Meshfree-based physics-informed neural networks for the unsteady Oseen equations

We propose the meshfree-based physics-informed neural networks for solving the unsteady Oseen equations.Firstly,based on the ideas of meshfree and small sample learning,we only randomly select a small number of spatiotemporal points to train the neural network instead of forming a mesh.Specifically,we optimize the neural network by minimizing the loss function to satisfy the differential operators,initial condition and boundary condition.Then,we prove the convergence of the loss function and the convergence of the neural network.In addition,the feasibility and effectiveness of the method are verified by the results of numerical experiments,and the theoretical derivation is verified by the relative error between the neural network solution and the analytical solution.

A fault diagnosis model based on weighted extension neural network for turbo-generator sets on small samples with noise

In data-driven fault diagnosis for turbo-generator sets,the fault samples are usually expensive to obtain,and inevitably with noise,which will both lead to an unsatisfying identification performance of diagnosis models.To address these issues,this paper proposes a fault diagnosis model for turbo-generator sets based on Weighted Extension Neural Network(W-ENN).WENN is a novel neural network which has three types of connection weights and an improved correlation function.The performance of the proposed model is validated against Extension Neural Network(ENN),Support Vector Machine(SVM),Relevance Vector Machine(RVM)and Extreme Learning Machine(ELM)based models.The results indicate that,on noisy small sample sets,the proposed model is superior to the other models in terms of higher identification accuracy with fewer samples and strong noise-tolerant ability.The findings of this study may serve as a powerful fault diagnosis model for turbo-generator sets on noisy small sample sets.