Lie Group Cohomology and (Multi)Symplectic Integrators: New Geometric Tools for Lie Group Machine Learning Based on Souriau Geometric Statistical Mechanics [PDF]
Entropy, 2020 In this paper, we describe and exploit a geometric framework for Gibbs probability densities and the associated concepts in statistical mechanics, which unifies several earlier works on the subject, including Souriau’s symplectic model of statistical ...
Frédéric Barbaresco +1 more
doaj +9 more sources
Lie Group Statistics and Lie Group Machine Learning Based on Souriau Lie Groups Thermodynamics & Koszul-Souriau-Fisher Metric: New Entropy Definition as Generalized Casimir Invariant Function in Coadjoint Representation [PDF]
Entropy, 2020 In 1969, Jean-Marie Souriau introduced a “Lie Groups Thermodynamics” in Statistical Mechanics in the framework of Geometric Mechanics. This Souriau’s model considers the statistical mechanics of dynamic systems in their “space of evolution” associated to
Frédéric Barbaresco
doaj +9 more sources
Higher Order Geometric Theory of Information and Heat Based on Poly-Symplectic Geometry of Souriau Lie Groups Thermodynamics and Their Contextures: The Bedrock for Lie Group Machine Learning [PDF]
Entropy, 2018 We introduce poly-symplectic extension of Souriau Lie groups thermodynamics based on higher-order model of statistical physics introduced by Ingarden. This extended model could be used for small data analytics and machine learning on Lie groups.
Frédéric Barbaresco
doaj +8 more sources
Survey on Lie Group Machine Learning
Big Data Mining and Analytics, 2020 Lie group machine learning is recognized as the theoretical basis of brain intelligence, brain learning, higher machine learning, and higher artificial intelligence. Sample sets of Lie group matrices are widely available in practical applications.
Mei Lu, Fanzhang Li
doaj +4 more sources
A Combination of Lie Group Machine Learning and Deep Learning for Remote Sensing Scene Classification Using Multi-Layer Heterogeneous Feature Extraction and Fusion [PDF]
Remote Sensing, 2022 Discriminative feature learning is the key to remote sensing scene classification. Previous research has found that most of the existing convolutional neural networks (CNN) focus on the global semantic features and ignore shallower features (low-level ...
Chengjun Xu, Guobin Zhu, Jingqian Shu
doaj +4 more sources
Alexandria Engineering Journal, 2023 When a consistent transverse magnetic field and heat radiation are present, the flow of boundary layer, Over porous wedge nanofluids, hybrid nanofluids, and ternary hybrid nanofluids have been studied., Water as base fluid, Hybrid nanofluid, Ternary ...
M. Dinesh Kumar +5 more
doaj +4 more sources
Rating Triggers for Collateral-Inclusive XVA via Machine Learning and SDEs on Lie Groups [PDF]
arXiv.org, 2022 In this paper, we model the rating process of an entity by using a geometrical approach. We model rating transitions as an SDE on a Lie group. Specifically, we focus on calibrating the model to both historical data (rating transition matrices) and market data (CDS quotes) and compare the most popular choices of changes of measure to switch from the ...
Kamm, Kevin, Muniz, Michelle
semanticscholar +5 more sources
Machine learning based state observer for discrete time systems evolving on Lie groups [PDF]
Engineering Applications of Artificial IntelligenceIn this paper, a machine learning based observer for systems evolving on manifolds is designed such that the state of the observer is restricted to the Lie group on which the system evolves. Conventional techniques involving machine learning based observers on systems evolving on Lie groups involve designing charts for the Lie group, training a machine
Soham Shanbhag, Dong Eui Chang
semanticscholar +5 more sources
Discovering sparse representations of Lie groups with machine learning [PDF]
Physics Letters B, 2023 Recent work has used deep learning to derive symmetry transformations, which preserve conserved quantities, and to obtain the corresponding algebras of generators. In this letter, we extend this technique to derive sparse representations of arbitrary Lie algebras.
Forestano, Roy T. +5 more
+7 more sources
A Lie Group Laplacian Support Vector Machine for Semi-Supervised Learning
NeurocomputingYue Zhang +3 more
semanticscholar +4 more sources