Deep Ritz Physics-Informed Neural Network Method for Solving the Variational Inequality
This addresses variational inequality problems in fields like mechanical engineering and fluid penetration, but it appears incremental as it builds on existing PINN and Ritz methods.
The paper tackled solving elliptic variational inequalities by proposing a Deep Ritz method based on Physics-Informed Neural Networks, which enhanced accuracy and efficiency, as numerical experiments showed it effectively approximated the analytical solution.
Variational inequalities are widely applied in mechanical engineering, fluid penetration, transportation, and other fields. In this paper, a Deep Ritz method based on Physics-Informed Neural Networks (PINNs) is proposed to enhance the accuracy and efficiency of solving elliptic variational inequalities. The Ritz variational method is firstly utilized to transform the variational inequality problem into an optimization problem. Then Bayesian optimization is employed to tune the weights of the loss function, and a residual-based adaptive dataset update strategy is introduced to improve the convergence and accuracy of the model. Numerical experiments show that the proposed method can effectively approximate the analytical solution.