# Partial Differential Equations for Modelling, Analysing and Simulating Data Rich Phenomena

Cambridge, 14-16 December, 2015

Main organisers: José Antonio Carrillo, Charlie Elliott, Yves van Gennip, Peter Markowich, Carola-Bibiane Schönlieb

Partial differential equations (PDE) are used in data science in different ways, either directly —e.g. for data assimilation, image processing and analysis, shape analysis, inverse problems, computer vision, crowd motion, opinion formation, and option pricing— or as inspiration of formulations and solutions of data problems on graphs and networks — e.g. the use of graph-discretised PDE for classification and community detection, linking graph and continuum models via Gamma-convergence.

This workshop brings together expert mathematicians and statisticians, working on nonlinear, nonlocal, and stochastic PDE models and on large, complex network problems, with industrial and academic data science users. Informal presentations and breakout sessions will identify promising research directions combining PDE and data science, such that the former can benefit from a wide variety of new and relevant questions, while the latter gains access to a range of strong methods.

Key questions:

- 1. Which directions of novel PDE approaches in data sciences are most promising?
- 2. What are the data science problems appropriate for PDE techniques?
- 3. Which numerical PDE based approaches are scalable to very large data sets?
- 4. How can model based PDE or variational inverse problems be used for dimension reduction of high dimensional data sets?
- 5. Which simple, analysable PDE models are capable of describing complex data phenomena?
- 6. How can stochastic PDE be used to assimilate new data into nonlinear or nonlocal models?

Key topics:

- 1. The role of nonlinear, nonlocal, or stochastic PDE models in data science
- 2. Theoretical insights and computational advances gained from the interplay between PDE and network models
- 3. Applications to science, society, and industry.
- 4. Open questions and future directions for nonlinear, nonlocal, and stochastic PDE in the data sciences, including novel interdisciplinary collaborations, e.g. with topological data analysis.