Compactness matters: Improving Bayesian optimization efficiency of materials formulations through invariant search spaces

Would you rather search for a line inside a cube or a point inside a square? Physics-based simulations and wet-lab experiments often have symmetries (degeneracies) that allow reducing problem dimensionality or search space, but constraining these degeneracies is often unsupported or difficult to implement in many optimization packages, requiring additional time and expertise. So, are the possible improvements in efficiency worth the cost of implementation? We demonstrate that the compactness of a search space (to what extent and how degenerate solutions and non-solutions are removed) affects Bayesian optimization search efficiency. Here, we use the Adaptive Experimentation (Ax) Platform by MetaTM and a physics-based particle packing simulation with eight or nine tunable parameters, depending on the search space compactness. These parameters represent three truncated log-normal distributions of particle sizes which exhibit compositional-invariance and permutation-invariance characteristic of formulation problems (e.g., chemical formulas, composite materials, alloys). We assess a total of four search space types which range from none up to both constraint types imposed simultaneously. In general, the removal of degeneracy through problem reformulation (as seen by the optimizer's surrogate model) improves optimization efficiency. The code is hosted at https://github. com/sparks-baird/bayes-opt-particle-packing. We recommend that optimization practitioners in the physical sciences carefully consider the trade-off between implementation cost and search efficiency before running expensive optimization campaigns.