Differential Equations and Variational Method by Yves van Gennip(.PDF)
File Size: 13.0 MB
Differential Equations and Variational Methods on Graphs: With Applications to Machine Learning and Image Analysis (Cambridge Monographs on Applied and Computational Mathematics) by Yves van Gennip, Jeremy Budd
Requirements: .PDF reader, 13.0 MB
Overview: 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.
The field of Machine Learning is concerned with the development of methods and algorithms to analyse data sets. ‘Learning’ in this context refers to the leveraging of properties of some collection of ‘training data’ (which may or may not be a part of the data set which is to be analysed) to draw conclusions about the data set. Machine Learning has taken an enormous flight in the twenty-first century. If it was not already part of the public consciousness due to the commercial success of the many tech companies that exist by the grace of data availability and the methods to learn from the data, then the enormous speed with which Deep Learning via Artificial Neural Networks is penetrating many areas of science, industry, and public and private life has ensured that terms like ‘Big Data’, ‘Machine Learning’, and ‘Artificial Intelligence’ have become commonplace for many people. Scientific curiosity goes hand-in-hand with a societal need to understand the methods that play such a big role in so many sectors.
Genre: Non-Fiction > Educational
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