Burgers' pinns with implicit euler transfer learning
Vitória Biesek Pedro Henrique de Almeida Konzen
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.