>The research is an applied study focused on the development and validation of advanced computational methods in structural engineering. It combines elements of theoretical development (modification of the PINN loss function) and empirical validation (numerical experiments on Euler-Bernoulli and Timoshenko beams).<br>### Method of Data CollectionFor validating the proposed methodology closed analytical form is utilized. This closed form solution is exciplicitly mentioned as exact solution function. These analytical solution is utilize for simulating the dynamics of beams on elastic foundations using both the traditional PINNs and the proposed transfer learning-based causal PINN framework.<br>### Type of Data<br>The type of data used in this research includes:   1. Training Data for Sequential experiments: Solutions (Data) to partial differential equations (PDEs) modeling the dynamics of Euler-Bernoulli and Timoshenko beams are simulated using physics informed neural networks.<br>### File type/extension included in the folder<br>All codes are implemented using python jupyter notebook(.ipynb), Trained model files (.pkl, .pth), Log files (.log) showing the results at every iteration, and (.sh) files to execute on the cluster, .pdf and .png are figures which are used in the main paper.<br>For Causal PINN experiments well-posed physical equations of Euler-Bernoulli and Timoshenko is utilized.<br>

### 研究目标
本研究的核心目标为提升因果物理感知神经网络（causal physics-informed neural networks, PINNs）在模拟弹性地基梁动力学行为时的泛化能力。针对传统PINNs在大时空域仿真与变初始条件场景下存在的局限，本研究通过在PINN框架中集成迁移学习（transfer learning）技术以解决上述问题。
### 研究类型
本研究属于应用研究，聚焦结构工程领域先进计算方法的开发与验证。研究融合了理论推导（修改PINN损失函数）与实证验证（针对欧拉-伯努利梁与铁木辛柯梁开展数值实验）两大核心模块。
### 数据收集方法
为验证所提方法的有效性，本研究采用闭合解析解作为基准。该闭合形式解被明确界定为精确解函数，同时将其用于传统PINNs与所提基于迁移学习的因果PINN框架的弹性地基梁动力学仿真实验。
### 数据类型
本研究使用的数据类型包括：
1. 序贯实验训练数据：通过物理感知神经网络模拟欧拉-伯努利梁与铁木辛柯梁动力学的偏微分方程（partial differential equations, PDEs）的解（数据集）。
### 文件夹包含的文件类型与扩展名
本研究的所有代码均通过Python Jupyter Notebook（.ipynb）实现，此外还包含训练好的模型文件（.pkl、.pth）、记录每轮迭代结果的日志文件（.log）、用于集群环境运行的Shell脚本（.sh），以及主论文中使用的图表文件（.pdf、.png）。因果PINN实验采用了适定的欧拉-伯努利梁与铁木辛柯梁物理方程。