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The Burgers equation is a well-established test case in the computationalmodeling of several phenomena such as fluid dynamics, gas dynamics, shocktheory, cosmology, and others. In this work, we present the application ofPhysics-Informed Neural Networks (PINNs) with an implicit Euler transferlearning approach to solve the Burgers equation. The proposed approach consistsin 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 nextnetwork model, which learns the current time solution by minimizing a lossfunction based on the implicit Euler approximation of the Burgers equation. Theapproach is tested for two benchmark problems: the first with an exact solutionand the other with an alternative analytical solution. In comparison to theusual PINN models, the proposed approach has the advantage of requiring smallerneural network architectures with similar accurate results and potentiallydecreasing computational costs.

Burgers' pinns with implicit euler transfer learning