10 papers
Discovering PDEs equivariant under rigid motions
Francesco Ballerin, Erlend Grong
We consider the problem of PDE discovery from possibly noisy observations under the hypothesis that the underlying dynamic is symmetric in all rigid motions. Rather than using a ge…
Effective normalization of sub-Riemannian connections
Erlend Grong, Jan Slovak
We give a new normalization condition for connections on sub-Riemannian manifolds with constant symbols. The condition is formulated in terms of Cartan connections and depends only…
Equivariant nonlinear partial differential operators on constant curvature spaces
Francesco Ballerin, Erlend Grong
Motivated by PDE-learning, we give a classifying space for nonlinear partial differential operators equivariant under the action of isometries. This classifying space is for operat…
SO(3)-Equivariant Neural Networks for Learning from Scalar and Vector Fields on Spheres
Francesco Ballerin, Nello Blaser, Erlend Grong
Analyzing scalar and vector fields on the sphere, such as temperature or wind speed and direction on Earth, is a difficult task. Models should respect both the rotational symmetrie…
Most probable paths for developed processes
Erlend Grong, Stefan Sommer
Optimal paths for the classical Onsager-Machlup function determining most probable paths between points on a manifold are only explicitly identified for specific processes, for exa…
Filtered complexes and cohomologically equivalent subcomplexes
Erlend Grong, Francesca Tripaldi
Inspired by Rumin's work on a subcomplex in sub-Riemannian manifolds which is cohomologically equivalent to the de Rham complex, we present a more general construction that produce…