Related papers: Symmetry preserving parameterization schemes
Applying Lie symmetry method, we find the most general Lie point symmetries group of the radiation natural convection flow equation(RNC). Looking the adjoint representation of the obtained symmetry group on its Lie algebra, we will find the…
The solution of a class of third order ordinary differential equations possessing two parameter Lie symmetry group is obtained by group theoretic means. It is shown that reduction to quadratures is possible according to two scenarios: 1) if…
Group-invariant probability distributions appear in many data-generative models in machine learning, such as graphs, point clouds, and images. In practice, one often needs to estimate divergences between such distributions. In this work, we…
The choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data,…
Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…
Extraction of structure, in particular of group symmetries, is increasingly crucial to understanding and building intelligent models. In particular, some information-theoretic models of parsimonious learning have been argued to induce…
The aim of this paper is to study symmetries of linearly singular differential equations, namely, equations that can not be written in normal form because the derivatives are multiplied by a singular linear operator. The concept of…
We explore the role of group symmetries in binary classification tasks, presenting a novel framework that leverages the principles of Neyman-Pearson optimality. Contrary to the common intuition that larger symmetry groups lead to improved…
Symmetry, which describes invariance, is an eternal concern in mathematics and physics, especially in the investigation of solutions to the partial differential equation (PDE). A PDE's nonlocally related PDE systems provide excellent…
We present a novel framework to overcome the limitations of equivariant architectures in learning functions with group symmetries. In contrary to equivariant architectures, we use an arbitrary base model such as an MLP or a transformer and…
This Letter probes the existence of physical laws invariant only in average when subjected to some transformation. The concept of a symmetry transformation is broadened to include corruption by random noise and average symmetry is…
Two new approaches to solving first-order quasilinear elliptic systems of PDEs in many dimensions are proposed. The first method is based on an analysis of multimode solutions expressible in terms of Riemann invariants, based on links…
Reparametrization invariance being treated as a gauge symmetry shows some specific peculiarities. We study these peculiarities both from a general point of view and on concrete examples. We consider the canonical treatment of…
In this paper, Lie symmetry group method is applied to find the lie point symmetries group of a PDE system that is determined general form of four-dimensional Einstein Walker manifold. Also we will construct the optimal system of…
We analyze the classical equations of motion for a particle moving in the presence of a static magnetic field applied in the $ z $ direction, which varies as $ {1\over{x^2}} $. We find the symmetries through Lie's method of group analysis.…
A definition of invariance in Lie's sense for a boundary value problem (BVP) with the basic evolution differential equations is proposed. A problem of group classification at a wide class of BVPs parameterized by arbitrary elements is…
In this paper, it is shown how a combination of approximate symmetries of a nonlinear wave equation with small dissipations and singularity analysis provides exact analytic solutions. We perform the analysis using the Lie symmetry algebra…
In the present paper, a class of partial differential equations related to various plate and rod problems is studied by Lie transformation group methods. A system of equations determining the generators of the admitted point Lie groups…
Many Euclidean Einstein manifolds possess continuous symmetry groups of at least one parameter and we consider here a classification scheme of $d$ dimensional compact manifolds based on the existence of such a one parameter group in terms…
We suggest two metrics for assessing the quality of atomistic configurations of disordered materials, both of which are based on quantifying the orientational distribution of neighbours around each atom in the configuration. The first…