An analytical solutions-enhanced neural network for high-accuracy modeling: A case study on gas turbine

• An analytical solutions-enhanced neural network is proposed. • The application of physics-informed neural networks is expanded. • The predictive error of proposed model has been significantly improved. • The proposed model can reduce the sample size by at least 35.45 %. Physics-informed neural networks have gained wide application due to their data efficiency and generation ability. Nevertheless, their application is restricted in practical engineering problems where complex physical mechanisms make it difficult to formulate or solve the corresponding partial differential equations. To solve the above problems, Analytical solutions are obtained by finite-step algebraic computation. Based on these solutions, an analytical solutions-enhanced physical model is trained using a multi-layer perceptron to replace conventional partial differential equations. By incorporating weighted loss functions into the multi-layer perceptron, an analytical solutions-enhanced neural network is developed to address complex problems in practical engineering applications. Taking gas turbines in the energy sector as a case, the proposed model is compared with conventional prediction models. Results indicate that the proposed model achieves a mean square error of 0.0606, a mean absolute error of 0.0867 on the test set, corresponding to maximum reductions of 99.17 % and 90.98 % relative to conventional prediction models, respectively. Additionally, sample size analyses indicate that the proposed model can reduce the sample size by at least 35.45 %. The analytical solutions-enhanced neural network established in this study provides a novel approach to integrating physical models and neural networks, thereby expending the application of physics-informed neural networks to real-word engineering problems.