基于物理信息神经网络的功能梯度材料稳态/瞬态热传导分析

采用物理信息神经网络PINN(Physics-informed Neural Networks)求解稳态和瞬态功能梯度材料(FGMs)热传导问题。该方法利用控制方程、边界及初始条件的残差构造损失函数,在无任何响应数据的情况下得到了更具泛化能力的神经网络模型,同时避免了传统数值方法在求解计算力学问题时所需的微分、积分公式推导以及繁重的建模和划分网格等前处理工作。本文探究了PINN及其域分解的扩展物理信息神经网络XPINN(eXtended Physics-informed Neural Networks)在求解稳态和瞬态FGMs热传导问题时的适用性,讨论了网络结构对预测结果的影响。研究结果表明,PINN/XPINN在解决几何复杂的稳态和瞬态FGMs热传导问题时仍具有较高的可靠性和简洁的求解流程,同时,为极端环境下求解复杂多场耦合和夹杂等问题提供了新思路。

Physics-informed neural networks for solving steady/transient heat conduction problems of functionally graded materials

In this paper,the physical-informed Neural Networks (PINN) was used to solve steady and transient heat conduction problems in Functionally Graded Materials (FGMs).The loss function in PINN is established by using the residuals of the governing equations,initial and boundary conditions,so that the neural network model with more generalization ability can be obtained even without any response data.In addition,the necessary work in traditional numerical methods such as differential and integral formula derivation,heavy modeling and meshing can be avoided when computational mechanics problems are solved.The applicability of PINN and extended physical-informed Neural Networks (XPINN) are investigated for solving steady and transient heat conduction in FGMs.Moreover,the complexity of network structures is discussed.The numerical results show that PINN and XPINN have high reliability and simple solution process for steady and transient heat conduction in FGMs when the geometry of the model is complex.In addition,this work provides a new way for solving complex multi-physical fields coupling and inclusion problems in extreme environments.