In order to help answer the questions in game changers 1 to 4 new multiscale computational and mathematical methods will be required. Multiscale mathematical models will help to mechanistically interpret the interactions and causal relations between biological molecules, cells, organisms and their environment. Chemical, biological, physical and astrophysical observations, experiments and simulations will produce expanding streams of big data, which must be integrated in order to generate new knowledge. The resulting multiscale mathematical models and multiscale data science methods will need to cover temporal scales from nanoseconds (chemistry) and hours (e.g., cell division) to billions of years (formation and evolution of planets and life), and spatial scales ranging from nanometers (chemistry) to tens of thousands of kilometers (planets). The aim of this game changer is to enforce breakthroughs within a time frame of five to ten years in the development of new computational and mathematical methods for multiscale modeling, simulation, and analysis of large, complex data.
For the geological and planetary sciences, better scale integration will enable new breakthroughs in formation and evolution of planets and their satellites, in particular of the earth. In this context, this game changer aims to model the multilevel coupling between the physicochemical mechanisms in the interior of the planet on the one hand, and the biosphere, hydrosphere and atmosphere on the other hand. This will lead to new insights into the mechanisms of global change, including climate change, changes in earth magnetisms, and plate tectonics that drive earthquakes. For the biological and physical sciences, these developments will help us understand how molecules can self-organise into self-replicating, living cells, how cells can join forces to form multicellular tissues and organisms, and how organisms form ecosystems. For the mathematical sciences, a key long-term interest is to predict collective behavior from individual behavior, and to develop the mathematical tools to analyze, in a rigorous manner, the range of behaviors that a collective system can exhibit. Another interest concerns the development of fast and accurate multiscale numerical methodology, ranging from multigrid PDEs to agent-based simulation algorithms. For computational and data science, a key interest is mutliscale data integration. New methodology should allow us to correlate events occurring in a large range of data sets at fast and small scales to larger trends occurring over longer times, or sudden rare, catastrophic events. Examples including prediction of earthquakes from seismological or other data, or prediction of large scale ecological catastrophic from observations in the ecosystem at smaller and faster time scales (early warnings). Here mathematical techniques will focus on causality and potentially: control of the system, whereas data science techniques focus on correlation and potentially: prediction of the system. The hope is that a combination of mathematical and computational techniques can help us exert the right level of control on complex ecological or geophysical systems at the right moment (prediction).
In order to achieve these aims, upscaling of capacity and accessibility of the national computing facilities is required. Modern High Performance Computing (HPC) enables numerical techniques including automated adaptive meshing, and massive parallel computing thanks to superfast interprocessor communication allowing numerical solutions to problems involving hundreds of millions of variables.
Realizing these breakthroughs requires, however, liberal access to large HPC systems containing millions of computing cores.