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Lie Point Symmetry and Physics-Informed Networks
Advances in Neural Information Processing Systems 36, 2023 Symmetries have been leveraged to improve the generalization of neural networks through different mechanisms from data augmentation to equivariant architectures. However, despite their potential, their integration into neural solvers for partial differential equations (PDEs) remains largely unexplored.
Tara Akhound-Sadegh +4 more
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Lie point symmetries for reduced Ermakov systems [PDF]
Physics Letters A, 2004 Reduced Ermakov systems are defined as Ermakov systems restricted to the level surfaces of the Ermakov invariant. The condition for Lie point symmetries for reduced Ermakov systems is solved yielding four infinite families of systems. It is shown that SL(2,R) always is a group of point symmetries for the reduced Ermakov systems.
Haas, F., Goedert, J.
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Lie point symmetries and first integrals: The Kowalevski top [PDF]
Journal of Mathematical Physics, 2003 We show how the Lie group analysis method can be used in order to obtain first integrals of any system of ordinary differential equations. The method of reduction/increase of order developed by Nucci [J. Math. Phys. 37, 1772–1775 (1996)] is essential. Noether’s theorem is neither necessary nor considered.
Marcelli M., NUCCI, Maria Clara
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Lie point symmetries of the Lane–Emden systems
Journal of Mathematical Analysis and Applications, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bozhkov, Yuri +1 more
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Automorphisms of real Lie algebras of dimension five or less [PDF]
, 2013 The Lie algebra version of the Krull-Schmidt Theorem is formulated and proved. This leads to a method for constructing the automorphisms of a direct sum of Lie algebras from the automorphisms of its indecomposable components.
Gray, RJ +8 more
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Lie point and variational symmetries in minisuperspace Einstein gravity [PDF]
Journal of Physics A: Mathematical and Theoretical, 2014 Latex source file 20 pages, no ...
Christodoulakis, T. +2 more
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Algebraic Properties of First Integrals for Scalar Linear Third-Order ODEs of Maximal Symmetry
Abstract and Applied Analysis, 2013 By use of the Lie symmetry group methods we analyze the relationship between the first integrals of the simplest linear third-order ordinary differential equations (ODEs) and their point symmetries. It is well known that there are three classes of linear
K. S. Mahomed, E. Momoniat
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Lie symmetry and exact homotopic solutions of a non-linear double-diffusion problem
Frontiers in Physics, 2023 The Lie symmetry method is applied, and exact homotopic solutions of a non-linear double-diffusion problem are obtained. Additionally, we derived Lie point symmetries and corresponding transformations for equations representing heat and mass transfer in ...
R. A. Khan +5 more
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Finding nonlocal Lie symmetries algorithmically [PDF]
, 2023 Here we present a new approach to compute symmetries of rational second order ordinary differential equations (rational 2ODEs). This method can compute Lie symmetries (point symmetries, dynamical symmetries and non-local symmetries) algorithmically.
da Mota, L. A. C. P. +2 more
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Lie Group Analysis of a Flow with Contaminant-Modified Viscosity
Journal of Applied Mathematics, 2007 A class of coupled system of diffusion equations is considered. Lie group techniques resulted in a rich array of admitted point symmetries for special cases of the source term.
Raseelo J. Moitsheki
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