Bridging Prediction and Planning: From Synthesis Temperature Distributions to Optimization-Guided Experiments

In solid-state synthesis, the same target material is synthesized across a range of temperatures, reflecting a one-to-many relationship in synthesis conditions. Experimentally identifying these feasible synthesis windows through trial-and-error is costly and time-consuming. This motivates machine learning approaches for synthesis-condition prediction. However, most existing approaches output point estimates without feasible-range information, and it remains unexplored whether such predictions improve downstream experimental planning. We propose an integrated framework that predicts synthesis temperatures as Gaussian distributions and empirically validates their downstream optimization gains through Bayesian optimization on realistic synthesis landscapes. On a text-mined solid-state synthesis dataset, our distributional predictor matches or improves mean prediction accuracy over point-estimation baselines while enabling synthesis window estimation. In BO experiments on realistic synthesis landscapes, distribution-based initialization with post-hoc calibration reduces cumulative regret by 20\% over quasi-random and 11\% over point-based alternatives across 4 material systems, confirming that distributional prediction enables more efficient experimental planning.