Research
Research Interests
- 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.
Papers
Mamud, R.; MIGON, H. S. ; SILVA NETO, A. J. . PARAMETER ESTIMATION IN THE POLLUTANT DISPERSION PROBLEM WITH PHYSICS-INFORMED NEURAL NETWORKS. (Submitted).
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/
Conferences
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;