We propose characteristic-informed neural networks (CINN), a simple and efficient machine learning approach for solving forward and inverse problems involving hyperbolic PDEs. Like physics-informed neural networks (PINN), CINN is a meshless machine learning solver with universal approximation capabilities. Unlike PINN, which enforces a PDE softly via a multi-part loss function, CINN encodes the characteristics of the PDE in a general-purpose deep neural network trained with the usual MSE data-fitting regression loss and standard deep learning optimization methods. This leads to faster training and can avoid well-known pathologies of gradient descent optimization of multi-part PINN loss functions. If the characteristic ODEs can be solved exactly, which is true in important cases, the output of a CINN is an exact solution of the PDE, even at initialization, preventing the occurrence of non-physical outputs. Otherwise, the ODEs must be solved approximately, but the CINN is still trained only using a data-fitting loss function. The performance of CINN is assessed empirically in forward and inverse linear hyperbolic problems. These preliminary results indicate that CINN is able to improve on the accuracy of the baseline PINN, while being nearly twice as fast to train and avoiding non-physical solutions. Future extensions to hyperbolic PDE systems and nonlinear PDEs are also briefly discussed.

翻译：我们建议采用基于特性的神经网络(CINN),这是一种简单高效的机器学习方法,用于解决涉及双曲PDE的前瞻性和反向问题。像物理学-知情神经网络(PINN)一样,CINN是一个全近近效功能的无模机学习解答器。与PINN不同,PINN通过多部分损失功能软性地执行PDE,CIN将PDE的特性编码成一个通用的深层神经网络,该网络通过通常的MSE数据适应回归损失和标准的深层学习优化方法来培训。这导致更快的培训,并可以避免多部分PINN损失功能的梯度下降优化的众所周知的病理。如果特征代码可以完全解决(在重要的情况下确实如此 ), CINN 的输出是PDE的精确解决方案, 即使在初始化时, 也防止非物理产出的出现。 否则, 代码必须大致解决, 但 CINNE仍然仅使用一个数据匹配的损失功能来进行短期的培训。 CINNN的绩效是前向前向和反向反向的双向双向双向双向双向的双向双向扩展的路径评估, 。这些初步结果是能够快速地改进到快速的路径, 。这些初步的结果是快速地成为快速的路径的路径, 快速的路径的路径是快速的路径的路径, 快速的路径是快速的路径。