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与传统的数据驱动的神经网络不同，PINNs 在学习过程中利用物理法则对模型进行指导，从而提高模型泛化能力，特别是在数据较少或噪声较大的情况下。 作者提出了一种基于元学习的新颖初始化方法，用于改进物理信息神经网络（PINNs）的性能。 作者利用元学习训练了一个通用的网络初始化模型，用于一系列介质参数（即速度模型），并将其作为新速度模型的PINN训练的初始模型。 Pinns allow for addressing a wide range of problems in computational science and represent a pioneering technology leading to the development of new classes of numerical solvers for pdes.
PINNs是一种将物理定律直接融入神经网络架构的深度学习模型。 传统神经网络主要基于数据训练，学习数据中的模式。 而PINNs更进一步，在训练过程中同时考虑物理规律。 例如，在求解偏微分方程（PDEs）时，PINNs把描述物理现象的PDE作为约束条件。 物理信息神经网络（PINNs）是一种结合了物理信息和神经网络的强大工具，用于解决各种复杂的科学问题。 本文将深入探讨PINNs的工作原理、优势和应用场景，以及如何实现PINNs。 物理信息神经网络 （Physics-Informed Neural Networks, PINNs）作为一种融合了物理定律与深度学习的新型建模方法，近年来在科学计算和工程领域取得了突破性进展。
物理信息神经网络（PINNs）为使用神经网络求解偏微分方程（PDEs）提供了一种有前景的解决方案，特别是在数据稀缺的情况下，得益于其无监督学习能力。
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