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Modularity-Free Conflict-Averse Training for Genera... | AI Research

Key Takeaways

  • Modularity-Free Conflict-Averse Training for Generalized PINNs Physics-informed neural networks (PINNs) are a popular tool for solving complex partial differ...
  • Physics-informed neural networks (PINNs) have become a powerful framework for solving PDEs by embedding physical laws into differentiable objectives.
  • 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{ this https URL }.
  • Modularity-Free Conflict-Averse Training for Generalized PINNs
Paper AbstractExpand

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{ this https URL }.

Modularity-Free Conflict-Averse Training for Generalized PINNs
Physics-informed neural networks (PINNs) are a popular tool for solving complex partial differential equations (PDEs) by embedding physical laws directly into the training process. While these networks are powerful, they are often fragile and difficult to train. Recent research has introduced "conflict-averse" optimization to help manage the competing demands of residual and boundary losses. However, this paper reveals that as these models grow in capacity (i.e., become larger and more complex), these optimization schemes often fail. The authors identify that large networks tend to "self-partition" into task-exclusive modules, effectively ignoring the need for the two objectives to interact, which ultimately hinders the model's ability to find an accurate solution.

The Problem: Capacity-Induced Failure

The researchers observed that when PINNs are overparameterized, they undergo a process called functional modularity. Instead of learning a unified representation that satisfies both the physics residual and the boundary conditions, the network splits into separate modules that optimize these tasks in isolation. This segregation suppresses the necessary cross-objective interaction, causing the gradients of the two tasks to become orthogonal. Consequently, conflict-averse training methods—which rely on these gradients interacting constructively—lose their effectiveness and can even perform worse than standard, simpler training methods.

The Solution: ModSync

To fix this, the authors propose Modular-Sparsity Synchronization (ModSync). This framework integrates structural optimization into the training process to prevent the network from segregating into isolated modules. ModSync works by dynamically identifying which connections in the network are becoming "task-exclusive" and penalizing them. Simultaneously, it preserves "interaction-promoting" pathways that allow the residual and boundary objectives to continue communicating. By using dual threshold vectors that track the needs of each objective, the model can prune redundant, exclusive connections while keeping the network structure focused on shared, meaningful learning.

Key Results and Performance

The authors tested ModSync across several challenging PDE benchmarks, including Helmholtz, Klein-Gordon, and Burgers’ equations in both 2D and 3D. Their experiments consistently showed that while existing conflict-averse methods suffer from performance degradation as model width increases, ModSync maintains stability and accuracy. By preventing the network from taking the "shortcut" of functional modularity, ModSync achieved state-of-the-art accuracy and proved to be a robust, scalable solution for training larger PINNs.

Why This Matters

This research highlights a critical, often overlooked aspect of training deep learning models for scientific discovery: the internal structure of the network matters as much as the gradient optimization itself. By demonstrating that model capacity can lead to unintended structural shortcuts, the paper provides a new way to ensure that PINNs remain reliable as they scale. The ModSync framework offers a practical path forward for researchers looking to apply larger, more complex neural networks to high-dimensional physics problems without sacrificing training stability.

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