Exploring Datasets to Solve Partial Differential Equations with TensorFlow

• Borzdynski, Oscar G. ^[1] ; Florentino Borondo ^{[1] [2]} ; Jezabel Curbelo ^{[1] [2]}
  1. [1] Universidad Autónoma de Madrid

     Universidad Autónoma de Madrid

     Madrid, España

     
  2. [2] Instituto de Ciencias Matemáticas

     Instituto de Ciencias Matemáticas

     Madrid, España

     
• Localización: 15th International Conference on Soft Computing Models in Industrial and Environmental Applications (SOCO 2020): Burgos, Spain ; September 2020 / coord. por Álvaro Herrero Cosío , Carlos Cambra Baseca , Daniel Urda Muñoz , Javier Sedano Franco , Héctor Quintián Pardo , Emilio Santiago Corchado Rodríguez , 2021, ISBN 978-3-030-57802-2, págs. 441-450
• Idioma: inglés
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• Resumen

  • This paper proposes a way of approximating the solution of partial differential equations (PDE) using Deep Neural Networks (DNN) based on Keras and TensorFlow, that is capable of running on a conventional laptop, which is relatively fast for different network architectures. We analyze the performance of our method using a well known PDE, the heat equation with Dirichlet boundary conditions for a non-derivable non-continuous initial function. We have tried the use of different families of functions as training datasets as well as different time spreadings aiming at the best possible performance. The code is easily modifiable and can be adapted to solve PDE problems in more complex scenarios by changing the activation functions of the different layers.