TY - GEN
T1 - A Novel Deep Learning Method for Solving PDE’s Applied to a Shallow Water Problem
AU - Palacios-García, Jose
AU - Ibarra-Fiallo, Julio
AU - Espín-Torres, Sevando
N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.
PY - 2025
Y1 - 2025
N2 - In this work we explain and implement a method that uses an artificial neural network to solve differential equations numerically. The method was applied to a model of the flow of water in an open channel described by the Saint-Venant Equations (SVE). These equations constitute a system of partial differential equations. The method was implemented in Python using the libraries Numpy and Pytorch to manage matrix operations and the construction of the artificial neural network. The results of the method were compared with a common numerical method using RK1, where an average relative error of 4,05% was obtained. The results show that the proposed method has a promising performance in the resolution of partial differential equations, especially because of the versatility that it offers to define boundary conditions in complex geometries. The execution time was comparable to traditional methods, thanks to common performance enhancements developed for training artificial neural networks. Possible improvements for further research are mentioned.
AB - In this work we explain and implement a method that uses an artificial neural network to solve differential equations numerically. The method was applied to a model of the flow of water in an open channel described by the Saint-Venant Equations (SVE). These equations constitute a system of partial differential equations. The method was implemented in Python using the libraries Numpy and Pytorch to manage matrix operations and the construction of the artificial neural network. The results of the method were compared with a common numerical method using RK1, where an average relative error of 4,05% was obtained. The results show that the proposed method has a promising performance in the resolution of partial differential equations, especially because of the versatility that it offers to define boundary conditions in complex geometries. The execution time was comparable to traditional methods, thanks to common performance enhancements developed for training artificial neural networks. Possible improvements for further research are mentioned.
KW - Gradient Descent
KW - Neural Networks
KW - Numerical Methods for Partial Differential Equations
KW - Partial Differential Equations
UR - https://www.scopus.com/pages/publications/105003903293
U2 - 10.1007/978-3-031-85902-1_15
DO - 10.1007/978-3-031-85902-1_15
M3 - Contribución a la conferencia
AN - SCOPUS:105003903293
SN - 9783031859014
T3 - Communications in Computer and Information Science
SP - 149
EP - 157
BT - Scientific Computing and Bioinformatics and Computational Biology - 22nd International Conference, CSC 2024, and 25th International Conference, BIOCOMP 2024, Held as Part of the World Congress in Computer Science, Computer Engineering and Applied Computing, CSCE 2024
A2 - Hodson, Douglas D.
A2 - Grimaila, Michael R.
A2 - Wagner, Torrey J.
A2 - Arabnia, Hamid R.
A2 - Deligiannidis, Leonidas
PB - Springer Science and Business Media Deutschland GmbH
T2 - 22nd International Conference on Scientific Computing and Bioinformatics, CSC 2024, and 25th International Conference on Computational Biology, BIOCOMP 2024, held as part of the World Congress in Computer Science, Computer Engineering and Applied Computing, CSCE 2024
Y2 - 22 July 2024 through 25 July 2024
ER -