Process modeling began with the use of first principles resulting in ‘white-box’ models which are complex but accurately explain the dynamics of the process. Recently, there has been tremendous interest towards data-based modeling as the resultant ‘black-box’ models are simple, and easy to construct, but their accuracy is highly dependent on the nature and amount of training data used. In order to balance the advantages and disadvantages of ‘white-box’ and ‘black-box’ models, we propose a hybrid model that integrates first principles with a deep neural network, and applied it to hydraulic fracturing process. The unknown process parameters in the hydraulic fracturing process are predicted by the deep neural network and then utilized by the first principles model in order to calculate the hybrid model outputs. This hybrid model is easier to analyze, interpret, and extrapolate compared to a ‘black-box’ model, and has higher accuracy compared to the first principles model.

过程建模始于使用第一条原则，从而产生了“白盒”模型，该模型虽然复杂但可以准确地解释过程的动态。最近，人们对基于数据的建模产生了极大的兴趣，因为生成的“黑匣子”模型简单，易于构建，但其准确性高度取决于所使用的训练数据的性质和数量。为了平衡“白盒”和“黑盒​​”模型的优缺点，我们提出了一种混合模型，该模型将第一原理与深层神经网络集成在一起，并将其应用于水力压裂过程。水力压裂过程中未知的过程参数由深层神经网络预测，然后由第一原理模型加以利用，以计算混合模型输出。这种混合模型更易于分析，