The arrival of exascale computers will open new frontiers in our ability to simulate highly complex engineered and natural systems. This will create new opportunities for the design and optimisation of new, highly integrated engineered systems for the future. It will also allow the development of 'digital twins' of complex natural systems, such has the human body and coastal/river regions, that will allow is to explore and manage engineering-led interventions in personalised healthcare and management of the natural environment. The exascale computers of the future will be highly parallel with hundreds of thousands, or millions of processes, working collectively. Exploiting this remarkable level of parallelism will require dramatic advances in the mathematics, numerical methods, software engineering and software tools that underpin simulation, and will depend on experts in each of these areas coming together. The simulation of the different but tightly coupled physical processes that characterises complex engineered and natural systems poses additional challenges of coordinating the simulation of multiple processes, such as the noise created by an airflow flow around a moving structure under the influence of a magnetic field, or the fluid, solid, electrical and chemical interactions a human body. This project brings together of working group of experts from computer science, mathematics and engineering to address the challenge of how to simulate coupled physical process at a system level on future exascale systems. It will also address how to integrate into the simulation process the vast quantity of data that can be collected from real systems, how to assess uncertainties and how to interpret the vast quantities of data that exascale simulations will generate. The working group will formulate roadmaps for enabling research for exascale computing, and support research software engineer training for exascale-ready software skills.