Machine Learning for Inverse Problems and Data Assimilation
It targets researchers in inverse problems and data assimilation by offering a mathematical perspective on machine learning, but it is incremental as it primarily reviews and synthesizes existing ideas.
The paper introduces machine learning concepts to researchers in inverse problems and data assimilation, providing a mathematical framework to bridge these fields.
The aim of these notes is to demonstrate the potential for ideas in machine learning to impact on the fields of inverse problems and data assimilation. The perspective is one that is primarily aimed at researchers from inverse problems and/or data assimilation who wish to see a mathematical presentation of machine learning as it pertains to their fields. As a by-product, we include a succinct mathematical treatment of various fundamental underpinning topics in machine learning, and adjacent areas of (computational) mathematics.