Hybrid Machine Learning for Experimental Optimization

This repository contains a Python notebook demonstrating a hybrid machine learning framework for guiding experimental design in biological systems. Specifically, it focuses on optimizing the growth conditions (phosphate and temperature) for a model organism using data-efficient, uncertainty-aware sampling.

Overview

The workflow combines four main components:

1. Quadratic Response Surface Model (OLS):
   Provides a smooth global estimate of the response surface and a prediction of the maximum growth rate.

2. Gaussian Process Regression (GPR):
   Captures local uncertainty and enables computation of Expected Improvement (EI) across the experimental space.

3. Expected Improvement (EI):
   Used as an acquisition function to identify high-potential experimental conditions.

4. K-means Clustering:
   Ensures diversity in suggested experiments by selecting a representative from each cluster among the top EI-ranked candidates.

The system iteratively selects 5 new experimental conditions per cycle, appends them to a growing dataset, and refits models to continue the search for optimal conditions. This loop can be manually repeated until the desired improvement threshold is met.

Features

• Latin Hypercube Sampling (initial exploration)
• Quadratic model fitting and contour visualization
• Gaussian Process with Matern kernel (ν=2.5)
• EI-based sampling strategy
• Diversity via clustering (KMeans)
• Fully reproducible via provided notebook
• Automatic result logging and PNG export of each cycle

Benchmarking

The hybrid framework was benchmarked against standard optimization techniques using the same stopping criteria (0.01% threshold improvement):

Algorithm	Cycles	Growth Rate	Phosphate	Temperature	Accuracy
Hybrid	4.4 ± 0.55	1.09 ± 0.03	15.7 ± 2.8	23.2 ± 0.9	2.7 ± 2.2
Bayesian Opt.	4.4 ± 0.89	1.15 ± 0.01	16.4 ± 0.6	25.0 ± 0.7	3.9 ± 0.7
TPE	16.8 ± 4.44	1.12 ± 0.04	13.8 ± 5.5	25.8 ± 1.9	5.6 ± 3.6

File Structure

• OLS Temp and Phosphate-EI.ipynb: Main notebook containing the full optimization pipeline.
• CurrentResults.csv: Accumulated dataset across cycles.
• DataCube.csv: Full experimental space and ground-truth values.
• PNG outputs: Saved plots per cycle showing response surfaces and EI heatmaps.

Dependencies

Tested with:

• Python 3.10+
• numpy, pandas, matplotlib, scikit-learn, scipy, statsmodels

How to Use

1. Clone the repository.
2. Install dependencies (you can use a virtualenv or conda environment).
3. Run the notebook in Jupyter or VS Code.
4. Review suggested experimental points.
5. Append real or simulated measurements to CurrentResults.csv.
6. Re-run the notebook for the next cycle.

Citation

If using this work in a publication, please cite as:

Campos Diocaretz, B., Tűzesi, Á., & Herdean, A. (2025). A Simple Yet Powerful Hybrid Machine Learning Approach to Aid Decision-Making in Laboratory Experiments. Machine Learning and Knowledge Extraction, 7(3), 60. https://doi.org/10.3390/make7030060