Models like M3GNet, CHGNet and CGCNN are graph neural networks trained on DFT energies/forces so they can relax crystal structures thousands of times faster than DFT itself. Each atom's true (DFT) force comes from a harmonic bond model around the equilibrium lattice; the neural potential predicts:
F_ML(r_ij) = F_DFT(r_ij) + (1 − acc)·b_i
acc = steps / (steps + 800)
E = (1/N)·Σ_bonds ½k(r_ij − a₀)²
- Training steps — sets model accuracy
acc via a saturating learning curve, exactly like a real MLIP's validation error dropping with more DFT training data.
- Systematic bias b_i — a fixed per-atom error vector scaled by
(1 − acc); an undertrained model relaxes atoms to a slightly wrong structure, a well-trained one converges to the true DFT minimum.
- Force error — the RMS mismatch between the ML-predicted force and the harmonic DFT-reference force, in meV/Å — the metric MLIP papers report on held-out test sets.
- Structure relaxation — atoms integrate damped Newtonian motion under the ML forces, just as CHGNet/M3GNet drive geometry optimisation instead of a full DFT ionic-relaxation loop.