Results 151 to 160 of about 59,568 (301)
Universal connection and curvature for statistical manifold geometry
, 2005 Statistical manifolds are representations of smooth families of probability density functions that allow differential geometric methods to be applied to problems in stochastic processes, mathematical statistics and information theory.
Dodson, CTJ +2 more
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, 2023 This paper deals with the applications of an optimization method on submanifolds, that is, geometric inequalities can be considered as optimization problems.
Alkhaldi, Ali Hussain +3 more
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Advanced Engineering Materials, EarlyView.We develop a data‐driven method to derive the mathematical expressions of the Flory–Huggins interaction parameter χ for the swelling behavior of temperature–responsive hydrogels. Starting from initial assumptions of χ, our workflow combines Bayesian optimization, Flory–Rehner theory, and symbolic regression to generate candidate χ expressions.
Yawen Wang +2 more
wiley +1 more source
Inequality Constraints on Statistical Submanifolds of Norden-Golden-like Statistical Manifold
This paper explores novel inequalities for statistical submanifolds within the framework of the Norden golden-like statistical manifold. By leveraging the intrinsic properties of statistical manifolds and the structural richness of Norden golden geometry,
Majid Ali Choudhary +3 more
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Geometry of statistical manifolds
Differential Geometry and its Applications, 1992 A statistical manifold \((M,g,\nabla)\) is a Riemannian manifold \((M,g)\) equipped with torsion-free affine connections \(\nabla,\nabla^*\) which are dual with respect to \(g\). A point \(p\in M\) is said to be \(\nabla\)- isotropic if the sectional curvatures have the same value \(k(p)\), and \((M,g,\nabla)\) is said to be \(\nabla\)-isotropic when \(
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Advanced Engineering Materials, EarlyView.Do not let thermal drift and instrument artifacts deceive high‐temperature nanoindentation results. We compare classical Oliver–Pharr and automatic image recognition analyses across steels and a Ni alloy to quantify these effects. Accounting for artifacts reveals systematic softening with temperature, while Cr and Ni additions boost resistance ...
Velislava Yonkova +2 more
wiley +1 more source
Probabilistic learning on manifold for optimization under uncertainties
, 2017 Plenary LectureInternational audienceThis paper presents a challenging problem devoted to the probabilistic learning on manifold for the optimization under uncertainties and a novel idea for solving it.
Ghanem, Roger, Soize, Christian
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Homogeneous statistical manifolds
Information GeometryThe methods of Information geometry have been glowing up to develop various subjects of theoretical physics, including quantum information systems. The present article has two purposes. The first one is to develop general theory of homogeneous statistical manifolds.
Inoguchi, Jun-ichi, Ohno, Yu
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Optimization of the Production of Rubber Compounds Using Mathematical Models
Advanced Engineering Materials, EarlyView.Rubber compounds were mixed in a batch internal mixer, and symbolic regression was used to derive mathematical models linking recipe and process parameters to ram path, torque, and mixing quality (incorporation, dispersion, distribution). Subsequent optimization with evolutionary algorithms identified operating conditions that reduce specific energy ...
Anke Bardehle +7 more
wiley +1 more source
Machine Learning on Statistical Manifold
, 2017 This senior thesis project explores and generalizes some fundamental machine learning algorithms from the Euclidean space to the statistical manifold, an abstract space in which each point is a probability distribution.
Zhang, Bo
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