EVENTO
Interplay of Physics-Informed Neural Networks and Multiscale Numerical Methods
Tipo de evento: Seminário de Avaliação - Série A
Physics-Informed Neural Networks (PINNs) are machine learning tools that approximate the solution of general Partial Differential Equations (PDEs) by adding them, in some way, as terms from the loss/cost function of a Neural Network (NN). The goal of this work is to explore the PINNs strategy for the resolution of PDE systems whose solutions present challenges for classical numerical methods when applied to physical models containing multiple scales. Typical examples are models with heterogeneous coefficients (oscillatory or high contrast) or singularly perturbed models (boundary layers). Initially, we assess the capacity of vanilla PINNs for approximating these models. We then investigated the reaction-advection-diffusion equation in boundary layers, and by incorporating physical coefficients as predictor variables in a PINN, we are able to obtain good predictions, suggesting potential for parametric studies. However, for highly oscillatory problems, we can observe a substantial impact on the results of PINNs, which fail to adequately approximate problems with multiple scales. Therefore, to mitigate the effects of these oscillations, we propose an approach to combine the Multiscale Hybrid-Mixed (MHM) method, which has mathematically proven properties, into conventional PINNs. In summary, within the MHM method, multiscale basis functions on the coarse mesh are obtained by solving completely independent local problems. Here, we propose an approach to estimate these multiscale basis functions through PINN models. Thus, the model is adjusted to generate subsequent basis functions, adapting to the structure and characteristics provided by the local domain, without relying solely on a previous set of training samples. Through numerical validations, we show the ability to approximate the basis functions for Poisson and Helmholtz problems.Para assistir acesse:meet.google.com/zps-recy-mwn
Data Início: 14/12/2023 Hora: 09:00 Data Fim: 14/12/2023 Hora: 12:00
Local: LNCC - Laboratório Nacional de Computação Ciêntifica - Virtual
Aluno: Larissa Miguez da Silva - - LNCC
Orientador: Antônio Tadeu Azevedo Gomes - Laboratório Nacional de Computação Científica - LNCC Frédéric Gerard Christian Valentin - Laboratório Nacional de Computação Científica - LNCC
Participante Banca Examinadora: Alvaro Luiz Gayoso de Azeredo Coutinho - Universidade Federal do Rio de Janeiro - COPPE/UFRJ Antônio Tadeu Azevedo Gomes - Laboratório Nacional de Computação Científica - LNCC Fabio André Machado Porto - Laboratório Nacional de Computação Científica - LNCC
Suplente Banca Examinadora: Gilson Antônio Giraldi - Laboratório Nacional de Computação Científica - LNCC
