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Page 8 of 23 Li et al. J. Mater. Inf. 2025, 5, 43 https://dx.doi.org/10.20517/jmi.2025.17

[54]
atom with force errors under 70 meV/Å for inorganic crystals . SevenNet-MF leverages multi-fidelity
[38]
training to deliver energy MAEs of ~10.8 meV/atom and force MAEs of ~18.3 meV/Å . EquiformerV2 is
an improved equivariant transformer, which achieves energy MAEs down to 9.6 meV/atom with force
MAEs near 43 meV/Å when pretrained on OMat24 datasets, and maintains competitive errors (~20 meV/
atom) under Matbench-Discovery compliance . Equivariant smooth energy network (eSEN) attains
[55]
leading static test-set performance on molecular benchmarks, with energy MAEs around 0.13 eV/atom and
force MAEs as low as 1.24 eV/Å , and achieves energy MAEs down to 18 meV/atom under Matbench-
[40]
[55]
Discovery compliance which is considered to be the best performing model currently. These results
underscore the potential of advanced equivariant models to deliver near-chemical accuracy while balancing
computational costs [Figure 3]. Although these models are expected to achieve precision below 1 meV/atom
on given datasets, most of them have a huge number of parameters. For example, the recent GNoME
model has 16.2 million parameters. The recent proprietary MatterSim model, trained on a 17-million-
[57]
structure dataset, can reach up to 182 million parameters . The high computational demand of quantum
[48]
mechanics calculations has traditionally limited their application in ML-IAPs. Thus, advanced training
architectures should be considered in this domain to accelerate model training and prediction.

Model and hardware optimization
Hierarchical model architectures may address multiscale complexity by cascading predictors of increasing
fidelity. For example, one can use initial modules with low-cost and coarse-grained networks to generate
rough potentials, whereas subsequent stages apply high-resolution models to refine these predictions. This
tiered strategy can markedly reduce computational costs without compromising accuracy . In addition,
[27]
mixed-precision computing smartly mixes single- and double-precision calculations during training,
helping to reduce computation time and cost while still keeping the results accurate and stable. Finally,
parallelization schemes through data-parallel or model-parallel across multicore CPUs and GPUs can
enable near-linear throughput scaling, extending ML-driven simulations to larger and more structurally
complex materials systems. Additionally, parallel computing techniques can significantly enhance
computational efficiency. Utilizing high-performance computing clusters or GPU acceleration can process
multiple tasks simultaneously, reducing overall computation time. Especially in training large models,
parallel computing can significantly reduce training time. Furthermore, developing models suitable for
quantum computers may break this limitation, though it remains controversial whether quantum bits or
quantum computing can practically accelerate quantum chemistry calculations [58,59] .

Additionally, transfer learning and multi-fidelity frameworks offer a potent means to alleviate the
dependence on large, high-fidelity datasets [Figure 1]. Transfer learning accelerates adaptation to new
chemical spaces by reusing representations learned from related tasks [45,49] . In practical terms, molecular
potentials pretrained on datasets such as ANI-1 can be fine-tuned for materials systems, thereby reducing
[27]
the volume of costly DFT annotations required . Multi-fidelity approaches further decrease computational
expense by integrating low-precision and high-precision data within a unified training hierarchy. More
recently, AI-predicted structures have been employed as initial configurations for subsequent DFT
relaxations, providing an efficient compromise between speed and accuracy. Finally, advanced robustness
techniques, such as domain adaptation and meta-learning , are increasingly being incorporated into
[60]
equivariant GNN architectures to bolster generalizability across diverse materials domains.

ML HAMILTONIAN
Although ML-driven IAPs have transformed atomic-scale simulations, an equally compelling frontier is the
creation of machine-learning Hamiltonian, ML-Ham, for direct electronic-structure prediction
[Figure 4A]. These “electronic-scale” networks aim to eliminate the costly SCF loops inherent to