How Many Experiments to Run?

The size of the design space and the number of experiments are closely connected.

To make the most out of Design of Experiments and Bayesian Optimization, it is important to choose a reasonably-sized reaction space and according number of experiments.

Exploring the Reaction Space - Design of Experiments

Minimum number of experiments. The minimum number of experiments is always double the number of values for the parameter with the most possible values.

For example, if you have 4 ligands, 3 solvents, 2 bases and 2 concentrations, the minimum number of experiments is \(4 \times 2 = 8\).

Using multiples of number of parameters. It is good practice for number of experiments to be a multiple of the possible values of number of parameters. This ensures that each parameter is tested the same number of times.

Using the same example of 4 ligands, 3 solvents, 2 bases and 2 concentrations, a good number of experiments could be 12, or 24.

Rule of thumb. The table below summarizes common number of experiments for different numbers of parameters and values.

Number of Possible Values for Each Parameter	Full Factorial	Recommended Experiments
\(2 + 2 + 2 \,(+ 2)\)	8 or 16	4, 8
\(3 + 3 + 3 \,(+ 3)\)	27 or 81	9
\(4 + 4 + 4 \,(+ 4)\)	64 or 256	16, 32
\(4 + 2 + 2 + 2 \,(+ 2)\)	32 or 64
\(4 + 4 + 2 + 2 \,(+ 2)\)	64 or 128
\(3 + 3 + 2 + 2 \,(+ 2)\)	36 or 72	18
\(4 + 3 + 2 + 2 \,(+ 2)\)	48 or 96	12, 24

Finding the Best Conditions - Bayesian Optimization

Unlike for DoE, the number of experiments for Bayesian Optimization is not as important, so you can decide based on your experimental setup.

Ideally in each batch you would run the maximum number of experiments that you can comfortably handle in parallel. In particular you should refrain from asking the software to suggest more experiments than you can handle and instead split it into multiple batches. That’s because after you run the first batch, the software will learn from it and make better suggestions for the second one.