Enhanced Physics-Informed Neural Networks Using Adaptive Residual Weighting for Flow Simulations

Le résumé fourni par la source

Physics-Informed Neural Networks (PINNs) have shown significant potential in solving partial differential equations (PDEs). However, effectively balancing residual contributions in the loss function remains an important challenge. To address this issue, we propose an improved PINN framework that incorporates an adaptive weighting strategy within the loss function, dynamically adjusting the weights of residual terms for different collocation points during training. Specifically, the optimization problem is formulated as a max-min loss problem, solved via Competitive Gradient Descent (CGD). We validate our approach across multiple PDE systems, demonstrating smoother convergence behavior and more balanced residual distributions compared to traditional PINN methods. The proposed adaptive weighting framework enhances the stability and accuracy of PINN-based solvers, offering a robust and general approach to solving complex PDE problems.

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