Machine Learning for Semi Linear PDEs
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Scientific Computing"
DOI: 10.1007/s10915-019-00908-3
Abstract: Recent machine learning algorithms dedicated to solving semi-linear PDEs are improved by using different neural network architectures and different parameterizations. These algorithms are compared to a new one that solves a fixed point problem by… read more here.
Keywords: semi linear; linear pdes; machine learning; learning semi ... See more keywords
On the reduction of high order linear PDEs to first order
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DOI: 10.1016/j.laa.2017.05.005
Abstract: Abstract Different first order representations of high order linear PDEs, depending on which notion of the degree of a polynomial is chosen, are possible. Two notions of degree, namely, the total degree and multi-degree, are… read more here.
Keywords: order linear; order; first order; linear pdes ... See more keywords
Polynomial solutions to linear PDEs with constant coefficients
Sign Up to like & getrecommendations! Published in 2019 at "Georgian Mathematical Journal"
DOI: 10.1515/gmj-2019-2017
Abstract: Abstract In this note we are concerned with the question: When are the polynomial solutions to a system of linear constant coefficient PDEs dense in the set of all its solutions? read more here.
Keywords: constant coefficients; pdes constant; polynomial solutions; linear pdes ... See more keywords