解决大模型下PINN训练崩溃问题，让物理约束与边界条件更好协同。
Modularity-Free Conflict-Averse Training for Generalized PINNs
- 通过惩罚任务专用连接，保持不同损失间的有效交互
- 在多种PDE测试中显著提升大模型精度与稳定性
- 适合追求高精度的科学计算与复杂方程求解场景
物理信息神经网络（PINNs）通过将物理定律嵌入可微目标来求解偏微分方程。尽管取得进展，其训练仍易受干扰：现有冲突规避优化方法在模型容量增大时效果下降。本文揭示一种容量诱发的失效模式——过度参数化网络会形成功能模块化，自我分裂为任务专属模块，抑制跨目标交互，阻碍收敛至帕累托平稳点。为此，提出新型框架ModSync，通过惩罚任务专属连接并保留促进交互的路径，将结构优化融入冲突规避训练。在多个典型PDE基准上的实验表明，ModSync能持续防止容量驱动的失败，维持稳定的跨目标耦合，并实现最优精度。代码已开源。
原文摘要 · Abstract (English)
Physics-informed neural networks (PINNs) have become a powerful framework for solving PDEs by embedding physical laws into differentiable objectives. Despite their advances, training PINNs remains fragile: recent conflict-averse optimization schemes alleviate gradient interference between residual and boundary losses, but we show that their effectiveness deteriorates as model capacity increases. In this paper, we identify a capacity-induced failure mode, where overparameterized networks undergo functional modularity, self-partitioning into task-exclusive modules that suppress cross-objective interaction and hinder convergence toward Pareto-stationary points. To address this issue, we propose a novel framework, Modular-Sparsity Synchronization (ModSync), which integrates structural optimization into conflict-averse training by penalizing task-exclusive connections while preserving interaction-promoting pathways. Extensive experiments across diverse PDE benchmarks demonstrate that ModSync consistently prevents capacity-driven failures, sustains robust cross-objective coupling, and achieves state-of-the-art accuracy. Codes are available at \url{https://github.com/heejokong/ModSync}.
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