Physics-informed neural networks (PINNs) have gained significant prominence
as a powerful tool in the field of scientific computing and simulations. Their
ability to seamlessly integrate physical principles into deep learning
architectures has revolutionized the approaches to solving complex problems in
physics and engineering. However, a persistent challenge faced by mainstream
PINNs lies in their handling of discontinuous input data, leading to
inaccuracies in predictions. This study addresses these challenges by
incorporating the discretized forms of the governing equations into the PINN
framework. We propose to combine the power of neural networks with the dynamics
imposed by the discretized differential equations. By discretizing the
governing equations, the PINN learns to account for the discontinuities and
accurately capture the underlying relationships between inputs and outputs,
improving the accuracy compared to traditional interpolation techniques.
Moreover, by leveraging the power of neural networks, the computational cost
associated with numerical simulations is substantially reduced. We evaluate our
model on a large-scale dataset for the prediction of pressure and saturation
fields demonstrating high accuracies compared to non-physically aware models.

通过将离散化的微分方程融入到 PINN 框架中，改进物理信息神经网络在处理不连续输入数据方面的准确性，并减少数值模拟的计算成本。