Physics-Informed Neural Networks with Hard Linear Equality Constraints
This work addresses the need for more accurate and physics-compliant surrogate models in chemical engineering, though it is incremental as it builds on existing PINN methods by adding strict constraint enforcement.
The authors tackled the problem of surrogate modeling for computationally expensive simulations by proposing KKT-hPINN, a physics-informed neural network that strictly enforces hard linear equality constraints, resulting in enhanced prediction accuracy for chemical engineering systems like CSTR units and distillation subsystems.
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.