🤖 AI Summary
This work addresses the limitation of existing physics-informed neural networks (PINNs), which enforce nonlinear equality constraints only as soft penalties during inference, thereby failing to guarantee strict feasibility. To overcome this, the authors propose a novel approach that integrates Karush–Kuhn–Tucker (KKT) conditions with a piecewise linear projection mechanism, extending hard-constraint enforcement—previously limited to simpler constraints—to general nonlinear equality settings. By employing an orthogonal projection, the network outputs are rigorously mapped onto the feasible manifold defined by the constraints. Evaluated on a continuous stirred-tank reactor (CSTR) benchmark, the method achieves prediction accuracy comparable to standard PINNs while substantially reducing constraint violations. Moreover, it demonstrates enhanced robustness and lower root-mean-square error (RMSE) under data-scarce conditions.
📝 Abstract
While physics-informed neural networks (PINNs) have shown strong potential for process modeling, physical equations are only enforced as soft constraints during training, and thus, they do not guarantee constraint satisfaction at inference. We propose a framework, called piecewise-linear Karush--Kuhn--Tucker hard-constrained PINNs (PL-KKT-hPINNs), that strictly enforces nonlinear equality constraints through piecewise-linear projection. This extends the KKT-hPINN framewor, which exactly enforces linear equalities through the Karush--Kuhn--Tucker (KKT) conditions associated with orthogonally projecting neural network outputs onto the constraint feasible region. The method is demonstrated on a continuous stirred-tank reactor (CSTR) case study for both one and two inputs. Results show that PL-KKT-hPINN preserves predictive accuracy comparable to that of a standard neural network while achieving substantially lower constraint violations. In addition, the proposed model shows improved robustness in low-data regimes, yielding lower RMSE than the unconstrained neural network for limited training sample sizes. These results demonstrate that PL-KKT-hPINN provides a computationally efficient and physically consistent framework for surrogate modeling of nonlinear chemical engineering systems.