In this study, the capabilities of the Physics-Informed Neural Network (PINN) method are investigated for three major tasks: modeling, simulation, and optimization in the context of the heat conduction problem. In the modeling phase, the governing equation of heat transfer by conduction is reconstructed through equation discovery using fractional-order derivatives, enabling the identification of the fractional derivative order that best describes the physical behavior. In the simulation phase, the thermal conductivity is treated as a physical parameter, and a parametric simulation is performed to analyze its influence on the temperature field. In the optimization phase, the focus is placed on the inverse problem, where the goal is to infer unknown physical properties from observed data. The effectiveness of the PINN approach is evaluated across these three fundamental engineering problem types and compared against conventional numerical methods. The results demonstrate that although PINNs may not yet outperform traditional numerical solvers in terms of speed and accuracy for forward problems, they offer a powerful and flexible framework for parametric simulation, optimization, and equation discovery, making them highly valuable for inverse and data-driven modeling applications.

翻译：本研究探讨了物理信息神经网络（PINN）方法在热传导问题建模、仿真与优化三大任务中的应用能力。在建模阶段，通过分数阶导数进行方程发现，重构了热传导控制方程，从而识别出最能描述物理行为的分数阶导数阶数。在仿真阶段，将热导率视为物理参数进行参数化仿真，分析其对温度场的影响。在优化阶段，聚焦于反问题，目标是从观测数据中推断未知物理性质。本研究评估了PINN方法在这三类基础工程问题中的有效性，并与传统数值方法进行了比较。结果表明，尽管PINN在前向问题的求解速度和精度上尚未超越传统数值求解器，但其为参数化仿真、优化及方程发现提供了强大而灵活的框架，使其在反问题和数据驱动建模应用中具有重要价值。