论文标题
通过元学习加速物理知识神经网络基于1D ARC模拟
Accelerating physics-informed neural network based 1D arc simulation by meta learning
论文作者
论文摘要
物理信息神经网络（PINN）具有广泛的应用，可替代血浆模拟中传统数值方法。但是，在某些基于PINN的建模的特定情况下，训练有素的PINN可能需要在训练阶段进行数以万计的优化迭代，以进行复杂的建模和巨大的神经网络，这有时非常耗时。在这项工作中，我们提出了一种元学习方法，即元细节，以减少基于PINN的1-D ARC模拟的训练时间。在Meta-Pinn中，首先，通过对等离子体建模的各种培训任务进行两循环优化的元网络，然后用于初始化基于Pinn的网络以进行新任务。我们通过四个病例证明了与1-D ARC模型在不同边界温度，电弧半径，电弧压力和气体混合物下的1-D ARC模型的功率。我们发现，训练有素的元网络即使在稍微超出训练范围的条件下，也可以为基于Pinn的ARC模型产生良好的初始权重。在我们研究的情况下，元小细胞的相对L2误差的加速范围从1.1倍至6.9倍。结果表明，meta-pinn是加速基于PINN的1-D ARC模拟的有效方法。
Physics-Informed Neural Networks (PINNs) have a wide range of applications as an alternative to traditional numerical methods in plasma simulation. However, in some specific cases of PINN-based modeling, a well-trained PINN may require tens of thousands of optimizing iterations during training stage for complex modeling and huge neural networks, which is sometimes very time-consuming. In this work, we propose a meta-learning method, namely Meta-PINN, to reduce the training time of PINN-based 1-D arc simulation. In Meta-PINN, the meta network is first trained by a two-loop optimization on various training tasks of plasma modeling, and then used to initialize the PINN-based network for new tasks. We demonstrate the power of Meta-PINN by four cases corresponding to 1-D arc models at different boundary temperatures, arc radii, arc pressures, and gas mixtures. We found that a well-trained meta network can produce good initial weights for PINN-based arc models even at conditions slightly outside of training range. The speed-up in terms of relative L2 error by Meta-PINN ranges from 1.1x to 6.9x in the cases we studied. The results indicate that Meta-PINN is an effective method for accelerating the PINN-based 1-D arc simulation.
