From digital hype to analogue reality: Universal simulation beyond the quantum and exascale eras

•When machine learning is applied in ignorance of fundamental laws of nature, it is likely to deliver unreliable answers.•With his colleagues, Peter Coveney has described the computational algorithms best suited for deployment on exascale architectures.•In the exascale era, we will combine models of the human heart and blood circulation to describe the cardiovascular system at the scale of a body.•Beyond the quantum and exascale computer eras, the future of simulation will rely more on analogue computing than has hitherto been expected. Many believe that the future of innovation lies in simulation. However, as computers are becoming ever more powerful, so does the hyperbole used to discuss their potential in modelling across a vast range of domains, from subatomic physics to chemistry, climate science, epidemiology, economics and cosmology. As we are about to enter the era of quantum and exascale computing, machine learning and artificial intelligence have entered the field in a significant way. In this article we give a brief history of simulation, discuss how machine learning can be more powerful if underpinned by deeper mechanistic understanding, outline the potential of exascale and quantum computing, highlight the limits of digital computing – classical and quantum – and distinguish rhetoric from reality in assessing the future of modelling and simulation, when we believe analogue computing will play an increasingly important role.