Bayesian Optimization

Introduction to Bayesian Optimization for Chemical Reactions

Bayesian optimization represents a paradigm shift in how chemists approach reaction optimization. Rather than relying solely on intuition and trial-and-error, this powerful machine learning technique uses statistical models to intelligently guide experimental design, dramatically reducing the number of experiments needed to find optimal reaction conditions.

What is Reaction Optimization?

When developing a chemical reaction, chemists need to find the best conditions (like temperature, concentrations, catalyst, solvent, etc.) to get the highest possible yield. However, there are often millions of possible combinations of these conditions, and testing them all would take far too long. Traditionally, chemists use their expertise and intuition to make educated guesses about which conditions might work best.

Note: The target Y variable does not always have to be yield! It can be enantioselectivity, cost, or even a combination of variables.

What is Bayesian Optimization?

Bayesian optimization is a smart strategy that uses statistics and machine learning to guide the search for optimal reaction conditions. Think of it like playing a game of "hot and cold" - but instead of a person giving hints, a computer model learns from each experiment to make increasingly better predictions about where the "hot" (high-yielding) conditions might be.

What is the difference between Design of Experiments (DoE) and Bayesian Optimization?

While Design of Experiments requires planning and running a fixed set of experiments upfront to map out the design space, Bayesian Optimization uses machine learning to adaptively learn from each experiment and intelligently select the next most informative one. This adaptive approach allows Bayesian Optimization to find optimal conditions with up to 95% fewer experiments than exhaustive screening or traditional DoE, dramatically reducing time, cost, and resource consumption in reaction optimization.

How Does It Work?

1. Initial Experiments: We start by running diverse experiments suggested by the software that broadly cover the parameter space.

2. Building a Model: The software creates a mathematical model that tries to predict the yield for any combination of conditions, based on the results we've seen so far. Importantly, this model also tells us how uncertain it is about its predictions.

3. Choosing New Experiments: The software then suggests new experiments by balancing two goals:

• Exploitation: Testing conditions that the model predicts will give high yields.
• Exploration: Testing conditions where the model is very uncertain.

4. Active Learning: After each new batch of experiments, the model updates its understanding and makes better predictions. This cycle continues until we find optimal conditions.

Why is it Useful?

• Efficiency: Bayesian optimization typically finds optimal conditions in fewer experiments than traditional approaches
• Systematic: Takes the guesswork out of optimization by using data to guide decisions
• Comprehensive: Can explore unusual combinations of conditions that chemists might not typically try
• Informative: Analysis of why the model makes certain predictions provides fundamental insights into the chemical system

How to use it in the lab

You'll be using software that handles all the complex mathematics behind the scenes. Your role will be to:

1. Input the possible variables for your reaction conditions
2. Run the experiments suggested by the software
3. Input the results back into the software
4. Repeat until you find optimal conditions
5. Analyze feature importances to understand the fundamentals driving the chemical system

IMPORTANT: While Bayesian optimization is a powerful tool, it works best when combined with chemical intuition and careful experimental technique. The usefulness of the machine learning model depends on the quality of the experimental data you provide!

The machine learning model

Gaussian Process Regression

The core of Bayesian optimization is a mathematical tool called a Gaussian Process Regressor (GPR). Think of it like fitting a line through data points, but instead of just getting a single line, you get:

1. A prediction line (mean μ)
2. A confidence band around that prediction (standard deviation σ)

Mathematically, for any new reaction conditions x, the model predicts:

• A mean yield: μ(x)
• An uncertainty: σ(x)

These predictions are based on all previous experiments using a formula called the "kernel function" which measures how similar different reaction conditions are to each other.

The Acquisition Function: How Does the Model Choose New Experiments?

The acquisition function is what helps us decide which experiment to run next. The most common one used is called "Expected Improvement" (EI). Here's how it works:

For any potential new reaction conditions, we have:

• μ = predicted yield
• σ = uncertainty in that prediction
• y_best = best yield we've seen so far

The Expected Improvement formula is:

Let's break down what this means:

1. The first term (μ - y_best)Φ(Z) is large when we predict a better yield than our current best
2. The second term σφ(Z) is large when we're very uncertain about our prediction
3. Φ and φ are mathematical functions that help combine these terms properly

This formula balances two goals:

• Testing conditions we think will give high yields (exploitation)
• Testing conditions where we're uncertain and might discover something new (exploration)

The model chooses the next experiment by finding the conditions that give the highest Expected Improvement value.

References

1. Bayesian reaction optimization as a tool for chemical synthesis: https://doi.org/10.24433/CO.3864629.v1

2. Accelerating the Development of Sustainable Catalytic Processes through Data Science: https://doi.org/10.1021/acs.oprd.4c00434

3. Closed-loop optimization of general reaction conditions for heteroaryl Suzuki-Miyaura coupling: DOI: 10.1126/science.adc8743