The Burgers equation is a well-established test case in the computational modeling of several phenomena such as fluid dynamics, gas dynamics, shock theory, cosmology, and others. In this work, we present the application of Physics-Informed Neural Networks (PINNs) with an implicit Euler transfer learning approach to solve the Burgers equation. The proposed approach consists in seeking a time-discrete solution by a sequence of Artificial Neural Networks (ANNs). At each time step, the previous ANN transfers its knowledge to the next network model, which learns the current time solution by minimizing a loss function based on the implicit Euler approximation of the Burgers equation. The approach is tested for two benchmark problems: the first with an exact solution and the other with an alternative analytical solution. In comparison to the usual PINN models, the proposed approach has the advantage of requiring smaller neural network architectures with similar accurate results and potentially decreasing computational costs.

通过使用物理信息神经网络（PINN）和隐式欧拉传递学习的方法，本文解决了Burgers方程。该方法使用一系列人工神经网络（ANNs）来寻求一个时间离散解，在每个时间步骤中，上一个ANN将它的知识传递给下一个网络模型，通过最小化基于Burgers方程隐式欧拉逼近的损失函数来学习当前时间的解。与常规的PINN模型相比，该方法具有较小的神经网络结构、类似准确的结果，并且有潜在降低计算成本的优势。

具有隐式欧拉转移学习的Burgers'方程针对问题