fig12

Figure 12. The evolution of representative atomistic MLP models from 2007 to 2024, which are roughly sorted by their public release dates (e.g., an arXiv preprint if available). These MLP models are categorized as follows: strictly local descriptor-based models (red), invariant (green) and equivariant (blue) MPNN-based models, and universal potential models (purple). In recent years, the development of atomistic MLPs has accelerated significantly. Reprinted with permission^[77]. Copyright 2025, RSC. MLPs: Machine learning potentials; BPNN: behler-parrinello neural network; SNAP: spectral neighbor analysis potential; MTP: moment tensor potential; DP: deep potential; wACSF: weighted atom-centered symmetry functions; FCHL: faber-christensen-huang-lilienfeld model; MEGNet: materials graph network; EANN: embedded atom neural network; SOAP: smooth overlap of atomic positions; DTNN: deep tensor neural network; LASP: large-scale atomic simulation package; HIPNN: hierarchically interacting particle neural network; ACE: atomic cluster expansion; GM-NN: gaussian moments neural network; aPIP: atomic permutationally invariant polynomial; NEP: neuroevolution potential; REANN: recursively embedded atom neural network; MACE: multi-atomic cluster expansion; SEGNN: steerable equivariant graph neural network; PFP: preferred potential; ALIGNN: atomistic line graph neural network; UNiTE: uniform neural network interatomic potential; PaiNN: polarizable atom interaction neural network; CACE: cartesian atomic cluster expansion; GPTFF: graph-based pre-trained transformer force field; CAMP: cartesian atomic moment potential; ALICNN-FF: atomistic local interaction convolutional neural network force field; HotPP: high-order tensor passing potential; CHGNet: crystal hamiltonian graph neural network; GNoME: graph networks for materials exploration.