CHGNet: Universal ML Interatomic Potential

• CHGNet is a charge-informed graph neural network-based force field pretrained on extensive DFT data to approximate the universal potential energy surface for inorganic materials.
• Its architecture employs message-passing with E(3)-equivariant updates that accurately capture energies, forces, stresses, and magnetic moments.
• Fine-tuning with targeted high-energy DFT snapshots mitigates systematic PES softening, enabling robust predictions in active learning and high-throughput materials screening.

The CHGNet Universal Machine Learning Interatomic Potential (uMLIP) is a charge-informed, graph neural network-based force field designed to approximate the universal potential energy surface for inorganic crystalline materials. Pretrained on an extensive dataset of density functional theory (DFT) energies, forces, stresses, and magnetic moments from the Materials Project, CHGNet aims to combine domain transferability across chemistries with near-DFT accuracy in predicting static and dynamic properties relevant to materials design, phase stability, ion transport, and defect physics (Deng et al., 2023, Lian et al., 3 Jul 2025).

1. Model Architecture and Representational Formalism

CHGNet encodes atomic configurations as undirected graphs $G = (V, E)$, where $V$ is a set of atomic nodes $i$ and $E$ is a set of edges $ij$ connecting neighbors within a cutoff $R_\mathrm{cut}$ (typically 5–6 Å). Node features $x_i$ are learnable embeddings of atomic number (one-hot or continuous), optionally extended to include atomic volume or site magnetic moment if available. Edge features $e_{ij}$ are formed by radial basis expansions of the interatomic distance $r_{ij} = |\mathbf{R}_j - \mathbf{R}_i|$; advanced variants include angular triplet features to capture three-body correlations (Deng et al., 2023, Huang et al., 7 Apr 2025, Pitfield et al., 24 Jul 2025).

The message-passing block comprises $L$ layers. For layer $\ell$:

• Message aggregation: $$m_i^{(\ell+1)} = \sum_{j\in N(i)} \varphi_m(h_i^{(\ell)}, h_j^{(\ell)}, e_{ij}^{(\ell)})$$
• Node update: $$h_i^{(\ell+1)} = \varphi_u(h_i^{(\ell)}, m_i^{(\ell+1)})$$ where the $\varphi$ functions are small feed-forward neural networks, which can be E(3)-equivariant (ensuring rotational equivariance in forces).

After $L$ passes, each atom’s embedding $h_i^{(L)}$ is mapped by a readout MLP $\epsilon(\cdot)$ to a per-atom energy, with total energy given by

$$E_\mathrm{tot}(\mathbf{R}) = \sum_{i=1}^N \epsilon(h_i^{(L)})$$

Atomic forces are obtained by gradient backpropagation:

$$\mathbf{F}_i = -\nabla_{\mathbf{R}_i} E_\mathrm{tot}(\mathbf{R})$$

The same differentiated model yields virial stress; for models with charge-informed nodes, on-site magnetic moments $m_i$ are predicted from intermediate features via a dedicated linear head, acting as a proxy for local charge or valence state (Deng et al., 2023).

2. Pretraining Dataset and Loss Functions

CHGNet is pretrained on the Materials Project Trajectory Dataset (MPtrj), comprising $>1.5$ million DFT labels covering 89–94 elements, drawn from static and relaxation trajectories of $\sim$146,000 distinct compounds. These include total energies, atomic forces, cell stresses, and magnetic moments in spin-polarized runs (Deng et al., 2023, Zhou et al., 30 Dec 2024, Huang et al., 7 Apr 2025).

The multi-task training objective is a weighted sum (usually mean squared error) over:

• Total energy per atom
• Atomic forces
• Virial stress
• Magnetic moments

Weighting is typically $$w_\mathrm{energy}:w_\mathrm{force}:w_\mathrm{stress}:w_\mathrm{magmom}=3:1:0.1:1$$ (Huang et al., 7 Apr 2025). Optimization employs Adam or RAdam with initial learning rates around $10^{-3}$, batch sizes $40$–$100$, and early stopping on a hold-out set. For computational efficiency, FastCHGNet accelerates the reference implementation via fused CUDA kernels, direct force/stress heads, and batch-parallel basis generation, reducing multi-GPU pretraining time from 8.3 days (A100) to 1.53 h (32×A100) while cutting memory by %%%%26$ij$27%%%% (Zhou et al., 30 Dec 2024).

3. Universality, Systematic Softening, and Fine-Tuning Strategies

CHGNet's universal character derives from extensive element coverage, cross-chemistry pretraining, and rotationally equivariant representations. The resulting model is directly transferable to out-of-sample inputs, enabling zero-shot prediction for previously unseen crystals, surfaces, or defected supercells (Deng et al., 2023, Deng et al., 11 May 2024, Lian et al., 3 Jul 2025).

However, models pretrained on equilibrium-centric data develop a systematic "softening" of the potential energy surface (PES): a global underestimation of PES curvature and energy barriers, manifesting as slopes $<$1 in parity plots of ML vs DFT forces, low phonon frequencies, and underestimated surface/defect/migration energies (Deng et al., 11 May 2024). This softening is formally a near-uniform rescaling in PES curvature across off-equilibrium configurations.

The bias can be dramatically reduced by fine-tuning the pretrained weights with a modest dataset—sometimes a single high-energy (e.g., transition-state or defect) DFT snapshot suffices. The protocol incorporates additional DFT labels via transfer learning (e.g., 1–100 structures), using the same multi-task loss and optimizer but with all or selected layers unfrozen (Deng et al., 11 May 2024, Žguns et al., 10 Sep 2025, Lian et al., 3 Jul 2025). In practice, fine-tuning on targeted high-energy configurations "re-anchors" the PES in the relevant region, yielding dramatic reductions in MAE and restoring parity slopes close to unity.

4. Validation: Performance Benchmarks and Applications

4.1. Bulk and Surface Structure Energetics

In bulk and relaxed structures, CHGNet attains MAE ≈ 30 meV/atom (energy), 77 meV/Å (force), and 0.35 GPa (stress) in held-out tests (Deng et al., 2023, Focassio et al., 7 Mar 2024). On surface calculations, zero-shot surface energy RMSE is $\sim$0.51 J/m$^2$ but is systematically underestimated due to training set bias; fine-tuning is recommended for accurate work on surfaces (Focassio et al., 7 Mar 2024, Deng et al., 11 May 2024).

4.2. NEB Barrier Prediction and Li-Ion Conductors

Fine-tuned CHGNet reduces migration-barrier MAE from 0.23–0.24 eV (pretrained) to 0.07–0.09 eV and $R^2$ from 0.94 to 0.98 on test and training sets. This enables reliable high-throughput NEB-based screening of candidate Li-ion conductor frameworks, achieving 100–1000$\times$ wall-clock speedup over DFT-based NEBs (Lian et al., 3 Jul 2025, Kang et al., 14 Aug 2025). For example, aliovalent-doped variants Li$_{0.5}$Mg$_{0.5}$Al$_{0.5}$PO$_4$ and Li$_{0.5}$TiPO$_{4.5}$F$_{0.5}$ were predicted with fine-tuned CHGNet to have low migration barriers and conductivities of 0.19 mS/cm, 0.024 mS/cm respectively.

4.3. Molecular Dynamics and Transport

Long-time molecular dynamics (MD) using CHGNet yields force and dynamical accuracy at the ab-initio level: e.g., 200–2000$\times$ speedup for 10$^5$–10$^6$-step trajectories in superionic conductors, and accurate Arrhenius behavior for Li/Na/Mg diffusion. When deployed as-is, universal CHGNet systematically underpredicts diffusion coefficients in defective materials (e.g., for H in Mg), but fine-tuning on a few thousand targeted ab-initio frames restores DFT-level transport and activation energies (Angeletti et al., 30 Jul 2024).

4.4. Alloy Mixing and Thermodynamics

In alloy theory, out-of-the-box CHGNet predictions for mixing enthalpy are typically accurate to $\sim$40–50 meV/atom RMSE, which does not suffice for thermodynamic topology (correct sign and relative ordering of phases). Augmenting the universal CHGNet with tens of DFT-labeled SQS supercells at key compositions enables fine-tuned models to reach the $\leq$10 meV/atom regime needed for reliable phase diagram prediction (Casillas-Trujillo et al., 25 Jun 2024, Zhu et al., 22 Nov 2024).

5. Integration with Active Learning and Global Optimization

CHGNet serves as the backbone for active-learning pipelines combining foundation uMLIP prediction with local correction via a $\Delta$-GPR (Gaussian Process Regression) model using Smooth Overlap of Atomic Positions (SOAP) descriptors (Pitfield et al., 24 Jul 2025). The workflow:

1. Propose trial structures (by RSS, Basin Hopping, GOFEE, Replica Exchange).
2. Relax with current CHGNet+$\Delta$ model.
3. Select promising structures for DFT evaluation.
4. Compute $\Delta E = E_\mathrm{DFT} - E_\mathrm{uMLIP}$, add to GPR training set.
5. Retrain the GPR correction; iterate.

The $\Delta$ model rectifies systematic errors in the universal backbone, accelerates global structure searches, and is particularly effective when the base uMLIP misorders global minima or mispredicts energetics in new chemical environments.

6. Limitations, Generalization Scope, and Future Directions

While CHGNet provides wide across-chemistry coverage and near-ab-initio accuracy after modest fine-tuning, its limitations stem from:

• Pronounced PES softening on surfaces, defects, and high-energy states absent from the training set (Deng et al., 11 May 2024, Lian et al., 3 Jul 2025).
• Lack of explicit electrostatics and van der Waals interactions in the baseline model (user-correctable via additive corrections).
• Incomplete transferability to liquid, highly disordered, or strongly correlated (e.g., $f$-electron) systems unless those states enter training/fine-tune sets.
• In alloy/CALPHAD applications, formation-energy errors of 30–100 meV/atom can qualitatively upset phase equilibria; only sub-10 meV/atom errors eliminate this risk (Zhu et al., 22 Nov 2024).

Future best practices include:

• Systematic expansion of the pretraining dataset to include high-energy (off-equilibrium) configurations, transition states, defects, and free surfaces (Deng et al., 11 May 2024, Žguns et al., 10 Sep 2025).
• Routine use of ultra-efficient fine-tuning (minimum $\sim$1–100 targeted DFT labels) before production in new compositional/structural regimes.
• Hybridization with E(3)-equivariant architectures and protocolized active learning to ensure coverage of critical phase-space regions, particularly for multi-phase or multi-valent systems.

7. Summary Table: Key Model Features and Performance Metrics

Property	Universal (Pretrained) CHGNet	Fine-Tuned CHGNet
Energy MAE (bulk/test)	30 meV/atom (Deng et al., 2023)	2 meV/atom (TS) (Lian et al., 3 Jul 2025)
Force MAE	77 meV/Å (Deng et al., 2023)	13 meV/Å (TS) (Lian et al., 3 Jul 2025)
MD/NEB Speedup vs DFT	$\sim$100–1000$\times$ (Lian et al., 3 Jul 2025)	$\sim$100–1000$\times$ (Lian et al., 3 Jul 2025)
Surface Energy RMSE	0.51 J/m$^2$ (Focassio et al., 7 Mar 2024)	Reduced after fine-tuning (Deng et al., 11 May 2024)
Alloy $\Delta H_\mathrm{mix}$	41.5 meV/atom (Casillas-Trujillo et al., 25 Jun 2024)	<10 meV/atom (with retraining)
Migration Barrier MAE	0.23–0.24 eV (Lian et al., 3 Jul 2025)	0.07–0.09 eV (Lian et al., 3 Jul 2025)
Transfer to new chemistry	High (across MP elements)	High (if covered in fine-tune)

Fine-tuning with a minimal set of high-energy DFT structures systematically eliminates the curvature softening endemic to universal pretraining, restores DFT-level accuracy, and enables robust, data-efficient adaptation of CHGNet to challenging regions of the potential energy surface critical for materials discovery (Deng et al., 11 May 2024, Žguns et al., 10 Sep 2025, Lian et al., 3 Jul 2025).