Related papers: Un-reduction
Stable concurrent learning and control of dynamical systems is the subject of adaptive control. Despite being an established field with many practical applications and a rich theory, much of the development in adaptive control for nonlinear…
Manifold optimization is ubiquitous in computational and applied mathematics, statistics, engineering, machine learning, physics, chemistry and etc. One of the main challenges usually is the non-convexity of the manifold constraints. By…
Many high-dimensional optimisation problems exhibit rich geometric structures in their set of minimisers, often forming smooth manifolds due to over-parametrisation or symmetries. When this structure is known, at least locally, it can be…
Problems in differentiable rendering often involve optimizing scene parameters that cause motion in image space. The gradients for such parameters tend to be sparse, leading to poor convergence. While existing methods address this sparsity…
This work introduces an unconventional inexact augmented Lagrangian method where the augmenting term is a Euclidean norm raised to a power between one and two. The proposed algorithm is applicable to a broad class of constrained nonconvex…
This paper develops the theory of Dirac reduction by symmetry for nonholonomic systems on Lie groups with broken symmetry. The reduction is carried out for the Dirac structures, as well as for the associated Lagrange-Dirac and…
We present a theory for Euclidean dimensionality reduction with subgaussian matrices which unifies several restricted isometry property and Johnson-Lindenstrauss type results obtained earlier for specific data sets. In particular, we…
Energy minimization algorithms, such as graph cuts, enable the computation of the MAP solution under certain probabilistic models such as Markov random fields. However, for many computer vision problems, the MAP solution under the model is…
A complete understanding of physical systems requires models that are accurate and obeys natural conservation laws. Recent trends in representation learning involve learning Lagrangian from data rather than the direct discovery of governing…
A new approach to relativistic mechanics is proposed, suitable to describe dynamics of different kinds of relativistic particles. Mathematically it is based on an application of the recent geometric theory of nonholonomic systems on fibred…
Constrained blackbox optimization is a difficult problem, with most approaches coming from the mathematical programming literature. The statistical literature is sparse, especially in addressing problems with nontrivial constraints. This…
We consider optimization problems on manifolds with equality and inequality constraints. A large body of work treats constrained optimization in Euclidean spaces. In this work, we consider extensions of existing algorithms from the…
Traditional lens design is a numerical and forward process based on ray tracing and aberration theory. This method has limitations because the initial configuration of the lens has to be specified and the aberrations of the lenses have to…
This paper presents a millisecond-level look-ahead control algorithm for energy storage with constant space complexity and worst-case linear run-time complexity. The algorithm connects the optimal control with the Lagrangian multiplier…
A geometric approach to integrability and reduction of dynamical system is developed from a modern perspective. The main ingredients in such analysis are the infinitesimal symmetries and the tensor fields that are invariant under the given…
We introduce a mathematical technique based on modifying a given Riemannian metric and we investigate its applicability to controlling and stabilizing constrained mechanical systems. In essence our result is based on the construction of a…
This article presents a unified synchronization framework with application to precision formation flying spacecraft. Central to the proposed innovation, in applying synchronization to both translational and rotational dynamics in the…
Although much research has been devoted to the problem of restoring Poissonian images, namely in the fields of medical and astronomical imaging, applying the state of the art regularizers (such as those based on wavelets or total variation)…
UMAP (Uniform Manifold Approximation and Projection) is a novel manifold learning technique for dimension reduction. UMAP is constructed from a theoretical framework based in Riemannian geometry and algebraic topology. The result is a…
The aim of the present text is twofold: to provide a compendium of Lagrangian and Hamiltonian geometries and to introduce and investigate new analytical Mechanics: Finslerian, Lagrangian and Hamiltonian. The fundamental equations (or…