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MFPML is a Python library for multi-/single-fidelity probabilistic machine learning. It provides tools for design of experiments, surrogate modeling, Bayesian optimization, and visualization – empowering researchers and engineers to optimize expensive, black-box systems efficiently.
Authors:
- Jiaxiang Yi (yagafighting@gmail.com) [1]
- Ji Cheng (jicheng9617@gmail.com) [2]
Affiliations:
- [1] Delft University of Technology
- [2] City University of Hong Kong
Efficient sampling methods to generate design points for optimization and modeling:
- Multi-Fidelity Samplers: Sampling with Sobol sequences and Latin Hypercube Sampling (LHS).
- Single-Fidelity Samplers: Random, Sobol, and LHS sampling.
Example:
import numpy as np
from mfpml.design_of_experiment.mf_samplers import MFSobolSequence
# Define the input design space
design_space = np.array([[0, 1], [0, 1]])
# define the sampler
sampler = MFSobolSequence(design_space=design_space, num_fidelity=2, nested=True)
# get samples
samples = sampler.get_samples(num_samples=[2, 5])
# print samples
print(samples)
[array([[0.64763958, 0.28450888],
[0.36683413, 0.68135563]]),
array([[0.64763958, 0.28450888],
[0.36683413, 0.68135563],
[0.48028161, 0.47841079],
[0.51099956, 0.61233338],
[0.92215368, 0.08658168]])]Model expensive functions with state-of-the-art surrogate techniques:
- Gaussian Process Regression (GPR)
- Co-Kriging for multi-fidelity modeling
- Hierarchical and Scaled Kriging variants
from mfpml.models.co_kriging import CoKriging
model = CoKriging(design_space=input_domain, # np.ndarray
optimizer_restart=10)
model.train(X_train, Y_train) # Train the model
Y_pred, sigma = model.predict(X_test, return_std=True) # Predict outputsEfficient optimization algorithms to solve black-box problems:
- Single-Fidelity Bayesian Optimization, see Example
- Multi-Fidelity Bayesian Optimization, see Example
from mfpml.problems.mf_functions import Forrester_1a
from mfpml.optimization.mf_uncons_bo import mfUnConsBayesOpt
from mfpml.optimization.mf_acqusitions import AugmentedEI,
# define problem
problem = Forrester_1a()
# define the optimizer
optimizer = mfUnConsBayesOpt(problem=problem,
acquisition=VFEI(),
num_init=[5, 20],
)
# execute the optimizer
optimizer.run_optimizer(max_iter=20, stopping_error=0.01, cost_ratio=5.0)Install MFPML via pip:
pip install mfpmlOr install from source:
git clone https://github.com/your_username/mfpml.git
cd mfpml
pip install .You can also explore the tutorials provided by sphinx online documentation or by Jupyter Notebooks:
To ensure everything works correctly, run the test suite using pytest:
pytest tests/Contributions are welcome! Follow these steps to contribute:
- Fork the repository.
- Create a new feature branch:
git checkout -b feature/your-feature-name. - Commit your changes:
git commit -m "Add new feature". - Push to your branch:
git push origin feature/your-feature-name. - Submit a pull request.
- Efficiency: Optimize expensive simulations with fewer samples.
- Flexibility: Use single or multi-fidelity methods tailored to your needs.
- Integration: Easy to integrate into engineering and scientific workflows.
- Open Source: Fully customizable and extendable.
This project is licensed under the MIT License.
We appreciate the open-source community and contributors who make this project better.
- Jiang, Ping, et al. "Variable-fidelity lower confidence bounding approach for engineering optimization problems with expensive simulations." AIAA Journal 57.12 (2019): 5416-5430.
- Cheng, Ji, Qiao Lin, and Jiaxiang Yi. "An enhanced variable-fidelity optimization approach for constrained optimization problems and its parallelization." Structural and Multidisciplinary Optimization 65.7 (2022): 188.
- Yi, Jiaxiang, et al. "Efficient adaptive Kriging-based reliability analysis combining new learning function and error-based stopping criterion." Structural and Multidisciplinary Optimization 62 (20 6496 20): 2517-2536.
- Yi, Jiaxiang, et al. "An active-learning method based on multi-fidelity Kriging model for structural reliability analysis." Structural and Multidisciplinary Optimization 63 (2021): 173-195.
- Yi, Jiaxiang, Yuansheng Cheng, and Jun Liu. "A novel fidelity selection strategy-guided multifidelity kriging algorithm for structural reliability analysis." Reliability Engineering & System Safety 219 (2022): 108247.