Architecture--Optimization Co-Design for Physics-Informed Neural Networks via Layer-wise Coordinate Adaptation and Gradient Conflict Resolution

תקציר מקורי באנגליתarXiv:2601.12971v2 Announce Type: replace Abstract: Physics-informed neural networks (PINNs) can be limited by coordinate representations and conflicting gradients from heterogeneous physical constraints. We propose Architecture--Conflict-Resolved PINN (ACR-PINN), combining Layer-wise Dynamic Adaptation (LDA) and Gradient-Conflict-Resolved PINN (GCR-PINN). LDA constructs layer-specific coordinate features and fuses two encoding branches through input-conditioned, feature-wise gates. GCR-PINN treats PDE, initial-condition, and boundary-condition losses as separate tasks and conditionally projects negatively aligned gradients before aggregation, without changing the physical loss formulation. Across seven benchmark problems, ACR-PINN achieves the lowest observed mean across all metrics among