These are lecture notes for various Summer and Winter schools that I have given. The notes describe the methodology called Variational Modelling, and focus on the application to the modelling of gradient-flow systems. I describe the methodology itself in great detail, and explain why this is a rational modelling route. A central example is diffusion, in combination with various other processes, and a large part of the notes are devoted to this phenomenon. In the Variational Modelling methodology, diffusion is commonly modelled by including entropic terms in the driving functional and Wasserstein-type terms in the dissipation. I explain how to understand these objects, motivate them from more basic models, and how to use them in new situations.
@article{arxiv.1402.1990,
title = {Variational Modelling: Energies, gradient flows, and large deviations},
author = {Mark A. Peletier},
journal= {arXiv preprint arXiv:1402.1990},
year = {2014}
}