4. Conclusions

This work evaluates data-driven parameter discovery for a one-dimensional Burgers' equation using a Physics-Informed Neural Network (PINN). The Burgers' equation is a fundamental partial differential equation (PDE) with derivatives in space and time, which is commonly solved by a numerical method. An evaluation of the relative error and required training time, performed in SDumont, is also presented for different hyperparameters and dataset sizes. It was possible to observe that adjusting the hyperparameters and the size of the dataset is important for obtaining performance when using PINN. The implementation also proved to be relatively simple, and the results easy to obtain. As deep learning technology continues to grow rapidly, both in terms of methodological and algorithmic developments, this could be a timely contribution that can benefit a wide range of scientific domains. As future work, it would be interesting to explore other PINN architectures, as well as taking advantage of the parallel use of GPU.

Acknowledgment

Authors thank LNCC (National Laboratory for Scientific Computing) for grant 205341 AMPEMI (call 2020-I), which allows access to the Santos Dumont supercomputer (node of the SINAPAD, the Brazilian HPC system).