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 can be estimated by adding the number of possible values for each parameter. For example, if you want to test 4 ligands, 3 solvents, 2 bases and 2 concentrations, you should be aiming for at least \(4+3+2+2=11\) experiments.

An exception is when using descriptors for a parameter with a large number of possible values. For example, it is possible to screen 30 ligands using 10 or 20 experiments, if the descriptors reflect their reactivity well.

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 better 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

For example, if you want to test 4 ligands, 3 solvents, 2 bases and 2 concentrations, there are \(4+3+2+2\) possible values for each parameter (last row of the table), and the recommended number of experiments is 12 or 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. A good starting point is 5 - 20 experiments per batch.

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.