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Documentation | Installation | GitHub | Tutorials

MFPML: Multi-Fidelity Probabilistic Machine Learning Library

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.

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👥 Authorship

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

🚀 Key Features

1. Multi-Fidelity Design of Experiments (DoE)

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]])]

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2. Advanced Surrogate Models

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

Example:

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 outputs

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3. Multi-Fidelity Bayesian Optimization

Efficient 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)

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📦 Installation

Install MFPML via pip:

pip install mfpml

Or install from source:

git clone https://github.com/your_username/mfpml.git
cd mfpml
pip install .

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📚 Documentation

You can also explore the tutorials provided by sphinx online documentation or by Jupyter Notebooks:

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✅ Testing

To ensure everything works correctly, run the test suite using pytest:

pytest tests/

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🤝 Contributing

Contributions are welcome! Follow these steps to contribute:

1. Fork the repository.
2. Create a new feature branch: git checkout -b feature/your-feature-name.
3. Commit your changes: git commit -m "Add new feature".
4. Push to your branch: git push origin feature/your-feature-name.
5. Submit a pull request.

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🌟 Why Use MFPML?

• 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.

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📄 License

This project is licensed under the MIT License.

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🙌 Acknowledgments

We appreciate the open-source community and contributors who make this project better.

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📝 References

1. Jiang, Ping, et al. "Variable-fidelity lower confidence bounding approach for engineering optimization problems with expensive simulations." AIAA Journal 57.12 (2019): 5416-5430.
2. 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.
3. Yi, Jiaxiang, et al. "Efficient adaptive Kriging-based reliability analysis combining new learning function and error-based stopping criterion." Structural and Multidisciplinary Optimization 62 (2020): 2517-2536.
4. 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.
5. 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.