Variational Modelling：能量、梯度流和大偏差
Variational Modelling: Energies, gradient flows, and large deviations
摘要：
这些是我给过的各种夏季和冬季学校的讲义。这些注释描述了称为变分建模的方法，并侧重于梯度流系统建模的应用。我非常详细地描述了方法本身，并解释了为什么这是一个理性的建模路线。一个中心的例子是扩散，与其他各种过程相结合，大部分的笔记都致力于这种现象。在变分建模方法中，扩散通常通过在驱动泛函中包括熵项和在耗散中包括Wasserstein型项来建模。我解释了如何理解这些对象，从更基本的模型中激发它们，以及如何在新的情况下使用它们。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
