Burgers' pinns with implicit euler transfer learning
This work addresses computational modeling challenges in fluid dynamics and related fields, but it is incremental as it builds on existing PINN methods with a transfer learning twist.
The authors tackled solving the Burgers equation using Physics-Informed Neural Networks (PINNs) with an implicit Euler transfer learning approach, resulting in smaller neural network architectures with similar accuracy and potentially lower computational costs compared to standard PINNs.
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.