The Food System is stretched to breaking point with current demands for food close to exceeding the planet’s capacity to supply. Projections suggest a worsening of this trend with a growing population, an increase in extreme weather events and the huge amount of food we currently waste. In addition only 50% of people globally are a healthy body weight. Urgent restructuring of the food system is required to make it environmentally, economically and socially sustainable. The proposed research at the interface of mathematical modelling and data science, particularly focused on understanding non linearities in the food system, will provide insights into where the risks are in the current system and what action is needed to avoid them. The non linearities we are particularly interested in are trade offs, feedback loops and tipping points. If we can parameterise models of the food system which include these non linearities then we can use our understanding of the underlying mathematics to determine how to use take advantage of these non linearities to make small changes in order to make large gains.