Research

My current postgraduate research project is related to Machine Learning (ML) and High Performance Computing (HPC), more specifically it is related to the use of HPC and artificial neural networks to solve differential equations that model and simulate physical phenomena.

The researches use the Santos Dumont supercomputer at LNCC, as part of the project AMPEMI.

Below are some links of interest to related works, mine and other authors.

1D Burgers PINN Discovery

Data-Driven Parameter Discovery of a One-Dimensional Burgers’ Equation Using a Physics-Informed Neural Network. This work evaluates the discovery of parameters of the Burgers’ equation through the use of PINN, for different hyperparameters and dataset sizes, seeking the best adjustment. The relative errors and processing times obtained are presented, running on the LNCC’s Santos Dumont supercomputer.

• Manuscript LaTeX sources: https://github.com/efurlanm/425/tree/main/manuscript
• Online version of the manuscript: https://efurlanm.github.io/425/
• Code repository: https://github.com/efurlanm/425/tree/main/project/
• DOI: 10.5281/zenodo.10676770

1D Burgers PINN GQM

Solution of a One-Dimensional Viscous Burgers' Equation Using a Physics-Informed Neural Network and a Gaussian Quadrature Method. This work compares the solutions of a one-dimensional viscous Burgers’ equation of a test problem using a Physics Informed Neural Network (PINN) and a numerical Gaussian Quadrature Method (GQM) method.

• Manuscript LaTeX sources: https://github.com/efurlanm/421/tree/main/manuscript
• Online version of the manuscript: https://efurlanm.github.io/421/
• Code repository: https://github.com/efurlanm/421/tree/main/project
• DOI: 10.5281/zenodo.10676900

My MSc work

This research project ran from 2019 to 2022 and resulted in three publications and a conference presentation. The theme of the work consists of implementing toy problems applying Python and Fortran resources in a High Performance Computing (HPC) environment, and evaluating the performance results. The material generated can be found at:

• Miranda, E. F. (2022). Common MPI-based HPC Approaches in Python Evaluated for Selected Test Cases. Master’s Thesis, National Institute for Space Research (INPE). http://urlib.net/ibi/QABCDSTQQW/46C4U9H

  • Thesis presentation: https://youtu.be/B_xOG9C04xs (in Portuguese)
  • Repository: https://github.com/efurlanm/msc22/
  • More information: https://efurlanm.github.io/msc22/

• Miranda, E. F., & Stephany, S. (2021). Comparison of High-performance Computing Approaches in the Python Environment for a Five-point Stencil Test Problem. XV Brazilian E-Science Workshop, at XLI Congress of the Brazilian Computer Society (CSBC-2021), 33–40. DOI: 10.5753/bresci.2021.15786

  • Source codes: https://github.com/efurlanm/bs21
  • Presentation DOI: 10.5281/zenodo.10672455 (in Portuguese)
  • Online version of the article: https://efurlanm.github.io/bs21

• Miranda, E. F., & Stephany, S. (2021a). Common HPC Approaches in Python Evaluated for a Scientific Computing Test Case. Revista Cereus, 13(2), 84–98. DOI: 10.18605/2175-7275/cereus.v13n2p84-98

My repositories

I maintain repositories at https://github.com/efurlanm with different subjects, such as:

• ml: repo dedicated to machine learning and also other random topics.
• 239, 351, etc. : repos containing several different activities from disciplines I took at INPE
• msc22, bs21, tama21: repos related to my publications during the course at INPE
• hpc: repo with subjects related to High Performance Computing (HPC)
• f90, ldi: repos targeted at computer programming languages
• teaching: repo dedicated to the materials of the disciplines I teach