Differential Equations and Variational Methods on Graphs With Applications to Machine Learning and Image Analysis
Book contents
- Frontmatter
- Contents
- Acknowledgments
- 1 Introduction
- 2 Set-up
- 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
1 - Introduction
Published online by Cambridge University Press: 24 April 2026
Book contents
- Frontmatter
- Contents
- Acknowledgments
- 1 Introduction
- 2 Set-up
- 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
Summary
This book presents a snapshot of a field that, at the time of writing in the early 2020s, is very active and developing into different directions – ranging from rigorous theoretical studies to very concrete applications in various other areas; a field that can broadly be characterised as the mathematical study of differential equations and variational methods on graphs and their applications to machine learning, image processing, and image analysis.
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- Differential Equations and Variational Methods on GraphsWith Applications to Machine Learning and Image Analysis, pp. 1 - 17Publisher: Cambridge University PressPrint publication year: 2026
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