A generic adaptive machine learning workflow for accelerating the search and discovery of new materials. It has four components: (1) Database, where the problem is defined, (2) machine Learning (using off-the-shelf or Bayesian inference methods), for establishing structure-property relationships. In addition, the formalism must also quantify prediction uncertainties. (3) Optimal Learning using utility functions, which takes the outcome from machine learning as input and recommends the next promising material(s) for validation, and (4) An “Oracle” (new experiment or computation) validates the recommended material. The training dataset is then augmented via a feedback loop and the process repeats until new materials with desired properties are discovered.