JuliaCon 2023

High-dimensional Monte Carlo Integration with Native Julia
07-27, 10:50–11:00 (US/Eastern), 32-124

This talk presents a new Julia package for efficient and generic Monte Carlo integration in high-dimensional and complex domains, featuring the Vegas algorithm for self-adaptive important sampling and an improved algorithm for increased robustness. The package demonstrates Julia's superiority over C/C++/Fortran and Python for high-dimensional Monte Carlo integration by enabling the easy creation of user-defined integrand evaluation functions with the speed of C and the flexibility of Python.


Evaluating integrals in high-dimensional spaces and complex domains is a common task in scientific research, and Monte Carlo methods provide robust and efficient solutions to this problem. To our knowledge, the Julia community currently lacks a native and feature-complete package for generic high-dimensional Monte Carlo integration. Our package addresses this gap by providing a carefully tested, well-documented, officially registered solution that supports multiple algorithms and both MPI and threading parallelization. In Monte Carlo integration, the user must implement an integrand evaluation function evaluated millions or even billions of times. Julia's speed and flexibility make this task significantly easier for the user compared to similar packages in C/C++/Fortran and Python. As such, our package offers a highly competitive Monte Carlo integration tool on the market. Detailed tutorials and the source code can be found at the link https://github.com/numericalEFT/MCIntegration.jl.

See also: slides (4.6 MB)

Kun Chen is a research fellow at the Center for Computational Quantum Physics (CCQ) at the Flatiron Institute. He leads a team that develops Julia packages under the Numerical Effective Field Theory (NEFT) framework (https://github.com/numericalEFT) for modeling real-world quantum materials using modern quantum field theory. These efforts have resulted in powerful tools such as MCIntegration.jl for high-dimensional Monte Carlo integration, Lehmann.jl for low-rank approximation of Green's function, and GreenFunc.jl for studying quantum many-body physics. With a PhD in 2018 from the University of Massachusetts Amherst, Kun is a Simons Postdoctoral Fellow at Rutgers University and later a research fellow at Flatiron Institute. His work in this area will enable scientists and researchers to gain a deeper understanding of quantum materials and their properties.

Xiansheng Cai is a PH.D. student at the Physics department of University of Massachusetts Amherst. He is actively involved in the development of Julia packages under the Numerical Effective Field Theory (NEFT) framework(https://github.com/numericalEFT) for modeling real-world quantum materials using modern quantum field theory. As the leading designer, his efforts have resulted in the creation of powerful tools CompositeGrids.jl for 1D grid representation, BrillouinZoneMeshes.jl for multi-dimensional Brillouin zone meshgrid representation.

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