Soluções Numéricas de Equações Diferenciais com Redes Neurais Artificiais

José Miguel Aroztegui; Thiago José Machado

doi:10.14295/vetor.v31i2.13793

Authors

José Miguel Aroztegui UFPB
Thiago José Machado UFPB

DOI:

https://doi.org/10.14295/vetor.v31i2.13793

Keywords:

Neural networks, Differential equations, Optimization

Abstract

In this article, we study a way to numerically solve differential equations using neural networks. Basically, we rewrite the differential equation as an optimization problem, where the parameters related to the neural network are optimized. The proposal of this work constitutes a variation of the formulation introduced by Lagaris et al. [1], differing mainly in the form of the construction of the approximate solution. Although we only deal with first and second order ordinary differential equations, the numerical results show the efficiency of the proposed method. Furthermore, this method has a great potential, due to the amount of differential operators and applications in which it can be used.

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