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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 of the work developed:

RADNN

Research related to the use of physics-based machine learning (PIML) in climate and climatic models schemes.

PINN and SINDy 1D Burgers'

Qualification and Proposal Exam. Comparison of the accuracy and processing time of PINN and a standard numerical method (SINDy) in the inverse and direct problem for the 1D Burgers problem, analysis of the size of the dataset and hyperparameters in the performance of PINN and proposal for a study of the use of PIML in the radiation module of an atmospheric model.

PINN Discovery 1D Burgers'

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.

PINN GQM 1D Burgers'

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.

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:

Publications

2023

  • Miranda, E. F., Santos, L. B. L., & Stephany, S. (2023). Data-Driven Parameter Discovery of a One-Dimensional Burgers’ Equation Using a Physics-Informed Neural Network [Manuscript]. DOI: 10.5281/zenodo.10676770 .

2022

  • 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). URI: http://urlib.net/ibi/QABCDSTQQW/46C4U9H .

  • Miranda, E. F., & Stephany, S. (2022). Common MPI-Based Solutions for High-Performance Processing in Python Evaluated on Selected Test Cases [Presentation]. DOI: 10.5281/zenodo.10676832 .

  • Miranda, E. F. (2022). Solution of a One-Dimensional Viscous Burgers' Equation Using a Physics-Informed Neural Network and a Gaussian Quadrature Method [Manuscript]. DOI: 10.5281/zenodo.10676900 .

  • Miranda, E. F. (2022). Comparison of CNN and MLP Artificial Neural Network Models for an Optical Character Recognition Test Case [Manuscript]. DOI: 10.5281/zenodo.10676917 .

2021

  • 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 .

  • Miranda, E. F., & Stephany, S. (2021). 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 .

  • Miranda, E. F., & Stephany, S. (2021). Comparison of high-performance computing approaches in the Python environment for a five-point stencil case study. XV Brazilian e-Science Workshop (BreSci), Online [Presentation]. DOI: 10.5281/zenodo.10672456 .




Last edited: 2024-11-18