aiqbench analysis
This research introduces ACR-PINN, a novel architecture designed to mitigate gradient conflicts in physics-informed neural networks through layer-wise coordinate adaptation and selective gradient projection. By decoupling different physical constraints within the loss function, the method significantly reduces relative $L_2$ error across benchmark problems without altering the underlying physical formulations. The study highlights that these accuracy gains stem from improved task-gradient compatibility rather than simply increasing parameter counts, offering a more efficient path for solving complex partial differential equations with AI.
Architecture--Optimization Co-Design for Physics-Informed Neural Networks via Layer-wise Coordinate Adaptation and Gradient Conflict Resolution
arXiv: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 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.
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.
Machine Learning (cs.LG)
arXiv:2601.12971 [cs.LG]
(or arXiv:2601.12971v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2601.12971 Focus to learn more arXiv-issued DOI via DataCite
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