arXiv:2603.10466cs.CVcs.AI2026-03

统一框架解决多流体方程联合求解难题,精度更高更稳定。

UniPINN: A Unified PINN Framework for Multi-task Learning of Diverse Navier-Stokes Equations

  • 分治架构分离通用物理规律与特定流动特征
  • 跨流注意力机制抑制干扰,提升关键信息捕捉
  • 动态权重分配缓解不同任务间损失差异问题

物理信息神经网络(PINNs)在求解不可压缩纳维-斯托克斯方程方面展现出潜力,但现有方法多针对单一流动场景。扩展至多流场景时面临三大挑战:(1) 难以同时捕捉共性物理规律与流体特异性;(2) 易受任务间负迁移影响导致精度下降;(3) 不同流动状态下损失量级差异大,引发训练不稳定。为此,我们提出UniPINN——一种统一的多流PINN框架,集成三项互补组件:共享-专用架构,实现通用物理规律与流体特性的解耦;跨流注意力机制,选择性强化相关模式并抑制无关干扰;动态权重分配策略,自适应平衡多目标优化中的损失贡献。在三个典型流动场景上的实验表明,UniPINN有效实现多流学习统一,显著提升预测精度,在异质流动条件下表现均衡,并成功缓解负迁移问题。

原文摘要 · Abstract (English)

Physics-Informed Neural Networks (PINNs) have shown promise in solving incompressible Navier-Stokes equations, yet existing approaches are predominantly designed for single-flow settings. When extended to multi-flow scenarios, these methods face three key challenges: (1) difficulty in simultaneously capturing both shared physical principles and flow-specific characteristics, (2) susceptibility to inter-task negative transfer that degrades prediction accuracy, and (3) unstable training dynamics caused by disparate loss magnitudes across heterogeneous flow regimes. To address these limitations, we propose UniPINN, a unified multi-flow PINN framework that integrates three complementary components: a shared-specialized architecture that disentangles universal physical laws from flow-specific features, a cross-flow attention mechanism that selectively reinforces relevant patterns while suppressing task-irrelevant interference, and a dynamic weight allocation strategy that adaptively balances loss contributions to stabilize multi-objective optimization. Extensive experiments on three canonical flows demonstrate that UniPINN effectively unifies multi-flow learning, achieving superior prediction accuracy and balanced performance across heterogeneous regimes while successfully mitigating negative transfer. The source code of this paper will be released on https://github.com/Event-AHU/OpenFusion

PINN流体力学多任务学习神经网络

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