Modularity-Free Conflict-Averse Training for Generalized PINNs

2026-06-18

AI Summary

This work addresses the challenge that high-capacity physics-informed neural networks (PINNs) often fail to converge to Pareto stationary solutions due to weakened inter-task gradient interactions caused by functional modularity. To overcome this limitation, we propose the Modular-Sparsity Synchronization (ModSync) framework, which for the first time uncovers the failure mechanism of functional modularity induced by excessive model capacity. ModSync introduces a structural sparsity synchronization mechanism that dynamically suppresses task-specific connections while preserving cross-objective coupling pathways during conflict-avoidance training. By integrating structural sparsity regularization with multi-objective optimization, our approach enables collaborative training without explicit modularity. Extensive experiments on multiple PDE benchmarks demonstrate that ModSync achieves state-of-the-art accuracy, effectively prevents training collapse in high-capacity PINNs, and substantially enhances the stability of multi-task optimization.

Abstract

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}.

Problem

• Physics-informed neural networks
• overparameterization
• functional modularity
• gradient conflict
• multi-objective optimization

Innovation

• ModSync
• conflict-averse training
• functional modularity
• physics-informed neural networks
• multi-objective optimization