Physics-Informed Neural Networks with Hard Linear Equality Constraints

These equations are derived from fundamental principles and mechanistic laws, such as the physical laws in thermodynamics and transport phenomena. High-fidelity models with these equations can serve as digital representations of the physical systems in the real world. However, the physically accurate representation is accompanied by a heightened mathematical complexity that elevates the computational expense of simulation. This impedes the use of high-fidelity physical models especially in applications where it is essential to simulate a system repeatedly in a timely manner. To efficiently generate simulation outputs, data-driven approaches have sought to substitute a high-fidelity physical model with a surrogate model (Misener and Biegler, 2023; Bhosekar and Ierapetritou, 2018; Bradley et al., 2022; Williams and Cremaschi, 2021), A surrogate model stands for a reducedorder model that aims for a computationally efficient approximation at the cost of a certain level of accuracy. This approach provides a more practical means of inferring a system's responses under a great variety of conditions.