Research

• Inverse Problems: 

  • Source and Parameter Reconstruction in Partial Differential Equations

• Partial Differential Equations:

  • Semigroup Theory and Approximation of Operators in Banach Spaces;

  • Control Theory. 

• Numerical Analysis:

  • Classical Numerical Methods (Finite Diference Method (FDM), Finite Element Method (FEM) and Spectral Methods) applied to solve numerically Partial Differential Equations; 

  • Meshless Methods, in particular, the Method of Fundamental Solutions (MFS) to solve Direct Problems;

  • Machine Learning. Neural Networks. Physics-Informed and Bayesian Neural Networks.

• Silva, R. M. G. da, Migon, H. dos S., & Silva Neto, A. J. da. (2023). Parameter estimation in the pollutant dispersion problem with Physics-Informed Neural Networks. Ciência E Natura, 45(esp. 3), e74615. https://doi.org/10.5902/2179460X74615 

• Carlos J. S. Alves, Roberto Mamud, Nuno F. M. Martins, and Nilson C. Roberty, On inverse problems for characteristic sources in Helmholtz equations, Mathematical Problems in Engineering, 2017: https://www.hindawi.com/journals/mpe/aip/2472060/

Oral presentation:

• Mamud, R.; MIGON, H. S. ; SILVA NETO, A. J. . PARAMETER ESTIMATION IN THE POLLUTANT DISPERSION PROBLEM WITH PHYSICS-INFORMED NEURAL NETWORKS. In: XXV Encontro Nacional de Modelagem Computacional (XXV ENMC), XIII Encontro de Ciência e Tecnologia de Materiais (XIII ECTM), 9a Conferência Sul em Modelagem Computacional (9º MCSul) e o IX Seminário e Workshop em Engenharia Oceânica (IX SEMENGO), 2022. Anais do Encontro Nacional de Modelagem Computacional, Encontro de Ciência e Tecnologia de Materiais, Conferência Sul em Modelagem Computacional e Seminário e Workshop em Engenharia Oceânica.

• ALBANI, V. ; Mamud, R. ; MIGON, H. S. ; SILVA NETO, A. J. . Estimation of pollution sources with Physics-Informed Neural Network. 2022. (Apresentação de Trabalho/Congresso). ENCIT 2022.

• CNMAC, Congresso Nacional de Matemática Aplicada e Computacional - On the Reconstruction of Characteristic Sources in Helmholtz equations using the Method of Fundamental Solutions, (2016);

Poster presentation:

• ICMC Summer Meeting on Differential Equations - Inverse Source Reconstruction and Identification Problem in Elliptic Equations (2016), book of abstracts, 62;

• ICMC Summer Meeting on Differential Equations - Analytical Observability of Symmetric Star Shaped Sources for Modified Helmholtz Model (2014), book of abstracts, pg. 98;

• VII Encontro Nacional de Análise Matemática e Aplicações - ENAMA - Boundary observability of star shaped sources in the modified Helmholtz equation (2013), caderno de resumos, pág. 212 - 213;

• 5th LNCC Meeting on Computational Modeling - Parameters Reconstruction in Second Order Partial Differential Equations  (2012)

• VI Encontro Nacional de Análise Matemática e Aplicações - ENAMA - Estabilização de um sistema de Boussinesq do tipo KdV-KdV (2012), livro de resumos, pág. 189 - 190;