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A physics-informed machine learning approach for solving heat transfer equation in advanced manufacturing and engineering applications

机译：一种物理知识机器学习方法，用于求解高级制造和工程应用中传热方程

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摘要

A physics-informed neural network is developed to solve conductive heat transfer partial differential equation CPDE), along with convective heat transfer PDEs as boundary conditions (BCs), in manufacturing and engineering applications where parts are heated in ovens. Since convective coefficients are typically unknown, current analysis approaches based on trial-and-error finite element (FE) simulations are slow. The loss function is defined based on errors to satisfy PDE, BCs and initial condition. An adaptive normalizing scheme is developed to reduce loss terms simultaneously. In addition, theory of heat transfer is used for feature engineering. The predictions for 1D and 2D cases are validated by comparing with FE results. While comparing with theory-agnostic ML methods, it is shown that only by using physics-informed activation functions, the heat transfer beyond the training zone can be accurately predicted. Trained models were successfully used for real-time evaluation of thermal responses of parts subjected to a wide range of convective BCs.
机译：开发了一种物理知识的神经网络以解决导电传热部分微分方程CPDE），以及对流热传递PDE作为边界条件（BCS），在制造和工程应用中，其中部件在烤箱中加热。由于对流系数通常是未知的，因此基于试验和误差有限元（FE）模拟的当前分析方法很慢。丢失功能是基于满足PDE，BCS和初始条件的错误。开发了一种自适应归一化方案以同时减少损耗术语。此外，传热理论用于特征工程。通过与FE结果进行比较，验证了1D和2D情况的预测。同时与理论无症ML方法进行比较，表明只有通过使用物理信息的激活功能，可以准确地预测训练区之外的传热。经过培训的模型已成功用于对经过各种对流BCS进行零件的热反应的实时评估。

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