Many modern industrial research and development problems involve a mixture of deterministic and stochastic dynamics where the principal challenge is the quantification and management of uncertainty at all levels of the product development cycle. Problems dealing with optimisation of stochastic processes, hierarchical modelling and coarse-graining, uncertainty quantification, model selection and risk assessment appear with increasing frequency at industry-academic meetings such as the regular Study Groups with Industry organised by the Smith Institute.

The classical framework of deterministic mathematical modelling in which a problem is reduced to an ordinary or partial differential equation to be solved by a mathematical scientist is inappropriate for such problems due to the high level of noise. Purely data-driven analyses based on the framework of classical statistics are equally unhelpful since they often under-emphasise the generative mechanisms underlying observed phenomena and lead to a proliferation of poorly understood "black boxes".

A mathematical modelling framework in which stochastic processes play a central role is essential to making progress in solving such problems. This requires the ability to combine the insight and understanding obtained from the mathematical analysis of deterministic mathematical models with the power of modern statistical inference to constrain the parameters and complexity of such models even in the presence of high levels of uncertainty or noise.

The academic expertise to frame such problems already exists within mathematics and statistics departments in the UK and at the University of Warwick in particular. A new generation of mathematical scientists are currently completing their PhDs in the likes of Warwick's Centre for Complexity Science and MASDOC Centre for Doctoral Training where mathematical modelling, analysis and statistical inference are taught side by side.

This one-day meeting at the Isaac Newton Institute brought together representatives from UK industry with early career researchers and PhD students to establish relationships which will facilitate the transfer of expertise in both directions across the academia-industry interface in the mathematical sciences.

Aims and Objectives

The aims of the meeting were:

• To form new links, and to strengthen existing links, between industry and academia based around a common interest in stochastic and statistical modelling of industrial problems. This would assist mathematical sciences departments in the UK to demonstrate the impact of their research expertise outside of academia.
• To expose PhD students to industrial problems which require mathematical expertise at an early stage of their careers with the ultimate objective of improving the pool of mathematical expertise available to the UK's industrial base.
• To allow academics to advertise cutting-edge work in the mathematical sciences to UK industry and vice versa in an environment which provided space for meaningful discussions to take place.
• To frame a set of suggestions/recommendations of how the flow of expertise between UK industry and academia in the mathematical sciences can be supported in the future.