A crystal-graph neural network (à la GNoME / Materials Project AI) represents a candidate structure as a graph: atoms are nodes, bonds are edges. Each round of message passing lets every atom update its state from its bonded neighbors, so information about a defect gradually reaches atoms further and further away in the graph — exactly the colored pulse you see spreading outward from doped (amber) sites here.
Message passing update:
h_v^(k+1) = σ( W · [ h_v^(k) + Σ_{u ∈ N(v)} h_u^(k) ] )
Predicted formation energy after K passes:
E(K) = E_true − gap₀ · e^(−K / 2.2)
gap₀ = 0.9 · dopant_fraction (bigger defect fraction ⇒ bigger initial blind spot)
E_true = E₀(family) + 1.8 · dopant_fraction
Stability score = clamp( −E(K) / 3.5 · 100%, 0, 100% )
GNN confidence = 100% · (1 − e^(−K / 2.2))
- Crystal family — sets the base lattice topology and coordination number, and therefore the baseline formation energy E₀ used above (perovskite ABX₃, rock-salt, or a van-der-Waals layered stack).
- Dopant substitution — the fraction of cation sites replaced by a foreign element; each doped site is a local strain source the network must reason about.
- GNN message-passing steps — how many rounds of neighbor-aggregation the network runs; with too few passes the model is "blind" to distant defects and over-predicts stability, exactly like early GNoME-style models before enough graph-convolution depth.
- Generate new candidate — samples a fresh random doping pattern (a new point in composition space) and re-screens it, incrementing the candidates-screened counter — mirroring how generative + GNN screening pipelines explore millions of hypothetical compounds.
Real pipelines (Google DeepMind's GNoME, Materials Project's ML models) work the same way at enormous scale: a generative model proposes candidate compositions/structures, and a graph neural network trained on DFT data predicts formation energy far faster than running quantum-chemistry calculations on every candidate — narrowing millions of hypotheses down to the handful worth verifying in the lab.