To develop a Gradient-Based Attention mechanism for enhanced boundary enforcement in PINNs, one approach is to amplify the attention weights at domain boundaries using gradient magnitudes from the physics-informed loss. By integrating a differentiable attention layer that modulates residual contributions based on gradient sensitivity at boundary points, the model can prioritize learning boundary behavior more effectively.

In my own work, I’ve used deep feature attention and optimization strategies in image-based diagnostic systems (Neurofusion, RegNet) where boundary learning is critical for accurate classification. These principles of gradient-guided spatial focus can be adapted to PINNs for physics-compliant and interpretable enforcement of boundary conditions

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thank you sir