arXiv:2503.18181cs.LGcs.AI2025-03综述被引 11

解决物理神经网络训练慢、难迁移的问题,提升求解微分方程效率。

Adaptive Physics-informed Neural Networks: A Survey

  • 用元学习和迁移学习加速PINN对新微分方程的适应
  • 实现少数据、低算力下快速收敛,突破传统方法瓶颈
  • 适合需要快速建模的科研与工程场景

物理信息神经网络(PINNs)因其无监督训练能力,在数据稀缺场景下求解偏微分方程(PDEs)展现出巨大潜力。然而,其收敛慢、参数变更需重新优化等问题限制了在科学与工程中的广泛应用。本文综述了通过迁移学习与元学习改进这些局限的研究进展。相关方法显著提升了训练效率,使PINN能以更少数据和计算资源快速适配新PDE。不同于传统数值方法直接求解方程,神经网络通过调整参数隐式学习解。一个重要优势是其可抽象泛化,保留、舍弃或调整已学表征以应对相似问题。通过探索这些技术在PINNs中的应用,本文指出了未来研究的重要方向,有望推动PINNs在更多领域落地。

原文摘要 · Abstract (English)

Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability. However, limitations related to convergence and the need for re-optimization with each change in PDE parameters hinder their widespread adoption across scientific and engineering applications. This survey reviews existing research that addresses these limitations through transfer learning and meta-learning. The covered methods improve the training efficiency, allowing faster adaptation to new PDEs with fewer data and computational resources. While traditional numerical methods solve systems of differential equations directly, neural networks learn solutions implicitly by adjusting their parameters. One notable advantage of neural networks is their ability to abstract away from specific problem domains, allowing them to retain, discard, or adapt learned representations to efficiently address similar problems. By exploring the application of these techniques to PINNs, this survey identifies promising directions for future research to facilitate the broader adoption of PINNs in a wide range of scientific and engineering applications.

物理神经网络微分方程元学习迁移学习

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