论文标题
具有扩散缩放的双曲线系统的渐近保护神经网络
Asymptotic-Preserving Neural Networks for hyperbolic systems with diffusive scaling
论文作者
论文摘要
随着机器学习技术的快速发展以及科学数据的可用性的大幅提高，数据驱动的方法开始在整个科学中逐渐流行，在证明是在社会许多领域具有直接影响的强大工具后，科学方法的根本转变。然而，当试图分析复杂的多尺度系统的动态时，标准的深神经网络（DNNS），甚至标准物理信息知识的神经网络（PINN）的使用可能会导致不正确的推断和预测，这是由于在学习过程中必须一致地应用的系统中降低或简化模型的小规模而导致的。在本章中，我们将根据具有扩散缩放的双曲线模型的开发中获得的最新结果来解决这些问题。几项数值测试表明，与标准DNN和PINN相比，APNN如何在问题的不同范围内提供更好的结果，尤其是在分析仅几乎没有少数信息的场景时。
With the rapid advance of Machine Learning techniques and the deep increase of availability of scientific data, data-driven approaches have started to become progressively popular across science, causing a fundamental shift in the scientific method after proving to be powerful tools with a direct impact in many areas of society. Nevertheless, when attempting to analyze dynamics of complex multiscale systems, the usage of standard Deep Neural Networks (DNNs) and even standard Physics-Informed Neural Networks (PINNs) may lead to incorrect inferences and predictions, due to the presence of small scales leading to reduced or simplified models in the system that have to be applied consistently during the learning process. In this Chapter, we will address these issues in light of recent results obtained in the development of Asymptotic-Preserving Neural Networks (APNNs) for hyperbolic models with diffusive scaling. Several numerical tests show how APNNs provide considerably better results with respect to the different scales of the problem when compared with standard DNNs and PINNs, especially when analyzing scenarios in which only little and scattered information is available.
