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

Abstract

A physics-informed neural network is developed to solve conductive heat transfer partial differential equation (PDE), 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.