arXiv:2501.06572cs.NEcs.CE2025-01中稿 · publication in IEE…被引 20

用进化算法优化物理信息神经网络,提升小样本下的精度与泛化能力。

Evolutionary Optimization of Physics-Informed Neural Networks: Evo-PINN Frontiers and Opportunities

  • 采用无梯度进化算法应对PINN训练中的复杂损失曲面。
  • 结合梯度下降与进化算法,优化网络结构并平衡物理约束项。
  • 适合关注物理引导机器学习的科研人员与工程师。

基于有限数据的深度学习模型对物理世界理解不完整。物理信息神经网络(PINNs)通过将自然规律以数学形式融入训练损失函数,使模型遵循物理法则,在数据稀缺场景下优于纯数据驱动模型,是迈向物理人工智能的重要路径。然而,实现高精度物理信息学习面临训练速度慢、精度不足和泛化能力差等挑战。本文聚焦于PINN的模型优化与泛化能力,强调需发展新算法以突破当前瓶颈。特别关注无梯度进化算法(EAs)在处理PINN独特复杂损失景观中的潜力。将梯度下降与进化算法协同用于定制神经架构设计,并平衡多目标物理学习目标,被视为未来重要方向。另一前沿是将进化算法作为通用PINN模型的元学习器。本文还综述近期文献成果,展示此类方法在解决PINN优化与泛化问题上的初步成效。

原文摘要 · Abstract (English)

Deep learning models trained on finite data lack a complete understanding of the physical world. On the other hand, physics-informed neural networks (PINNs) are infused with such knowledge through the incorporation of mathematically expressible laws of nature into their training loss function. By complying with physical laws, PINNs provide advantages over purely data-driven models in limited-data regimes and present as a promising route towards Physical AI. This feature has propelled them to the forefront of scientific machine learning, a domain characterized by scarce and costly data. However, the vision of accurate physics-informed learning comes with significant challenges. This work examines PINNs in terms of model optimization and generalization, shedding light on the need for new algorithmic advances to overcome issues pertaining to the training speed, precision, and generalizability of today's PINN models. Of particular interest are gradient-free evolutionary algorithms (EAs) for optimizing the uniquely complex loss landscapes arising in PINN training. Methods synergizing gradient descent and EAs for discovering bespoke neural architectures and balancing multiple terms in physics-informed learning objectives are positioned as important avenues for future research. Another exciting track is to cast EAs as a meta-learner of generalizable PINN models. To substantiate these proposed avenues, we further highlight results from recent literature to showcase the early success of such approaches in addressing the aforementioned challenges in PINN optimization and generalization.

物理信息神经网络进化算法科学机器学习小样本学习

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