Multi-Level Monte Carlo with Python
MLMCPy - Multi-Level Monte Carlo with Python
MLMCPy is an open source implementation of the Multi-Level Monte Carlo (MLMC) method in Python. It was developed with ease of use in mind.
MLMCPy is intended for use with Python 2.7.
- mpi4py (for using with mpirun)
- pytest (for running unit tests)
Well over one hundred tests are included to thoroughly test MLMCPy.
import numpy as np import sys from MLMCPy.input import RandomInput from MLMCPy.mlmc import MLMCSimulator # Add path for example SpringMassModel to sys path. sys.path.append('./examples/spring_mass/from_model/spring_mass') import SpringMassModel ''' This script demonstrates MLMCPy for simulating a spring-mass system with a random spring stiffness to estimate the expected value of the maximum displacement using multi-level Monte Carlo. Here, we use Model and RandomInput objects with functional forms as inputs to MLMCPy. See the /examples/spring_mass/from_data/ for an example of using precomputed data in files as inputs. ''' # Step 1 - Define random variable for spring stiffness: # Need to provide a sampleable function to create RandomInput instance in MLMCPy def beta_distribution(shift, scale, alpha, beta, size): return shift + scale*np.random.beta(alpha, beta, size) stiffness_distribution = RandomInput(distribution_function=beta_distribution, shift=1.0, scale=2.5, alpha=3., beta=2.) # Step 2 - Initialize spring-mass models. Here using three levels with MLMC. # defined by different time steps model_level1 = SpringMassModel(mass=1.5, time_step=1.0) model_level2 = SpringMassModel(mass=1.5, time_step=0.1) model_level3 = SpringMassModel(mass=1.5, time_step=0.01) models = [model_level1, model_level2, model_level3] # Step 3 - Initialize MLMC & predict max displacement to specified error. mlmc_simulator = MLMCSimulator(stiffness_distribution, models) [estimates, sample_sizes, variances] = \ mlmc_simulator.simulate(epsilon=1e-1, initial_sample_sizes=100, verbose=True)
UQ Center of Excellence
NASA Langley Research Center
This software was funded by and developed under the High Performance Computing Incubator (HPCI) at NASA Langley Research Center.
Copyright 2018 United States Government as represented by the Administrator of the National Aeronautics and Space Administration. No copyright is claimed in the United States under Title 17, U.S. Code. All Other Rights Reserved.
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