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2024 | OriginalPaper | Chapter

Physics Informed Cellular Neural Networks for Solving Partial Differential Equations

Authors : Angela Slavova, Elena Litsyn

Published in: New Trends in the Applications of Differential Equations in Sciences

Publisher: Springer Nature Switzerland

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Abstract

Physics-Informed Neural Networks (PINNs) are a scientific machine learning technique used to solve a broad class of problems. PINNs approximate problems’ solutions by training a neural network to minimize a loss function; it includes terms reflecting the initial and boundary conditions along the space-time domain’s boundary. PINNs are deep learning networks that, given an input point in the integration domain, produce an estimated solution in that point of a differential equation after training. The basic concept behind PINN training is that it can be thought of as an unsupervised strategy that does not require labelled data, such as results from prior simulations or experiments. In this paper we generalize the idea of PINNs for solving partial differential equations by introducing physics informed cellular neural networks (PICNNs). We shall present example of the solutions of reaction-diffusion obtained by PICNNs. The advantages of the proposed new method are in the fastest algorithms and real time solutions.

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previous chapter Graphical Portraits of the Solutions of Binary First Order Nonlinear Ordinary Differential Equation Near Their Singular Point
next chapter Several Relationships Connected to a Special Function Used in the Simple Equations Method (SEsM)
Literature
1.
F.Chen, D. Sondak, P. Protopapas, et al. Neurodiffeq: A python package for solving differential equations with neural networks. J. Open Source Softw. 5:46, 1931, 2020.
2.
L.O.Chua, L. Yang. Cellular Neural Network: Theory and Applications. IEEE Trans. CAS. vol. 35, p.1257, 1988.
3.
L. Lu, X. Meng, Z. Mao, et al. DeepXDE: A deep learning library for solving differential equations. SIAM Rev. 63:1, 208–228, 2021.
4.
S. Mishra, R. Molinaro. Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs. IMA J. Numer. Anal. ,2021.
5.
S.Mishra, R. Molinaro. Estimates on the generalization error of physics-informed neural networks for approximating PDEs. IMA J. Numer. Anal., p drab093, 2022.
6.
M. Raissi, P. Perdikaris, G.E.Karniadakis. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. 378, 686–707, 2019.
7.
Y. Shin, J.Darbon, G.E.Karniadakis. On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs. Commun. Comput. Phys. 28:5, 2042–2074, 2020.
8.
A.Slavova. Cellular Neural Networks: Dynamics and Modelling, Kluwer Academic Publishers, 2003.
Metadata
Title
Physics Informed Cellular Neural Networks for Solving Partial Differential Equations
Authors
Angela Slavova
Elena Litsyn
Copyright Year
2024
Book
New Trends in the Applications of Differential Equations in Sciences

Print ISBN: 978-3-031-53211-5

Electronic ISBN: 978-3-031-53212-2

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-3-031-53212-2_3

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