论文标题
DPM：一种用于外推的物理信息神经网络的新型培训方法
DPM: A Novel Training Method for Physics-Informed Neural Networks in Extrapolation
论文作者
论文摘要
我们提出了一种学习通过时间依赖性非线性偏微分方程（PDE）描述的复杂物理过程动力学的方法。我们特别的兴趣在于，及时推断解决方案超出了训练中使用的时间领域的范围。我们对基线方法的选择是物理知识的神经网络（PINN）[Raissi等，J。Comput。 Phys。，378：686--707，2019]，因为该方法不仅参数化了解决方案，还可以将描述物理过程动力学的方程式参数。我们证明，在许多基准问题中，Pinn在外推任务上的表现较差。为了解决这个问题，我们提出了一种新的方法，可以更好地训练PINN，并证明我们新增强的Pinns可以准确地推断解决方案。就标准L2-norm度量而言，我们的方法显示出比现有方法小72％的错误。
We present a method for learning dynamics of complex physical processes described by time-dependent nonlinear partial differential equations (PDEs). Our particular interest lies in extrapolating solutions in time beyond the range of temporal domain used in training. Our choice for a baseline method is physics-informed neural network (PINN) [Raissi et al., J. Comput. Phys., 378:686--707, 2019] because the method parameterizes not only the solutions but also the equations that describe the dynamics of physical processes. We demonstrate that PINN performs poorly on extrapolation tasks in many benchmark problems. To address this, we propose a novel method for better training PINN and demonstrate that our newly enhanced PINNs can accurately extrapolate solutions in time. Our method shows up to 72% smaller errors than existing methods in terms of the standard L2-norm metric.
