Reliable Numerical Computation with Parallel Unreliable Technologies

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Imagine a world where mathematical dynamical models of processes in medicine, transport, finance and energy, are routinely constructed and refined, on the fly, by personalised hardware devices. With sufficient computational power, such devices could make intelligent decisions, for example utilising advanced control techniques for real-time intervention in diabetic patients and for pacemakers or defibrilators, or to automatically re-route personalised transport options based on up-to-the-minute information. The vision is a powerful one, but highlights many limitations of today's digital technologies, limitations that will not be overcome with simple scaling of technology, but which need a fundamental rethink of the way in which massively parallel computation can be performed. The focus of this proposal is therefore not on any one of the above grand challenges, but rather on the fundamental scientific problems enabling this revolution. The proposed research could enable computation at orders of magnitude better energy/performance ratio than would be possible by extending today's techniques to tomorrow's technologies, opening up a step change in current practices at both the low power end of computation (sophisticated personal devices) and the high power end (advancements in computational physics, chemistry, biology and finance).Over the next decade, there will be a number of radical shifts to the way in which computation is performed. In particular, rather than computing with a single computational core equipped with a numerical computational unit, or with a traditional inter-processor network of such cores, two differences are becoming increasingly apparent. Firstly, if we allow process technology to scale at the rate it could, then each computational device will become increasingly unreliable. Secondly, under the same assumption, this lack of reliability will be compensated by massive parallelism. Independently, each of these issues requires considerable research effort to overcome the lack of reliability and the current inability to make efficient use of massive parallelism in a portable manner, and there is much ongoing international research in these distinct fast-moving areas.These seemingly distinct challenges, however, have an untapped common research core. Massive parallelism in numerical computation mandates a way to effectively deal with numerical imprecision in computation, even in fully reliable circuitry. One must have in mind a specification of tolerable numerical accuracy. Once such a specification exists, and can be formalised, it opens up the potential to use this specification as input to a powerful specialised optimising compiler, capable of optimising numerical hardware and software in order to achieve the specification with maximum performance within a given power envelope. Lack of reliability in future devices will propagate to numerical computation as noticeable numerical errors in the hardware. One way of overcoming these errors is to utilise parallelism in some kind of redundant fashion. A radical alternative is to `hide' the numerical errors caused by unreliable components within the tolerance specification already required. For a fixed silicon area, the emerging multi-core revolution in computational hardware brings to the fore a tension between numerical precision and computational performance; one can no longer afford to pay the price in performance for over-designed hardware.At the core of this research will therefore be the development of mathematical techniques to reason about the compilation of numerical software into parallel hardware, broadening applicability to general classes of nonlinear and control-intensive algorithms, requiring the application of nonlinear systems theory to reason about the convergence of classes of algorithm under numerical perturbation, and mechanising algebraic approaches to reasoning about accuracy in numerical algorithms.