Bayesian vs DoE for Reaction Optimization: What Chemists Should Know

The short version: DoE and Bayesian optimisation are not rival brands of the same method. DoE is a broad framework for designing informative experiments and estimating effects. Bayesian optimisation is a sequential strategy for choosing where to measure next when the objective is costly to evaluate. The right choice depends on the decision—not on which method sounds more advanced.

Chemists often meet this question as a false binary: use a traditional design of experiments (DoE), or replace it with Bayesian optimisation. In practice, both are toolkits. They make different assumptions, produce different kinds of evidence and can be combined in the same development programme.

The useful question is therefore not “Which method wins?” It is “What must this campaign learn, and what evidence will the team need afterwards?”

What DoE gives you

DoE selects combinations of factor settings so that specified effects can be estimated efficiently. The family includes full and fractional factorial designs, screening designs, central composite and Box–Behnken response-surface designs, mixture designs and computer-generated optimal designs.

Depending on the design and analysis plan, DoE can help a team:

• compare alternatives under controlled conditions;
• screen a larger set of factors for important main effects;
• estimate specified interactions;
• fit a local response surface, including curvature;
• study robustness around a proposed operating point;
• quantify experimental variation through replication and blocking.

The important phrase is specified effects. A design is built around a model the experimenter intends to estimate. Fractional designs gain efficiency by accepting defined aliasing between effects. Response-surface designs place experiments where they can estimate curvature in a chosen region. The analysis is only as relevant as the objective, factor ranges and model assumptions behind it.

The NIST design-selection guidance explicitly separates comparative, screening and response-surface objectives. It also recommends leaving budget for centre points and replacement runs rather than consuming every available experiment in the initial design.

What Bayesian optimisation gives you

Bayesian optimisation treats the experimental response as an expensive-to-evaluate function. After an initial set of observations, it fits a surrogate model that predicts both the response and uncertainty across the feasible space. An acquisition function scores possible experiments according to a policy—often balancing predicted performance with the value of exploring uncertain regions.

The workflow is sequential:

1. define the factors, responses and constraints;
2. run an initial set of experiments;
3. fit the surrogate model;
4. select one or a batch of candidate conditions;
5. run and measure those conditions;
6. update the model and repeat.

This adaptivity is useful when each reaction is expensive and the team is willing to let early results influence later experiments. The method can work with continuous and categorical variables, but the implementation must represent each type appropriately. It can also handle multiple objectives and constraints, although those choices make the decision policy more complex.

Bayesian optimisation does not remove the need for experimental design. It still needs an informative initial set, a carefully bounded space, controls, consistent measurements and confirmation runs. It also does not guarantee that a global optimum has been found within a fixed budget.

A more useful comparison

Campaign question	DoE	Bayesian optimisation
How do predefined factors and interactions affect the response?	Direct fit when the chosen design supports those terms	Surrogate can show relationships, but inference depends on model and sampling path
Which condition should we run next?	Usually set by the design or an explicitly planned augmentation	Central purpose of the acquisition step
Can later runs adapt to early results?	Yes in sequential or augmented DoE, but not in a fixed one-shot design	Yes; adaptation is built into the loop
Do we need broad process understanding?	Strong choice when estimable effects and uncertainty are planned in advance	Useful for locating performance; not automatically a substitute for an inferential study
Are experiments costly and the immediate goal is to find strong conditions?	Efficient designs are available, especially in a focused region	Often well matched to this objective
Do we have mixed continuous and categorical factors?	Possible with a suitable classical or optimal design	Possible with suitable encodings, kernels or surrogate models
Must the result support a regulated development narrative?	Familiar framework for systematic development and design-space evidence	Can contribute evidence, but strategy, validation and interpretation must be justified

Neither column says “few experiments” by default. Run count depends on the number and type of factors, the model complexity, noise, batch structure, constraints, prior data and the confidence needed for the decision.

Choose DoE when the model itself is the deliverable

DoE is often the clearer starting point when the team needs interpretable estimates of selected effects or a defined local response surface. Examples include:

• screening process parameters before scale-up;
• estimating two-factor interactions identified as scientifically important;
• building a quadratic model over a well-defined operating region;
• studying robustness against small deliberate perturbations;
• separating treatment effects from known batch or equipment effects through blocking.

In pharmaceutical development, ICH Q8(R2) describes DoE as one element that can support a systematic development approach alongside prior knowledge, quality risk management and lifecycle knowledge. It does not prescribe a particular design or imply that collecting more data is inherently better; the scientific understanding and its justification matter.

Choose Bayesian optimisation when the next condition is the decision

Bayesian optimisation becomes attractive when:

• each experiment has a meaningful material, time or analytical cost;
• the immediate objective is to locate high-performing feasible conditions;
• results can be returned quickly enough to influence the next batch;
• the response may be nonlinear and a simple local polynomial is not assumed;
• the team wants an explicit mechanism for trading exploration against exploitation;
• constraints or multiple objectives need to enter candidate selection.

Published reaction studies demonstrate the workflow in specific settings. Shields and co-workers benchmarked Bayesian optimisation on a palladium-catalysed direct arylation dataset and applied it to laboratory optimisation campaigns. Taylor and co-workers reported a multi-objective platform and applied it to yield and enantioselectivity in a Ni/photoredox coupling.

These are useful demonstrations, not universal run-count promises. Performance from one reaction, search space or acquisition strategy should not be copied into a new project as a guarantee.

The hybrid workflow is often the practical answer

A chemistry programme can use the methods in sequence.

1. Screen

Use mechanistic knowledge and a screening design to identify important factors, obvious interactions and impractical regions. Include controls, blocking and replication appropriate to the execution plan.

2. Optimise

Carry the reduced set of influential factors into a Bayesian loop. Use the model to propose conditions within chemical, safety and operational constraints. Review each batch before it reaches the laboratory.

3. Characterise

Once a promising region is found, use a response-surface or optimal design to characterise local behaviour and quantify effects that matter for the process decision.

4. Confirm and test robustness

Repeat the proposed operating condition independently. Deliberately vary critical parameters and relevant noise factors. A model prediction is not a confirmation experiment.

This is not the only valid sequence. A Bayesian campaign may reveal a region that motivates a new screening study; a DoE may be augmented sequentially; historical data may alter the initial design. The common requirement is that each phase has a clear objective.

A campaign example

Consider a reaction with five candidate ligands, three bases and continuous temperature, concentration and catalyst loading. The team wants a condition that balances assay yield against a difficult impurity and is practical on a parallel reactor.

A full factorial across arbitrarily chosen levels would be a poor default, but “use Bayesian optimisation” is not yet a complete plan either.

The team could:

1. remove chemically incompatible ligand–base combinations;
2. define feasible numeric ranges and analytical responses;
3. use a balanced initial design covering categories and continuous space;
4. reserve reactions for repeats and controls;
5. run a multi-objective Bayesian loop to identify useful trade-offs;
6. choose a candidate based on chemistry and process requirements;
7. design a local robustness study around that candidate.

The result is a programme of evidence: broad enough to avoid an obvious blind spot, adaptive where experiments are valuable, and confirmatory where the development decision demands it.

Questions to settle before choosing a method

• Is the objective screening, explanation, optimisation, robustness—or more than one?
• Which effects must be estimated, rather than merely predicted?
• How quickly can analytical results return to the campaign?
• Are reactions run one at a time or in fixed-size batches?
• Which constraints and category combinations are non-negotiable?
• How much experimental noise is expected, and where will replication enter?
• What evidence will another chemist, process team or reviewer need to trust the conclusion?
• What is the stopping rule?

The strongest campaigns do not begin with an algorithm. They begin with a development decision, then choose the experimental strategy capable of supporting it.

Read how to choose the right variables, see how AutoRxn works, follow the guided walkthrough, or contact the team to discuss an optimisation workflow.

References and further reading

1. NIST/SEMATECH, e-Handbook of Statistical Methods: Choosing an experimental design.
2. International Council for Harmonisation, ICH Q8(R2): Pharmaceutical Development.
3. Shields, B. J. et al., “Bayesian reaction optimization as a tool for chemical synthesis”, Nature 590, 89–96 (2021).
4. Taylor, C. J. et al., “A Multi-Objective Active Learning Platform and Web App for Reaction Optimization”, J. Am. Chem. Soc. 144, 19999–20007 (2022).