Constructing first-principles models is usually a challenging and time-consuming task due to the complexity of the real-life processes. On the other hand, data-driven modeling, and in particular neural network models often suffer from issues such as overfitting and lack of useful and highquality data. At the same time, embedding trained machine learning models directly into the optimization problems has become an effective and state-of-the-art approach for surrogate optimization, whose performance can be improved by physics-informed training. In this study, it is proposed to upgrade piece-wise linear neural network models with physics informed knowledge for optimization problems with neural network models embedded. In addition to using widely accepted and naturally piece-wise linear rectified linear unit (ReLU) activation functions, this study also suggests piece-wise linear approximations for the hyperbolic tangent activation function to widen the domain. Optimization of three case studies, a blending process, an industrial distillation column and a crude oil column are investigated. For all cases, physics-informed trained neural network based optimal results are closer to global optimality. Finally, associated CPU times for the optimization problems are much shorter than the standard optimization results.

翻译：构建第一性原理模型通常因实际过程的复杂性而成为一项具有挑战性且耗时的任务。另一方面，数据驱动建模，尤其是神经网络模型，常面临过拟合以及缺乏高质量可用数据等问题。同时，将训练好的机器学习模型直接嵌入优化问题已成为替代优化的有效且前沿方法，而通过物理知识增强的训练可进一步提升其性能。本研究提出将分段线性神经网络模型升级为具备物理知识增强能力的模型，以解决含嵌入神经网络模型的优化问题。除采用广泛接受且天然分段线性的整流线性单元（ReLU）激活函数外，本研究还建议对双曲正切激活函数进行分段线性近似，以拓宽应用域。通过三个案例研究（混合过程、工业蒸馏塔和原油蒸馏塔）进行优化分析。所有案例中，基于物理知识增强训练得到的神经网络优化结果更接近全局最优。最后，相关优化问题的CPU时间远短于标准优化结果。