  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. It is shown that using engineered
features, heat transfer beyond the training zone can be predicted. Trained
model allows for fast evaluation of a range of BCs to develop feedback loops,
realizing Industry 4.0 concept of active manufacturing control based on sensor
data.
