Design of Experiments
Design of experiments is the planning of which input settings to measure so that the effects of interest can be estimated efficiently and with known precision. Classical designs fix the set of runs in advance, from evenly spaced scans of one variable to factorial, Latin square and response surface designs that vary several factors at once. Model-based approaches such as active learning and Bayesian optimization choose runs sequentially using a surrogate model and its uncertainty, so the total number of experiments is not known in advance and a stopping criterion is needed.
Iterative response surface optimization of photocatalyst compositions (2022)
Bhat and coworkers fit a quadratic response surface (linear, cross and squared terms) by ordinary least squares to H2 yields from a parallel photoreactor, then centered the next design on the predicted optimum with tighter bounds, repeating until the predicted optimum moved by less than 1 µmol H2 (Bhat et al. 2022). Box-Behnken designs were used for the three-factor (metal, ligand, photosensitizer) space and central composite inscribed designs once the photosensitizer was fixed. Up to six iterations per metal brought the standard error of the predicted optimum to about 0.2 µmol H2, and the whole study used fewer than 1,000 wells instead of an estimated 16,000 for a replicated grid. Summary: bhat2022.
Sequential sampling for classification boundaries (2023)
Bhat and Kitchin compared three sequential batch designs against full factorial grids for locating the boundary between two classes in a two-dimensional input space (Bhat 2023). Broad initial sampling starts from a sparse Latin hypercube and then concentrates samples on poorly sampled parts of the predicted boundary; low point density grows the sampled region outward from a starting point and targets boundary regions with few or class-imbalanced samples; path tracing walks along the local tangent of the boundary with adaptive steps. On an analytic shower mixing problem, a digitized Ni-Fe-Al oxidation boundary and the van der Waals two-phase region, the sequential designs recovered the true region more accurately than grids of 100 or 169 points, with path tracing and broad sampling usually needing fewer runs (for example 49 versus 169 for the oxidation boundary with broad sampling). Summary: bhat2023a.
Response surface and fractional factorial designs for catalyst discovery (2023)
In a search over Cu, Ru and Fe nanoparticle catalysts for photo-driven hydrogen evolution, Bhat et al. combined response surface and fractional factorial designs, managed with their gespyranto software, to survey bimetallic and trimetallic composition spaces and then sample sequentially toward active regions (Bhat et al. 2023). Experimental constraints such as the 440 µL well volume, a lower detection limit and an upper tape saturation limit of about 25 µmol H2 were built into the designs. The authors credit the combination of design, data processing and parallel experiments for the speed of the study, which found a new active CuRuFe ternary catalyst. Summary: bhat2023.
Designs on a remote instrument (2025)
In a tutorial on automating the Claude-Light instrument, Kitchin moved from a one-variable scan fit by linear regression, to a nine-run Latin square (generated with pycse) estimating the effect of three LED inputs on three photometer outputs, to a Gaussian process with a linear kernel fit to twenty runs and inverted with Nelder-Mead to hit target outputs (Kitchin 2025). He notes that output scaling and a white-noise kernel were needed for sensible uncertainty, which matters because over- or underestimated uncertainty makes sequential designs either never finish or stop at the wrong answer. He argues that sequential designs keep the same loop structure as classical ones, as used in self-driving laboratories. Summary: kitchin2025b.
Model-driven plate design for surfactant mixtures (2025)
Chilkunda, Kitchin and Tilton used a physical model to place experiments for mapping the critical micelle concentration of a binary surfactant mixture (Chilkunda et al. 2025). After measuring the pure-component CMCs, they drew five constant-ratio lines through composition space and put trials where each line crosses the regular solution theory boundary predicted for seven interaction parameters between -6 and 0, plus two trials well below and one above to calibrate low and high fluorescence. Duplicating all but the top trial filled 95 wells of a single plate, concentrating samples near the expected boundary. Only a rough prior range for the interaction parameter is needed, and the authors suggest an iterative broad-then-narrow search when even that is unknown. See also high-throughput experimentation. Summary: chilkunda2025.