An Improved Method for Physics-Informed Neural Networks That Accelerates Convergence
An Improved Method for Physics-Informed Neural Networks That Accelerates Convergence
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DOI：
10.1109/access.2024.3354058
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发表时间：
2024
期刊：
影响因子：
3.9
通讯作者：
Liangliang Yan;You Zhou;Huan Liu;Lingqi Liu
中科院分区：
文献类型：
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作者：
Liangliang Yan;You Zhou;Huan Liu;Lingqi Liu
物理信息神经网络（pinn）在求解高维偏微分方程（PDEs）方面已经被证明是非常有效的，在各种具有挑战性的场景中显示出巨大的潜力。然而，传统的pinn （vanilla pinn）通常基于全连接神经网络（FCNN），经常面临收敛和参数冗余的问题。本文提出了一种利用多输入残差网络，结合多步训练范式来促进无监督训练的新方法。这种改进方法可以提高传统pin码的收敛速度和稳定性，我们称之为MultiInNet pin码。我们的实验表明，与FCNN、ResNet和UNet等其他网络相比，MultiInNet pinn以更少的参数实现了更好的收敛。具体来说，多步训练使收敛速度提高了约45%，而multiinet增强又提高了50%，从而使总速度提高了约70%。这种加速的收敛速度使pinn能够通过实现更快的收敛来降低计算成本。此外，我们的MultiInNet pinn提供了在pinn中分别处理初始条件和边界条件（I/ bc）的潜在方法。
Physics-Informed Neural Networks (PINNs) have proven highly effective for solving high-dimensional Partial Differential Equations (PDEs), having demonstrated tremendous potential in a variety of challenging scenarios. However, traditional PINNs (vanilla PINNs), typically based on fully connected neural networks (FCNN), often face issues with convergence and parameter redundancy. This paper proposes a novel approach that utilizes a multi-input residual network, incorporating a multi-step training paradigm to facilitate unsupervised training. This improved method, which we named MultiInNet PINNs, can enhance the convergence speed and the stability of traditional PINNs. Our experiments demonstrate that MultiInNet PINNs achieve better convergence with fewer parameters than other networks like FCNN, ResNet, and UNet. Specifically, the multi-step training increases convergence speed by approximately 45%, while the MultiInNet enhancement contributes an additional 50%, leading to a total improvement of about 70%. This accelerated convergence speed allows PINNs to lower computational costs by achieving faster convergence. Moreover, our MultiInNet PINNs provides a potential method for handling initial and boundary conditions (I/BCs) separately within PINNs.