用分段线性投影让神经网络严格满足非线性物理约束，提升模型可靠性。
PL-KKT-hPINN: Enforcing Nonlinear Equality Constraints on Neural Networks via Piecewise-Linear Projection
- 通过分段线性投影强制神经网络输出满足非线性等式约束
- 在连续搅拌釜反应器案例中，约束违反率显著降低，预测精度与标准网络相当
- 小样本下仍具鲁棒性，误差低于无约束神经网络
物理信息神经网络（PINNs）在过程建模中潜力巨大，但物理方程仅作为训练中的软约束，无法保证推理时满足。本文提出分段线性卡鲁什-库恩-塔克硬约束神经网络（PL-KKT-hPINN），通过分段线性投影严格实现非线性等式约束。该方法扩展了原有的基于KKT条件的正交投影机制，可精确处理线性等式约束。在单输入和双输入连续搅拌釜反应器（CSTR）案例中，结果表明，PL-KKT-hPINN在保持与标准神经网络相当的预测精度的同时，显著降低了约束违反率；且在低数据条件下表现出更强鲁棒性，训练样本有限时均方根误差（RMSE）低于无约束网络。这证明PL-KKT-hPINN为非线性化工系统代理建模提供了一种计算高效、物理解释一致的框架。
原文摘要 · Abstract (English)
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.
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