Fundamental differences between materials originate from the unique nature of their constituent chemical elements. Before specific differences emerge according to the precise ratios of elements (the composition) in a given crystal structure (a phase), a material can be represented by its phase field defined simply as the set of the constituent chemical elements. By working at the level of the periodic table, classification of materials at the level of their phase fields reduces the combinatorial complexity to accelerate screening, and circumvents the challenges associated with composition-level approaches – poor extrapolation within phase fields, and the impossibility of exhaustive sampling. Here, we demonstrate that phase fields can be classified with respect to the maximum expected value of a target functional property and ranked according to synthetic accessibility. We develop and present PhaseSelect, an end-to-end machine learning model that combines the representation, classification, and ranking of phase fields. First, PhaseSelect constructs elemental characteristics from the co-occurrence of chemical elements in computationally and experimentally reported materials, then it employs attention mechanisms to classify the phase fields by their functional performance. At the level of the periodic table, PhaseSelect quantifies the probability of observing a functional property within a phase field and also ranks its synthetic accessibility, which we demonstrate with significant accuracy for three avenues of materials’ applications: high-temperature superconductivity, high-temperature magnetism, and targeted bandgap energy.