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# ACMD Seminar: PAGANI and m-Cubes: Parallel Adaptive GPU Algorithms for Numerical Integration

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Ioannis Sakiotis*Ph.D. Candidate, Computer Science Dept. Old Dominion University*

Tuesday, November 15, 2022, 3:00-4:00 EDT (1:00 - 2:00 MDT)

**A video of this talk is available to NIST staff in the Math channel on NISTube, which is accessible from the NIST internal home page.**

**Abstract**: The task of multi-dimensional numerical integration is frequently encountered in physics and other scientific fields. High computational intensity causes existing libraries to often require prohibitively long execution times on challenging integrands. Adaptive algorithms have demonstrated the best performance on serial systems, but efficient many-core utilization is difficult to achieve because the adaptive workload can vary greatly across the integration space and is impossible to predict a priori. As a result, there is a shortage of efficient and robust parallel numerical integration libraries.

We present PAGANI and m-Cubes, two algorithms tailored for GPU execution, based on the popular Cuhre and VEGAS algorithms. PAGANI utilizes quadrature techniques while m-Cubes is Monte Carlo based. Different integrand characteristics can make either algorithm more appropriate, but both offer high-performance solutions to multi-dimensional integrands.

CUDA implementations executed on the V100 and A100 GPUs show orders of magnitude speedup over the serial algorithms as well superior reliability and performance over other deterministic and probabilistic GPU implementations.

A modern C++ interface header-only implementation makes both algorithms portable, allowing their utilization in complicated pipelines with easy to define stateful integrals and without requiring knowledge of either parallel or CUDA programming constructs.

**Bio**: Ioannis Sakiotis is a computer science Ph.D. candidate at Old Dominion University. He earned his B.S. and M.S. in Modeling and Simulation Engineering at Old Dominion University in 2014 and 2016 respectively. He has experience working on agent-based simulations, but his research interests primarily lie with High Performance Computing. He has been working in the HPC field as a researcher since 2018 and is the lead author behind PAGANI and m-Cubes, two parallel algorithms for adaptive multi-dimensional numerical integration.

**Host:** Brian D. Cloteaux

**Note:**This talk will be recorded to provide access to NIST staff and associates who could not be present to the time of the seminar. The recording will be made available in the Math channel on NISTube, which is accessible only on the NIST internal network. This recording could be released to the public through a Freedom of Information Act (FOIA) request. Do not discuss or visually present any sensitive (CUI/PII/BII) material. Ensure that no inappropriate material or any minors are contained within the background of any recording. (To facilitate this, we request that cameras of attendees are muted except when asking questions.)

**Note:** Visitors from outside NIST must contact Lochi Orr (301) 975-3800; at least 24 hours in advance.

Mathematics and statistics

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                -  Brian D. Cloteaux  brian.cloteaux@nist.gov      (301) 975-4793   
                -  Zachary Grey  zachary.grey@nist.gov      (303) 497-5920   
                -  Lochi Orr  lochi.orr@nist.gov      (410) 598-6986   

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