Conflict-Aware Physics-Informed Neural Networks

Due to the mesh-free property and the capability to directly embed physical laws into deep learning models, Physics-Informed Neural Networks (PINNs) have become a promising tool for solving partial differential equations (PDEs). Although these methods have made significant progress, gradients associated with different loss terms can differ substantially in both magnitude and direction, leading to gradient conflicts and difficulties in stable and efficient optimization. While existing balancing methods can mitigate such conflicts to some extent, they typically rely on predefined loss reweighting or gradient manipulation rules that do not explicitly adapt to the evolving conflict state during training. In this paper, we propose Conflict-Aware Physics-Informed Neural Networks (CA-PINNs), which introduces an Adaptive Conflict Modulation mechanism to dynamically adjust the strength of conflict mitigation during training. Specifically, we first quantify the conflict state by considering both directional disagreement and gradient-norm imbalance. Then, we propose Adaptive Conflict Modulation that leverages these two complementary signals to dynamically regulate the constraint radius of the optimization problem, therey balancing conflict resolution with optimization progress. Extensive experiments on five PDE benchmarks demonstrate that our CA-PINNs achieve competitive and consistent predictive accuracy across different physical systems and loss decompositions.