基于物理信息的神经网络求解功能梯度材料热力学问题
Physics-informed neural networks for solving thermo-mechanics problems of functionally graded material
摘要：
微分方程是工程学中必不可少的，因此也是创新中必不可少的。近年来，物理信息神经网络（PINN）已经成为一种新的方法来解决微分方程。PINN方法具有无网格、可扩展的优点，并且在将从求解一个微分方程学到的知识转移到另一个微分方程方面可能是智能的。在这一领域的探索主要局限于解决线弹性问题，裂纹扩展问题。本研究使用PINNs来解决具有功能梯度性质的材料的热-力学耦合问题。通过理解训练数据集、模型架构和损失函数，对PINN框架进行了深入分析。PINN模型在求解热力学微分方程的有效性已被衡量，通过比较所获得的解决方案，无论是与解析解或有限元法为基础的解决方案。虽然在预测位移和温度场等主要变量时，R2得分超过99%，但对于应力等次要变量，实现相同的R2得分更具挑战性。这项研究是第一个实现PINN框架解决复合材料的热-力学耦合问题。这项研究有望加深对PINN新框架的理解，并将为PINN的进一步研究奠定基础。
英文摘要：
Differential equations are indispensable to engineering and hence to innovation. In recent years, physics-informed neural networks (PINN) have emerged as a novel method for solving differential equations. PINN method has the advantage of being meshless, scalable, and can potentially be intelligent in terms of transferring the knowledge learned from solving one differential equation to the other. The exploration in this field has majorly been limited to solving linear-elasticity problems, crack propagation problems. This study uses PINNs to solve coupled thermo-mechanics problems of materials with functionally graded properties. An in-depth analysis of the PINN framework has been carried out by understanding the training datasets, model architecture, and loss functions. The efficacy of the PINN models in solving thermo-mechanics differential equations has been measured by comparing the obtained solutions either with analytical solutions or finite element method-based solutions. While R2 score of more than 99% has been achieved in predicting primary variables such as displacement and temperature fields, achieving the same for secondary variables such as stress turns out to be more challenging. This study is the first to implement the PINN framework for solving coupled thermo-mechanics problems on composite materials. This study is expected to enhance the understanding of the novel PINN framework and will be seminal for further research on PINNs.
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