使用物理信息神经网络在早期和晚期对逆流自发渗吸进行模拟与预测
Simulation and Prediction of Countercurrent Spontaneous Imbibition at Early and Late Times Using Physics-Informed Neural Networks
AI总结：
本文首次利用物理信息神经网络（PINNs）求解一维逆流自发渗吸问题，提出基于物理启发的变量替换方法将问题表述为三种等价形式，有效降低了非线性，提升了求解精度与计算效率。
摘要：
本文首次研究了物理信息神经网络（PINNs）在求解一维逆流自发渗吸（COUCSI）早期和晚期问题（即渗吸前缘遇到不流动边界之前和之后）中的应用。我们引入了变量替换技术来提升PINNs的性能。通过改变自变量，我们将COUCSI问题表述为三种等价形式：第一种将饱和度描述为归一化位置X和时间T的函数；第二种描述为X和Y=T^0.5的函数；第三种仅作为Z=X/T^0.5的函数（仅在早期有效）。PINN模型使用前馈神经网络生成，并通过最小化加权损失函数进行训练，该函数包括物理信息损失项以及对应初始和边界条件的项。三种形式均能紧密近似正确解，在早期阶段，XT和XY形式的水饱和度平均绝对误差分别约为0.019和0.009，Z形式约为0.012。Z形式完美捕捉了系统早期的自相似性，而XT和XY形式对此捕捉较弱。饱和度的总变差在Z形式中得以保持，且XY形式比XT形式保持得更好。基于物理启发变量重新定义问题，降低了问题的非线性程度，实现了更高的求解精度、更高程度的损失景观凸性、更少的所需配置点、更小的网络规模以及更具计算效率的解。
英文摘要：
The application of Physics-Informed Neural Networks (PINNs) is investigated for the first time in solving the one-dimensional Countercurrent spontaneous imbibition (COUCSI) problem at both early and late time (i.e., before and after the imbibition front meets the no-flow boundary). We introduce utilization of Change-of-Variables as a technique for improving performance of PINNs. We formulated the COUCSI problem in three equivalent forms by changing the independent variables. The first describes saturation as function of normalized position X and time T; the second as function of X and Y=T^0.5; and the third as a sole function of Z=X/T^0.5 (valid only at early time). The PINN model was generated using a feed-forward neural network and trained based on minimizing a weighted loss function, including the physics-informed loss term and terms corresponding to the initial and boundary conditions. All three formulations could closely approximate the correct solutions, with water saturation mean absolute errors around 0.019 and 0.009 for XT and XY formulations and 0.012 for the Z formulation at early time. The Z formulation perfectly captured the self-similarity of the system at early time. This was less captured by XT and XY formulations. The total variation of saturation was preserved in the Z formulation, and it was better preserved with XY- than XT formulation. Redefining the problem based on the physics-inspired variables reduced the non-linearity of the problem and allowed higher solution accuracies, a higher degree of loss-landscape convexity, a lower number of required collocation points, smaller network sizes, and more computationally efficient solutions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
