Graph Neural Networks
Graph neural networks (GNNs) represent a molecule or crystal as a graph whose nodes are atoms and whose edges connect neighboring atoms. Interaction (message-passing or convolution) blocks repeatedly update each atom’s embedding from its neighbors, using distances and, in some architectures, bond and dihedral angles, and output blocks map the final embeddings to a target such as an energy, force or atomic property. Because the features are learned, GNNs avoid hand-built descriptors, but they still inherit the usual regression problems of data imbalance and limited interpretability. See also interpretable machine learning, imbalanced data and magnetic moments.
Benchmarking GNNs on transition metal complexes (2023)
Garrison and coworkers trained SchNet, SpinConv, PaiNN and GemNet-T from the Open Catalyst Project on total energies of about 86,500 single-metal transition metal complexes. Models trained on the original TPSSh-level tmQM data consistently underpredicted a cluster of mostly Fe, Ru and Os complexes, even in the training set, which the authors used as a diagnostic of inconsistent reference data. On the recomputed tmQMwB97MV set the cluster vanished and the ranking was GemNet-T > PaiNN ≈ SpinConv > SchNet. Because none of the models take total charge as input, neutral-only training gave lower errors but learning curves that flattened, while training that included charged complexes kept improving with more data, which points to the need for architectures that encode charge and spin (Garrison et al. 2023). Summary: garrison2023.
GemNet adsorption energies compared against experiment (2023)
A pretrained GemNet model from the Open Catalyst Project was used to relax (90 steps) and score about 16 million hydrogen adsorption configurations on bimetallic surfaces, enabling a direct comparison of machine-learned DFT surrogates with thousands of photocatalytic HER experiments (Broderick et al. 2023). The comparison showed that such predictions can prune roughly half of a bimetallic search space, while also showing where single-descriptor screening fails for in situ nanoparticles. Summary: broderick2023.
Embeddings reused for magnetic moment regression (2024)
Sanspeur and Kitchin used GemNet-OC as a per-atom classifier (magnetic or non-magnetic) and then regressed moment magnitudes from its 256-dimensional atom embeddings, reaching a mean absolute error of 0.1 µB. They also found a limitation: because the local convolutions are symmetric, atoms in equivalent environments with opposite spins receive nearly identical embeddings, so the network cannot predict the sign of a moment or the collinear ordering without an explicit spin feature in the input (Sanspeur 2024). Summary: sanspeur2024.
Physics inside a graph network (2024)
The TinNet framework of Huang and coworkers uses a graph convolutional network to predict the parameters of a tight-binding d-band model, keeping the accuracy of a black-box network while producing physically interpretable quantities (Huang et al. 2024). Summary: huang2024.
Atom embeddings as search fingerprints (2022)
Yang, Liu and Kitchin used the last-interaction-block atom embeddings of a modified GemNet-dT, trained on energies, as fingerprints for similarity search in QM9, the Materials Project and OC20. The embeddings encoded element identity and local geometry well enough that queries returned atoms of the same element in similar sites without any explicit element filter, and adsorbed O and acetylene matches in OC20 also had similar projected densities of states. Because the embeddings are learned against energy, molecules they retrieve were far more useful for training a Gaussian process to predict the query energy than Morgan fingerprint neighbors (Yang et al. 2022). Summary: yang2022a. See also Similarity search.
Open challenges for GNNs trained on OC20 (2022)
Kolluru et al. (2022) reviewed the first wave of GNN models on the Open Catalyst 2020 dataset and broke down GemNet-dT errors by material class and adsorbate. Nonmetals were markedly worse than metalloids despite similar training shares, intermetallics were best, and bidentate adsorbates and those containing N or O were among the hardest, with no correlation between error and adsorbate size. The perspective lists open problems for large GNNs: whether one universal model beats subset-specific models (splitting off nonmetals hurt), uncertainty quantification and active learning at this scale, inference cost of ever larger models, merging datasets computed at different levels of theory, and adding physics such as charge densities or tight-binding features as inputs. Summary: kolluru2022.
GNNs that predict electron densities (2023)
Sunshine et al. (2023) adapted a SchNet model in the Open Catalyst Project code to predict the pseudo-valence electron density of OC20 adsorbate-surface structures at grid points (probes) that join the graph as message receivers only. Forcing zero density beyond the cutoff and enforcing the total valence electron count made the predictions usable by physics codes, and a neighbor search that skips probe-probe edges made graph construction scale as O(A(A+P)) rather than O((A+P)2). The authors note that probe counts in the millions make many-body architectures such as GemNet impractical, so message passing must scale linearly with the number of probes. Summary: sunshine2023.
Uncertainty-aware stability screening of oxides (2024)
Abed and coworkers trained a CGCNN with hyperparameter tuning and dropout uncertainty (CGCNN-HD) on 36,465 Materials Project oxides to predict formation energy per atom as a Pourbaix stability proxy. Inputs were unrelaxed structures pre-scaled with a bond-statistics lattice scaling method, and predictions were shifted to the lower 95% confidence bound to tolerate non-ideal structures. The model reached 77 meV per atom mean absolute error, agreed with DFT on 676 oxides, and screened 2070 hypothetical rutile oxides, leading to an experimentally validated acid-stable OER catalyst (Abed et al. 2024). Summary: abed2024.
Limits of local-cutoff GNN potentials for magnetic oxides (2024)
In relaxations of OC22 oxides accelerated with GemNet potentials, Wang et al. (2024) found an AgIrO4 case where two runs reached nearly identical atomic positions but different total magnetization and energy. Because spin adds a degree of freedom that a structure-only, local-cutoff GNN cannot see, the one-to-one mapping from structure to energy breaks down, and the authors call for potentials that encode magnetic information, citing CHGNet as an example. Summary: wang2024.
Rotational equivariance and latent space distances (2024)
Musielewicz and coworkers found that the full rotationally equivariant latent embedding of EquiformerV2 is a poor basis for distance-based uncertainty: UMAP projections showed noisy, overlapping metal clusters that became dense and well separated when only invariant channels were used (Musielewicz et al. 2024). Invariant l=0 node and edge-aligned m=0 embeddings worked much better, and the invariant latent space of GemNet-OC, a less accurate model, predicted EquiformerV2’s errors better than EquiformerV2’s own. Per-atom distances generally outperformed distances between system-averaged embeddings. Summary: musielewicz2024.
Shallow-ensemble uncertainty in SchNet (2025)
By replacing SchNet’s final layer with 64 output heads and training on the negative log-likelihood, Vinchurkar and coworkers gave a GNN an uncertainty estimate at roughly the cost of one extra hidden layer, and evaluated it on QM9, on OC20 intermetallic versus nonmetal slabs (fine-tuning only the last layer of a pretrained checkpoint), and on gold molecular dynamics frames (Vinchurkar et al. 2025). The approach separated chemically distinct out-of-domain data well but was overconfident for same-element structural changes, a limitation relevant to fine-tuned GNN potentials generally. Summary: vinchurkar2025.