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.
翻译:不同方程式是工程学所不可或缺的,因此也是创新所不可或缺的。近年来,物理知情神经网络(PINN)已成为解决差异方程式的新颖方法。 PINN方法的优点是,它具有将解决一个差异方程式所学知识传授给另一个差异方程式的优势,具有将知识传授给另一个方程式的智慧。这一领域的探索主要限于解决线性弹性问题,即裂变传播问题。这项研究利用PINN解决具有功能性能的材料的热机问题。对PINN框架进行了深入分析,通过了解培训数据集、模型结构以及损失功能,对PINN框架进行了深入分析。PINN模型在解决热机械方程式差异方程式方面所学的功效通过比较获得的解决办法与分析解决方案或有限要素方法解决方案进行比较来衡量。在预测流离失所和温度领域等初级变量时,R2得99%以上得分以上,对压力等次级变量也取得了同样的成绩。这一研究通过了解培训数据集模型、模型结构和PIN框架的预期问题将进一步提升PIN框架。这一研究将进一步推进PIN。