Sampler Creation

The Sampler controls the execution and management of MLMC (Multilevel Monte Carlo) samples. This example demonstrates how to configure all essential components for an MLMC simulation.

Basic Setup

First, import the mlmc package and define basic MLMC parameters.

import mlmc

# Define number of MLMC levels
n_levels = 3

# Simulation step sizes at the coarsest and finest levels
step_range = [0.5, 0.005]

# Compute level parameters (simulation steps per level)
level_parameters = mlmc.estimator.determine_level_parameters(n_levels, step_range)

# Alternatively, you can specify level_parameters manually as a list of lists.

Simulation Definition

Prepare a simulation instance. The simulation class must inherit from mlmc.sim.simulation.Simulation.

simulation_factory = mlmc.SynthSimulation()

This factory will be used by the sampler to create individual simulation runs.

Sampling Pool

Next, create a sampling pool that controls how samples are executed.

sampling_pool = mlmc.OneProcessPool()

The mlmc.sampling_pool.OneProcessPool executes samples sequentially within a single process.

You can also use:

• mlmc.sampling_pool.ProcessPool — executes samples in parallel across multiple processes.

• mlmc.sampling_pool_pbs.SamplingPoolPBS — submits jobs to a PBS (Portable Batch System) cluster for distributed computation.

Sample Storage

The sample storage keeps all data related to simulation results.

# Memory storage keeps samples in main memory
sample_storage = mlmc.Memory()

Alternatively, use persistent file-based storage:

• mlmc.sample_storage_hdf.SampleStorageHDF — stores results in an HDF5 file for long-term reuse and analysis.

Sampler Initialization

Finally, create the Sampler instance. It coordinates sample scheduling, simulation execution, and result collection.

sampler = mlmc.Sampler(
    sample_storage=sample_storage,
    sampling_pool=sampling_pool,
    sim_factory=simulation_factory,
    level_parameters=level_parameters
)

The sampler is now ready to generate and manage MLMC samples.

Next Steps

Proceed to the next example: Samples Scheduling