Extreme scale computational simulation techniques

Current computational models in diverse areas of science can simulate systems with up to ~1E12 discrete
degrees of freedom. Some of the largest models being for atomistic molecular dynamics of materials
plasticity, cracking, or transport of molecules across membranes in bio-systems; climate and weather
modelling using hydrodynamic models and ensembles of models; galactic and cosmological gravitational
evolution using tree and fast multipole summation methods for long range forces. These approaches require
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substantial parallel supercomputer resources and modern simulation algorithms (featuring as some of the
major applications on the world top 500 supercomputers, and driving active development in many leading
research groups and national laboratories world wide. The best of these methods scale linearly with the size
of the system or duration of the modelled processes.
There are however a few approaches which require computational resources that scale far better than linear,
either when increasing simulated system size (accessing exponentially larger systems) or simulated system
timescale (enabling investigation of qualitatively different long time phenomena). Perhaps the best known
examples are the renormalisation group methods and Gosper's 'hashlife' acceleration of cellular automata. In
these techniques, either an approximate hierarchical transformation of the model under study is made to
increasingly longer and longer length scales, or an exact 'recycling' of intermediate results is performed to
exponentially accelerate the time evolution of the model. In both cases, improved and strongly sub-linear
scaling has been demonstrated when studying processes like phase transitions or dynamics of Turing
complete rule sets.
This proposal aims for another >1E12 step-change in performance for general physical simulation techniques
via a new stable of such strongly sub-linear approaches, and to bring these techniques to the general
theoretical and computational audience. The development of general approaches to efficiently study systems
contain examples of approximately repeating motifs occurring in different spatial regions and occurring on
different length scales. In the former case this includes self similar regions of a crystal undergoing dynamical
processes (deposition of atoms, crack nucleation and propagation, ...), or the repeat of molecular machinery
across both one biological cell and between cells in a population (ribosomes, mitochondria, channel proteins
in cell membranes, ...).
The objectives for this project are centred on
* Demonstration of meaningful speed up for summations of general long range
interactions via a new hybrid exploitation of multiscale and self-similar
spatial structure. Development of a simulation software library for
self-similar representations within and across scales and the managed
recycling of interactions will be a key outcome of this objective (enabling
both dissemination of these ideas and the opening up of commercialisation of
this approach, perhaps via existing licensing contact to Dassault Systèmes.).
* Demonstration of robust acceleration of local interactions in kinetic models,
showing sub-linear scaling across both length and time scale via an innovative
controlled approximate multiscale Green's function method. Provisional results
of this approach were presented for the Ising model at an invited talk, IMRC
conference 2015, but here we will generalise to a much wider range of
molecular and discrete lattice models.