GitHub

MultilevelMonteCarlo.jl

A Julia package for Multilevel Monte Carlo (MLMC) estimation with support for multiple quantities of interest, adaptive sample allocation, sample storage (including NetCDF I/O), and PDF/CDF estimation via kernel density and maximum entropy methods.

Features

  • MLMC estimation with the classical telescoping-sum estimator
  • Adaptive MLMC with iterative optimal sample allocation
  • Multiple QoIs computed simultaneously from the same model evaluations
  • Online statistics via Welford's algorithm (no sample storage required for means)
  • Optional threading with Chan's parallel merge algorithm
  • Sample collection and persistence to NetCDF files
  • PDF/CDF estimation from MLMC samples using:
    • Kernel density estimation (Gaussian kernel)
    • Maximum entropy method (Legendre polynomial basis, Newton solver)

Quick Start

using MultilevelMonteCarlo

# Define model levels (coarse → fine)
levels = Function[
    params -> my_model(params; resolution=0.1),
    params -> my_model(params; resolution=0.01),
    params -> my_model(params; resolution=0.001),
]

# Define quantities of interest
qoi_functions = Function[
    output -> output.distance,
    output -> output.max_height,
]

# Draw random parameters
draw_parameters() = rand_params()

# MLMC estimation
samples_per_level = [10000, 1000, 100]
estimates = mlmc_estimate(levels, qoi_functions, samples_per_level, draw_parameters)

Installation

using Pkg
Pkg.add(url="https://github.com/sintefmath/MultilevelMonteCarlo.jl")