An MIT math professor recently broke the record for the largest ever Compute Engine cluster, with 220,000 cores on Preemptible VMs, the largest known high-performance computing cluster to ever run in the public cloud.
Andrew V. Sutherland is a computational number theorist and Principal Research Scientist at MIT, and is using Compute Engine to explore generalizations of the Sato-Tate Conjecture and the conjecture of Birch and Swinnerton-Dyer to curves of higher genus. In his latest run, he explored 1017hyperelliptic curves of genus 3 in an effort to find curves whose L-functions can be easily computed, and which have potentially interesting Sato-Tate distributions. This yielded about 70,000 curves of interest, each of which will eventually have its own entry in the L-functions and Modular Forms Database (LMFDB).
It also requires a lot of compute cycles: For each curve that’s examined, its discriminant must be computed; the discriminant of a curve serves as an upper bound on the complexity of computing its L-function. This task is trivial in genus 1, but in genus 3 may involve evaluating a 50 million term polynomial in 15 variables. Each curve that’s a candidate for inclusion in the LMFDB must also have many other of its arithmetic and geometric invariants computed, including an approximation of its L-function and Sato-Tate distribution, as well as information about any symmetries it may possess. The results can be quite large, and some of this information is stored as Cloud Storage nearline objects. Researchers can browse summaries of the results on the curve’s home page in the LMFDB, or download more detailed information to their own computer for further examination. The LMFDB provides an online interface to some 400 gigabytes of metadata housed in a MongoDB database that also runs on Compute Engine.
Sutherland began using Compute Engine in 2015. For his first-ever job, he fired up 2,250 32-core instances and completed about 60 CPU-years of computation in a single afternoon.
Before settling on Compute Engine, Sutherland ran jobs on his own 64-core machine, which could take months, or wrangled for compute time on one of MIT’s clusters. But getting the number of cores he needed often raised eyebrows, and he was limited by the software configurations he could use. By running on Compute Engine, Sutherland can install exactly the operating system, libraries and applications he needs, and thanks to root access, he can update his environment at will.
Sutherland considered running his jobs on AWS before choosing Google but was dissuaded by its Spot Instances model, which forces you to name your price up front, with prices that can vary significantly by region and fluctuate over time. A colleague encouraged him to try Compute Engine Preemptible VMs. These are full-featured instances that are priced up to 80% less than regular equivalents, but can be interrupted by Compute Engine. That was fine with Sutherland. His computations are embarrassingly parallel — they can be easily separated into multiple, independent tasks — and he grabs available instances across any and all Google Cloud Regions. An average of about 2-3% of his instances are typically preempted in any given hour, but a simple script automatically restarts them as needed until the whole job is complete.
To coordinate the instances working on a job, Sutherland uses a combination of Cloud Storage and Datastore. He used the python client API to implement a simple ticketing system in Datastore that assigns tasks to instances. Instances periodically checkpoint their progress on their local disks from which they can recover if preempted, and they store their final output data in a Cloud Storage bucket, where it may undergo further post-processing once the job has finished.
All told, having access to the scale and flexibility of Compute Engine has freed Sutherland up to think much bigger with his research. For his next run, he hopes to expand his search to non-hyperelliptic curves of genus 3, breaking his own record with a 400,000-core cluster. “It changes your whole outlook on research when you can ask a question and get an answer in hours rather than months,” he said. “You ask different questions.”