Differential Equations and Variational Methods on Graphs: With Applications to Machine Learning and Image...

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Yves van Gennip (Technische Universiteit Delft, The Netherlands) Jeremy Budd (University of Birmingham)

Differential Equations and Variational Methods on Graphs

Name: Differential Equations and Variational Methods on Graphs
Price: 196.74 AUD
Availability: OutOfStock
ISBN: 9781009556682

With Applications to Machine Learning and Image Analysis

Yves van Gennip (Technische Universiteit Delft, The Netherlands), Jeremy Budd (University of Birmingham)

$245.95 $196.74

Hardback

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English

Cambridge University Press
14 May 2026

Differential calculus & equations; Mathematical theory of computation; Machine learning

Series: Cambridge Monographs on Applied and Computational Mathematics

The burgeoning field of differential equations on graphs has experienced significant growth in the past decade, propelled by the use of variational methods in imaging and by its applications in machine learning. This text provides a detailed overview of the subject, serving as a reference for researchers and as an introduction for graduate students wishing to get up to speed.

The authors look through the lens of variational calculus and differential equations, with a particular focus on graph-Laplacian-based models and the graph Ginzburg-Landau functional. They explore the diverse applications, numerical challenges, and theoretical foundations of these models. A meticulously curated bibliography comprising approximately 800 references helps to contextualise this work within the broader academic landscape. While primarily a review, this text also incorporates some original research, extending or refining existing results and methods.

By: Yves van Gennip (Technische Universiteit Delft The Netherlands), Jeremy Budd (University of Birmingham)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Weight: 740g
ISBN: 9781009556682
ISBN 10: 1009556681
Series: Cambridge Monographs on Applied and Computational Mathematics
Pages: 389
Publication Date: 14 May 2026
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

1. Introduction; 2. Setup; 3. Important models on graphs; 4. Applications; 5. Implementation; 6. Connections between Allen–Cahn, MBO, and MCF; 7. Discrete-to-continuum convergence; 8. Connections with other fields and open questions; Appendix A. Γ-convergence; Appendix B. Steady states of two mass-conserving fidelity-forced diffusion equations; References; Index.

Yves van Gennip is Associate Professor in the Delft Institute of Applied Mathematics (DIAM) at Delft University of Technology. Jeremy Budd is Assistant Professor of Mathematics and its Applications at the University of Birmingham.