We present FO-PINNs, physics-informed neural networks that are trained using the first-order formulation of the Partial Differential Equation (PDE) losses. We show that FO-PINNs offer significantly higher accuracy in solving parameterized systems compared to traditional PINNs, and reduce time-per-iteration by removing the extra backpropagations needed to compute the second or higher-order derivatives. Additionally, unlike standard PINNs, FO-PINNs can be used with exact imposition of boundary conditions using approximate distance functions, and can be trained using Automatic Mixed Precision (AMP) to further speed up the training. Through two Helmholtz and Navier-Stokes examples, we demonstrate the advantages of FO-PINNs over traditional PINNs in terms of accuracy and training speedup.
翻译:我们介绍FO-PINNs,即利用部分差别损失的第一阶配方进行训练的物理知情神经网络;我们显示,FO-PINNs比传统的PINNs在解决参数化系统方面提供比传统的PINN高得多的精确度,并通过去除计算第二级或更高级衍生物所需的额外反射来减少时间-每占用时间;此外,FO-PINNs不同于标准PINNs,FO-PINNs可以用近似距离功能精确地强加边界条件,也可以使用自动混合精度(AMP)来进一步加速培训;我们通过两个Helmholtz和Navier-Stokes的例子,展示FO-PINNs在准确性和培训速度方面优于传统的PINNs。