Exploring Datasets to Solve Partial Differential Equations with TensorFlow

Autor: Oscar G. Borzdynski, Florentino Borondo, Jezabel Curbelo
Přispěvatelé: Universitat Politècnica de Catalunya. Departament de Matemàtiques
Rok vydání: 2020
Předmět:
0209 industrial biotechnology
TensorFlow
Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcials [Àrees temàtiques de la UPC]
Computer science
Neural Network
02 engineering and technology
symbols.namesake
020901 industrial engineering & automation
0202 electrical engineering
electronic engineering
information engineering
Code (cryptography)
Network architecture
Partial differential equation
Artificial neural network
Equacions en derivades parcials
business.industry
Deep learning
Function (mathematics)
Differential equations
Partial
Dirichlet boundary condition
symbols
020201 artificial intelligence & image processing
Heat equation
Partial derivative equations
Artificial intelligence
business
35 Partial differential equations [Classificació AMS]
Algorithm
Keras
Zdroj: Advances in Intelligent Systems and Computing ISBN: 9783030578015
SOCO
UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)
DOI: 10.1007/978-3-030-57802-2_42
Popis: The version of record is available online at: http://dx.doi.org/10.1007/978-3-030-57802-2_42 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. This work has been partially supported by the Spanish Ministry of Science, Innovation and Universities, Gobierno de España, under Contracts No. PGC2018-093854-BI00, and ICMAT Severo Ochoa SEV-2015-0554, and from the People Programme (Marie Curie Actions) of the European Union’s Horizon 2020 Research and Innovation Program under Grant No. 734557.
Databáze: OpenAIRE
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