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*What can we do with bespoke, effectively free random number generation? *

The future of probabilistic computing with such a novel capability stands to revolutionize how we approach problems. We may enable fundamental advantages over problems best approached today with deterministic methods. One such example could be turbulent flow modeling. These are typically modeled expensively in whole scale or through (still expensive) reduced order type models that utilize aggregate behavior over partitioned domains. As both are expensive, probabilistic approaches are often not considered feasible due to the added Monte Carlo cost. On the other hand, particle methods, like direct simulation Monte Carlo (DSMC) used in numerous aerodynamic and fluid problems, are already a strong consumer of probability. An ability to represent a whole DSMC simulation as a probabilistic computing circuit could provide the means for high fidelity simulation of critical problems with the potential for new and innovative intrusive uncertainty quantification.

Beyond simulation, COINFLIPS stands to impact AI tasks through improved Bayesian learning. State-of-the-art Bayesian neural networks train stochastic weights or activation functions using Bayesian inference techniques. The training inevitably requires sampling from a posterior distribution – a distribution that is updated with gained knowledge. This distribution is often complicated and high-dimensional. While such a distribution can be sampled with Monte Carlo techniques, most practitioners opt to sample from simplifications. If COINFLIPS can eliminate bulky rejection sampling schemes or accelerate posterior sampling through efficient Monte Carlo methods, large-scale Bayesian learning will become feasible.

The distribution of probabilistic applications COINFLIPS can impact is infinitely supported with heavy tails. To guide our co-design approach for generating useful and ubiquitous random numbers, we have chosen to focus on two aspects of heavy ion colliding physics: simulation of jets and jet triggering & detection. The former is a mod/sim problem and the latter is a classification and learning problem.

Quantum chromodynamics, in general, has accelerated understanding of the proton, driven by the study of its components and how those components contribute toward the spin, momentum, and other transport properties of the proton. Both our understanding of the transport properties in the perturbative quantum chromodynamics regime and other proton subcomponent attributes are active areas of research. These require data on the various sub-components of a proton in order to study transport properties like spin asymmetries and cross sections – a probability measure for particular colliding processes to occur. One tool to acquire such data is through simulation of proton collisions through methods similar to cosmic ray Monte Carlo. When a proton collides with another proton or ion at relativistic speeds under the right conditions, the quarks and gluons are liberated and undergo a hadronization process where they decay into hadrons. The distribution of these hadrons, termed a jet, can be measured by a special detector called a calorimeter. In a typical simulation of such a collision, on the order of 200K uniform random numbers are drawn. In order to understand the physics, scientists need to simulate up to billions of collisions!

During simulation, random number generation can account for more than 40% of simulation time. Uniform random numbers drawn in this simulation are typically converted to samples from some to some other distribution, like the exponential. This can occur through a rejection sampling process. While random number generation or conversion is certainly not the most complicated operation in the code, this is a key example of how heavy consumers of random number generation can be dramatically accelerated through efficient distribution sampling.

**The COINFLIPS team aims to impact simulation of jets by providing the devices, circuits, and algorithms to accelerate random number sampling from the necessary distributions.**

Jets can also be measured via calorimeters through experiment with colliders. The Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory is one such collider. RHIC can accelerate two particles in opposite directions along a 2.4-mile track. At intersections along the track, particles travelling in opposite directions have a chance to collide. Again, if a collision occurs in just the right way, a jet can be measured by a calorimeter. Data must be able to be acquired at the rate particles pass through the intersection points, which is about 10 MHz, or about 10 million events per second. This is quite extreme and would produce a lot of data if ran for any amount of time. Not all crossings are going to produce collisions too, meaning that if all data were kept a large portion of it would not be jets from collisions. In order to save only the most important data, a trigger examines data and determines whether to send it off for analog-digital conversion and saving. A so-called fast trigger capable of examining and ‘triggering on’ data at fast speeds is the STAR trigger.

Once data is acquired, the hadron energy patterns must be sifted through with only the most relevant parts separated from any underlying events. This second process is called **jet finding**. The process of data acquisition and jet finding currently happen separately or on different time scales. Ideally, the saving, or triggering, of data and the jet finding could happen at the same time or could be done with more intelligence, targeting explicit hadrons of interest. Such an approach would require probabilistic and machine learning approaches in order to learn distributions of interest and both trigger and select the important components of data for saving.

The COINFLIPS team is examining how Bayesian Neural Networks can provide the necessary toolset for learning and selecting data that matches distributions of interest while providing confidence and uncertainty estimates. Bayesian methods are notoriously difficult to train due to the need to sample from unwieldy posterior distributions on model parameters. Similar to the jet simulation above, a COINFLIPS device circuit capable of simulating directly from a given distribution will revolutionize the Bayesian network approach with lasting impact to this application area.

Acknowledgements

Copyright © 2023 Funded under the DOE National Laboratory Announcement Microelectronics Co-Design Research. SAND2022-3825 C and SAND2022-16196 O

We acknowledge support from the DOE Office of Science's Advanced Scientific Computing Research (ASCR) program and Basic Energy Sciences (BES) programs, Microelectronics Co-Design project *COINFLIPS*.

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