Information geometry of dynamics on graphs and hypergraphs
書誌事項
- 公開日
- 2023-12-22
- 資源種別
- journal article
- 権利情報
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- https://creativecommons.org/licenses/by/4.0
- https://creativecommons.org/licenses/by/4.0
- DOI
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- 10.1007/s41884-023-00125-w
- 10.48550/arxiv.2211.14455
- 公開者
- Springer Science and Business Media LLC
この論文をさがす
説明
<jats:title>Abstract</jats:title><jats:p>We introduce a new information-geometric structure associated with the dynamics on discrete objects such as graphs and hypergraphs. The presented setup consists of two dually flat structures built on the vertex and edge spaces, respectively. The former is the conventional duality between density and potential, e.g., the probability density and its logarithmic form induced by a convex thermodynamic function. The latter is the duality between flux and force induced by a convex and symmetric dissipation function, which drives the dynamics of the density. These two are connected topologically by the homological algebraic relation induced by the underlying discrete objects. The generalized gradient flow in this doubly dual flat structure is an extension of the gradient flows on Riemannian manifolds, which include Markov jump processes and nonlinear chemical reaction dynamics as well as the natural gradient. The information-geometric projections on this doubly dual flat structure lead to information-geometric extensions of the Helmholtz–Hodge decomposition and the Otto structure in <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^{2}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math></jats:alternatives></jats:inline-formula>-Wasserstein geometry. The structure can be extended to non-gradient nonequilibrium flows, from which we also obtain the induced dually flat structure on cycle spaces. This abstract but general framework can broaden the applicability of information geometry to various problems of linear and nonlinear dynamics.</jats:p>
収録刊行物
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- Information Geometry
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Information Geometry 7 (1), 97-166, 2023-12-22
Springer Science and Business Media LLC
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キーワード
- Mathematics - Differential Geometry
- Chemical Physics (physics.chem-ph)
- FOS: Computer and information sciences
- Computer Science - Information Theory
- Information Theory (cs.IT)
- FOS: Physical sciences
- Mathematics - Statistics Theory
- Statistics Theory (math.ST)
- Differential Geometry (math.DG)
- Physics - Chemical Physics
- Physics - Data Analysis, Statistics and Probability
- FOS: Mathematics
- Data Analysis, Statistics and Probability (physics.data-an)
詳細情報 詳細情報について
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- CRID
- 1360302866831725696
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- ISSN
- 2511249X
- 25112481
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- 資料種別
- journal article
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- データソース種別
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- Crossref
- KAKEN
- OpenAIRE
