基于物理信息的神经网络在复合材料模具热化学固化过程建模中的应用
Physics-Informed Neural Network for Modelling the Thermochemical Curing Process of Composite-Tool Systems During Manufacture
摘要：
提出了一种物理信息神经网络（PINN）来模拟复合材料在高压釜中固化过程中的热化学演化。特别是，我们解决了管理耦合系统的微分方程-包括传导热传递和树脂固化动力学-通过优化参数的深度神经网络（DNN）使用基于物理的损失函数。为了解释热传导和树脂固化的巨大不同行为，我们设计了一个由两个断开的子网络组成的PINN，并开发了一种顺序训练算法，该算法减轻了传统训练方法中存在的不稳定性。此外，我们将明确的不连续性到DNN的复合材料工具接口和强制执行已知的物理行为直接在损失函数，以改善界面附近的解决方案。我们训练的PINN的技术，自动适应相应的PDE，边界，接口和初始条件的损失条款的权重。最后，我们证明了可以将问题参数作为模型的输入-从而产生一个代理，为一系列问题设置提供实时模拟-并且可以使用迁移学习来显着减少与初始训练模型类似的问题设置的训练时间。在不同材料厚度和热边界条件的多个场景下，所提出的PINN的性能得到了证明。
英文摘要：
We present a Physics-Informed Neural Network (PINN) to simulate the thermochemical evolution of a composite material on a tool undergoing cure in an autoclave. In particular, we solve the governing coupled system of differential equations -- including conductive heat transfer and resin cure kinetics -- by optimizing the parameters of a deep neural network (DNN) using a physics-based loss function. To account for the vastly different behaviour of thermal conduction and resin cure, we design a PINN consisting of two disconnected subnetworks, and develop a sequential training algorithm that mitigates instability present in traditional training methods. Further, we incorporate explicit discontinuities into the DNN at the composite-tool interface and enforce known physical behaviour directly in the loss function to improve the solution near the interface. We train the PINN with a technique that automatically adapts the weights on the loss terms corresponding to PDE, boundary, interface, and initial conditions. Finally, we demonstrate that one can include problem parameters as an input to the model -- resulting in a surrogate that provides real-time simulation for a range of problem settings -- and that one can use transfer learning to significantly reduce the training time for problem settings similar to that of an initial trained model. The performance of the proposed PINN is demonstrated in multiple scenarios with different material thicknesses and thermal boundary conditions.
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