DOODL learns a dictionary of spectral dynamics to approximate a manifold of related dynamical systems, enabling compact representations and improved operator estimation from short or partial trajectories.
Optimization on the biorthogonal manifold
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abstract
In this paper, we consider optimization problems w.r.t. to pairs of orthogonal matrices $XY = I$. Problems of this form arise in several applications such as finding shape correspondence in computer graphics. We show that the space of such matrices is a Riemannian manifold, which we call the biorthogonal manifold. To our knowledge, this manifold has not been studied before. We give expressions of tangent space projection, exponential map, and retraction operators of the biorthogonal manifold, and discuss their numerical implementation.
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Geometric Dictionary Learning of Dynamical Systems with Optimal Transport
DOODL learns a dictionary of spectral dynamics to approximate a manifold of related dynamical systems, enabling compact representations and improved operator estimation from short or partial trajectories.