  Surrogate modeling is used to replace computationally expensive simulations.
Neural networks have been widely applied as surrogate models that enable
efficient evaluations over complex physical systems. Despite this, neural
networks are data-driven models and devoid of any physics. The incorporation of
physics into neural networks can improve generalization and data efficiency.
The physics-informed neural network (PINN) is an approach to leverage known
physical constraints present in the data, but it cannot strictly satisfy them
in the predictions. This work proposes a novel physics-informed neural network,
KKT-hPINN, which rigorously guarantees hard linear equality constraints through
projection layers derived from KKT conditions. Numerical experiments on Aspen
models of a continuous stirred-tank reactor (CSTR) unit, an extractive
distillation subsystem, and a chemical plant demonstrate that this model can
further enhance the prediction accuracy.
