As computer system technology approaches the end of Moore's law, new computing paradigms that improve performance become a necessity. One such paradigm is approximate computing (AC). AC can present significant performance improvements, but a challenge lies in providing confidence that approximations will not overly degrade the application output quality. In AC, application domain experts manually identify code regions amenable to approximation. However, automatically guiding a developer where to apply AC is still a challenge. We propose Puppeteer, a novel method to rank code regions based on amenability to approximation. Puppeteer uses uncertainty quantification methods to measure the sensitivity of application outputs to approximation errors. A developer annotates possible application code regions and Puppeteer estimates the sensitivity of each region. Puppeteer successfully identifies insensitive regions on different benchmarks. We utilize AC on these regions and we obtain speedups of$1.18\times, 1.8\times$, and$1.3\times$for HPCCG. DCT, and BlackScholes, respectively.

As we approach the limits of Moore's law, researchers are exploring new paradigms for future high-performance computing (HPC) systems. Approximate computing has gained traction by promising to deliver substantial computing power. However, due to the stringent accuracy requirements of HPC scientific applications, the broad adoption of approximate computing methods in HPC requires an in-depth understanding of the application's amenability to approximations.

First-Principles Molecular Dynamics (FPMD) methods, although powerful, are notoriously expensive computationally due to the quantum modeling of electrons. Traditional FPMD approaches have typically been limited to a few thousand atoms at most, due to O(N3) or worse solver complexity and the large amount of communication required for highly parallel implementations. Attempts to lower the complexity have often introduced uncontrolled approximations or systematic errors. Using a robust new algorithm, we have developed an O(N) complexity solver for electronic structure problems with fully controllable numerical error. Its minimal use of global communications yields excellent scalability, allowing for very accurate FPMD simulations of more than a million atoms on over a million cores. At these scales, this approach provides multiple orders of magnitude speedup compared to the standard plane-wave approach typically used in condensed matter applications, without sacrificing accuracy. This will open up entire new classes of FPMD simulations, e.g. dilute aqueous solutions.