论文标题
用于求解非线性扩散率和BIOT方程的物理信息神经网络
Physics-informed Neural Networks for Solving Nonlinear Diffusivity and Biot's equations
论文作者
论文摘要
本文提出了应用物理信息的神经网络来解决非线性多物理问题的潜力，这对于许多领域，例如生物医学工程，地震预测和地下能量收集至关重要。具体而言，我们研究了如何扩展物理知识神经网络的方法，以解决与非线性扩散性和BIOT方程相关的正向和反向问题。我们探讨了具有不同训练的示例大小和超参数的选择的物理知识神经网络的准确性。还研究了各种训练实现之间随机变化的影响。在反情况下，我们还研究了嘈杂测量的效果。此外，我们解决了选择反向模型的超参数的挑战，并说明了如何将这种挑战链接到针对前向的挑战。
This paper presents the potential of applying physics-informed neural networks for solving nonlinear multiphysics problems, which are essential to many fields such as biomedical engineering, earthquake prediction, and underground energy harvesting. Specifically, we investigate how to extend the methodology of physics-informed neural networks to solve both the forward and inverse problems in relation to the nonlinear diffusivity and Biot's equations. We explore the accuracy of the physics-informed neural networks with different training example sizes and choices of hyperparameters. The impacts of the stochastic variations between various training realizations are also investigated. In the inverse case, we also study the effects of noisy measurements. Furthermore, we address the challenge of selecting the hyperparameters of the inverse model and illustrate how this challenge is linked to the hyperparameters selection performed for the forward one.
