EVENTO
INTERPLAY OF PHYSICS-INFORMED NEURAL NETWORKS AND MULTISCALE NUMERICAL METHODS
Tipo de evento: Exame de Qualificação
PHYSICS-INFORMED NEURAL NETWORKS (PINNS) ARE MACHINE LEARNING TOOLS THAT APPROXIMATE THE SOLUTION OF GENERAL PARTIAL DIFFERENTIAL EQUATIONS (PDES) BY ADDING THEM IN SOME FORM AS TERMS OF THE LOSS/COST FUNCTION OF A NEURAL NETWORK. MOST PIECES OF WORK IN PINNS TACKLE NON-LINEAR PDES. NEVERTHELESS, MANY INTERESTING PROBLEMS INVOLVING LINEAR PDES MAY BENEFIT FROM PINNS; THESE INCLUDE PARAMETRIC STUDIES, MULTI-QUERY PROBLEMS, AND PARABOLIC (TRANSIENT) PDES. THE PURPOSE OF THIS WORK IS TO EXPLORE PINNS FOR LINEAR PDES WHOSE SOLUTIONS MAY PRESENT CHALLENGES TO CLASSICAL NUMERICAL METHODS , SUCH AS THOSE WITH SHARP CONTRAST FEATURES OR HIGHLY OSCILLATORY COEFFICIENTS. MORE SPECIFICALLY, WE ARE INTERESTED IN THE INTERPLAY OF PINNS AND DOMAIN DECOMPOSITION TECHNIQUES PRESENT IN MULTISCALE NUMERICAL METHODS TO EFFICIENTLY APPROXIMATE THE PDES LOCALLY AT EACH PARTITION OF THE SPATIOTEMPORAL DOMAIN. AS PROOF OF CONCEPT, WE EXPLORED THE STEADY-STATE REACTION-ADVECTION-DIFFUSION EQUATION IN BOUNDARY LAYER REGIMES IN WHICH THE DIFFUSIVE COEFFICIENT IS SMALL IN COMPARISON WITH THE REACTIVE OR ADVECTIVE COEFFICIENTS . WE SHOWED THAT ADDING INFORMATION ABOUT THESE COEFFICIENTS AS PREDICTOR VARIABLES IN A PINN RESULTS IN BETTER PREDICTION MODELS THAN A PINN THAT ONLY USES SPATIAL INFORMATION AS PREDICTOR VARIABLES. THIS IS INDICATIVE THAT A PDE MAY BE APPROXIMATED LOCALLY BY A PINN IN A PARTITIONED DOMAIN WITHOUT RESORTING TO DIFFERENT LEARNED PINN MODELS AT EACH OF ITS PARTITIONS. BESIDES, EVEN THOUGH USING EQUATION COEFFICIENTS WHEN TRAINING A PINN MODEL IS A COMMON STRATEGY FOR INVERSE PROBLEMS, CONSIDERING THESE COEFFICIENTS FOR PARAMETRIC DIRECT PROBLEMS IS STILL IN ITS INFANCY.Pra assistir acesse:meet.google.com/xfw-fppv-hff
Data Início: 19/12/2022 Hora: 09:00 Data Fim: 19/12/2022 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 Fabio Andre Machado Porto - Laboratório Nacional de Computação Científica - LNCC Pablo Javier Blanco - Laboratório Nacional de Computação Científica - LNCC
