38 citations · 81 across the 15 of their papers we have counts for
8 papers · 1 filter
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…
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…
Symmetry Preserving Numerical Schemes for Partial Differential Equations and their Numerical Tests
Raphaël Rebelo, Francis Valiquette
The method of equivariant moving frames on multi-space is used to construct symmetry preserving finite difference schemes of partial differential equations invariant under finite-d…
Discretization of partial differential equations preserving their physical symmetries
Francis Valiquette, Pavel Winternitz
A procedure for obtaining a "minimal" discretization of a partial differential equation, preserving all of its Lie point symmetries is presented. "Minimal" in this case means that…