New Training Method Improves Physics-Informed Neural Networks by Preventing Modularity.

Physics-informed neural networks (PINNs) are powerful tools for solving partial differential equations (PDEs) by integrating physical laws into their training objectives. However, their training can be unstable, especially as model capacity increases. Existing conflict-averse optimization methods, designed to mitigate gradient interference between different loss components (like residual and boundary losses), become less effective with larger networks. This research identifies a specific problem: overparameterized PINNs tend to develop "functional modularity." This means the network self-partitions into specialized modules, each handling a specific task, which suppresses the necessary interaction between different objectives and hinders convergence to optimal solutions. To counteract this, a novel framework called Modular-Sparsity Synchronization (ModSync) is proposed. ModSync integrates structural optimization into the training process by actively penalizing connections that become exclusive to a single task while preserving pathways that promote interaction across objectives. Extensive experiments on various PDE benchmarks demonstrate that ModSync consistently prevents these capacity-driven failures, maintains strong cross-objective coupling, and achieves superior accuracy.