Abstract
Machine learning (ML) reduces reliance on computationally expensive first-principles simulation while capturing complex nonlinear behaviors. However, poor extrapolation, overfitting, limited interpretability, and lack of strict consistency with governing laws limit the use of ML models in process applications. Current methods for learning optimization policies also struggle with constraint satisfaction and optimality guarantees. Approaches such as physics-informed neural networks (PINNs) incorporate constraints "softly" and do not ensure strict constraint enforcement-an issue that can be particularly detrimental in safety-critical applications, where even minor violations may lead to unsafe or infeasible decisions. To resolve these issues, we develop an ML framework with a differential projection layer that allows computationally efficient process modeling, parameter estimation, and nonlinear optimization with feasibility and optimality guarantees. The framework is general in a sense that, depending on the loss function and the projection layer, it provides different functionalities. For instance, an ANN followed by a distance minimization-based projection leads to a hybrid mechanistic/data-driven process simulator, KKT-HardNet, that ensures inference with strict satisfaction of linear/nonlinear equality/inequality constraints. An ANN with a gradient-based loss function and a Taylor approximation-based pointwise projection leads to DAE-HardNet, which solves and/or estimates parameters of ODE/PDE-based governing equations. Lastly, an ANN with a distance-minimization based projection followed by objective-based loss function leads to KKT-OptNet, which learns to solve nonlinear optimization problems for different parameter instances. We illustrate the use of these tools for the modeling, optimization, and parameter estimation of complex processes systems.