基于Meta学习的物理信息神经网络一维电弧仿真加速
Accelerating physics-informed neural network based 1D arc simulation by meta learning
摘要：
物理信息神经网络（PINNs）作为传统数值方法的替代，在等离子体模拟中有着广泛的应用。然而，在基于PINN的建模的某些特定情况下，对于复杂的建模和庞大的神经网络，训练良好的PINN可能需要数万次优化迭代，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Meta-PINN，以减少基于PINN的一维圆弧模拟的训练时间。在Meta-PINN中，Meta网络首先通过对等离子体建模的各种训练任务的双循环优化来训练，然后用于初始化基于PINN的网络以用于新任务。我们展示了Meta-PINN的功率对应于1-D电弧模型在不同的边界温度，电弧半径，电弧压力，和气体混合物的四种情况下。我们发现，一个经过良好训练的Meta网络可以为基于PINN的弧模型生成良好的初始权重，即使在稍微超出训练范围的条件下也是如此。在我们研究的情况下，Meta-PINN在相对L2误差方面的加速范围从1.1倍到6.9倍。结果表明，Meta-PINN是一种有效的方法来加速基于PINN的一维电弧模拟。
英文摘要：
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.
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