38 citations · 81 across the 15 of their papers we have counts for
16 papers
Moving Frames for Lie Pseudo-groups: A Recursive Implementation
Peter J. Olver, Francis Valiquette
A new recursive implementation of the equivariant moving frame method for infinite-dimensional Lie pseudo-group actions is presented. It allows pseudo-group normalizations to be pe…
Convergence of Normal Form Power Series for Infinite-Dimensional Lie Pseudo-Group Actions
Peter J. Olver, Masoud Sabzevari, Francis Valiquette
We prove the convergence of normal form power series for suitably nonsingular analytic submanifolds under a broad class of infinite-dimensional Lie pseudo-group actions. Our theore…
Invariant Physics-Informed Neural Networks for Ordinary Differential Equations
Shivam Arora, Alex Bihlo, Francis Valiquette
Physics-informed neural networks have emerged as a prominent new method for solving differential equations. While conceptually straightforward, they often suffer training difficult…
Normal forms, moving frames, and differential invariants for nondegenerate hypersurfaces in C^2
Peter J. Olver, Masoud Sabzevari, Francis Valiquette
We use the method of equivariant moving frames to revisit the problem of normal forms and equivalence of nondegenerate real hypersurfaces M \subset C^2 under the pseudo-group actio…
Invariant Variational Schemes for Ordinary Differential Equations
Alex Bihlo, James Jackaman, Francis Valiquette
We propose a novel algorithmic method for constructing invariant variational schemes of systems of ordinary differential equations that are the Euler-Lagrange equations of a variat…
Invariants of Surfaces in Three-Dimensional Affine Geometry
Örn Arnaldsson, Francis Valiquette
Using the method of moving frames we analyze the algebra of differential invariants for surfaces in three-dimensional affine geometry. For elliptic, hyperbolic, and parabolic point…