A Novel Physics-Informed Neural Network Framework with Adaptive Weighting for 2D Frictionless Contact Problems

Standard Physics-Informed Neural Networks (PINNs) often struggle with convergence in contact mechanics due to gradient imbalances caused by nonlinear boundary conditions. To address this, we propose an enhanced PINNs framework for high-precision displacement prediction, integrating an improved GradNorm-based adaptive weighting strategy with dynamic non-uniform sampling. The method employs the Fischer-Burmeister function for contact constraints and hard constraints for essential boundaries. By dynamically balancing gradients between singular contact regions and the domain interior, the proposed approach effectively overcomes the optimization stagnation typical of fixed-weight models. Numerical experiments on a flat punch indentation problem demonstrate that the framework achieves high-fidelity agreement with Finite Element Method benchmarks in global displacement reconstruction, validating its robustness for mesh-free deformation analysis.