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

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 four core architecture--optimizer combinations, reducing mean relative $L_2$ error by approximately 56--97\% relative to Std-PINN and improving on the better single-component variant. Capacity-controlled comparisons and gate interventions indicate that these gains reflect the learned coordinate-fusion pathway rather than parameter count alone. Gradient diagnostics suggest that LDA can improve task-gradient compatibility and reduce the correction required by GCR-PINN, with effects depending on the problem and update rule. Comparisons with representative PINN baselines and tests over sampling and temporal-horizon changes support the observed accuracy gains within the studied settings, while equal-time experiments reveal an accuracy--cost trade-off from the richer LDA representation.