MatterSim: Universal ML Interatomic Potential

• MatterSim is a universal machine learning interatomic potential that uses E(3)-equivariant message-passing neural networks and active learning to deliver near-first-principles accuracy across diverse material systems.
• It leverages a graph-based architecture with radial and angular features to predict energies, forces, and stresses directly from large-scale DFT data with high fidelity.
• MatterSim demonstrates robust transferability and practical performance in applications including bulk materials, zeolite frameworks, ion conductors, and nanoparticle catalysts.

MatterSim is a universal machine learning interatomic potential (uMLIP) for atomistic modeling of materials, designed to deliver near-first-principles accuracy for energies, forces, and stresses across wide regions of the periodic table, temperatures (0–5000 K), and pressures (up to 1000 GPa). It is architected around E(3)-equivariant message-passing neural networks (MPNNs), trained using active learning on large-scale density functional theory (DFT) data. MatterSim has been established as a leading approach among uMLIPs for its performance in diverse benchmarking contexts that range from bulk elemental systems, complex zeolite frameworks, solid-state ion conductors, to supported nanoparticle catalysts (Yang et al., 2024, Tahmasbi et al., 23 Dec 2025, Du et al., 14 Feb 2025, Ito et al., 9 Sep 2025, Xu et al., 4 Dec 2025).

1. Model Architecture and Inductive Biases

MatterSim employs a message-passing graph neural network (GNN) that enforces full rotational and translational equivariance (E(3) symmetry). Each structure—bulk crystal, molecule, or nanoparticle—is encoded as a periodic 3D graph $\mathcal{G} = (Z, V, R, L, S)$, where each node corresponds to an atom with an initial embedding (elemental identity and attributes), and edges connect atoms within a cutoff radius $r_c$ (typically 6–7 Å), implemented with smooth cutoff functions. Edge features include relative distances encoded via a learnable radial basis, angular dependencies via spherical harmonics (up to degree $\ell=2$), and element-type information.

Message-passing is executed over $M$ layers (exact $M$ is model-variant dependent; e.g., "5M" for $\mathcal{O}(10^7)$ parameters, "1M" for $\mathcal{O}(10^6)$ parameters):

• At each layer, atomic embeddings $\mathbf{h}_i^{(l)}$ are updated by aggregating message functions $\Phi$ over neighbors, where

$$\mathbf{h}_i^{(l+1)} = \mathbf{h}_i^{(l)} + \sum_{j \in \mathcal{N}(i)} \Phi\left(\mathbf{h}_i^{(l)}, \mathbf{h}_j^{(l)}, \mathbf{e}_{ij}\right)$$

and $\mathbf{e}_{ij}$ reflects both distance and direction, ensuring equivariance.

• Three-body and higher-order local geometric information is handled via explicit angular features (three-body tensor products) as in M3GNet backbones, and by incorporating a Graphormer-style attention mechanism for efficient message propagation.

After $L$ layers, final node embeddings are passed to small element-wise multi-layer perceptrons (MLPs) that output per-atom energies:

$$E_\text{tot} = \sum_{i=1}^N E_i(\mathbf{h}_i^{(L)})$$

Forces $\mathbf{F}_i = -\partial E / \partial \mathbf{r}_i$ and Cauchy stress tensors are obtained via automatic differentiation. Inductive biases include: strict SO(3)/E(3) equivariance, locality (finite neighbor cutoff), and explicit atomic energy decomposition (Yang et al., 2024, Tahmasbi et al., 23 Dec 2025, Ito et al., 9 Sep 2025, Xu et al., 4 Dec 2025, Du et al., 14 Feb 2025).

2. Training Data, Protocol, and Active Learning

The MatterSim training pipeline is built around large-scale, actively curated DFT datasets:

• Core DFT Data: Up to 17 million unique DFT-labeled atomic configurations, spanning Z = 1–89, are aggregated from the Materials Project, Alexandria, Open Catalyst, and Open Materials datasets. Configurations cover bulk crystals, molecular systems, nanoclusters, surfaces, adsorbates, high-temperature/pressure MD snapshots, and explicitly strained or distorted phases (Yang et al., 2024, Ito et al., 9 Sep 2025, Tahmasbi et al., 23 Dec 2025, Xu et al., 4 Dec 2025, Du et al., 14 Feb 2025).
• Active Learning: Periodic uncertainty-based sampling is used to populate training with out-of-distribution (OOD) structures, including off-equilibrium configurations and rare event geometries. Explorers employ ensemble disagreement metrics on energies and forces to propose new DFT calculations, specifically targeting regions with low training density or high predicted variance. For application-specific fine-tuning (e.g., Li3YCl6/NaxLi3-xYCl6 in SSEs), short AIMD at multiple temperatures/pressures and targeted NPT/active-learned frames are added (Du et al., 14 Feb 2025).
• Loss Function: Training optimizes a composite loss over total energies, atomic forces, and stresses:

$$\mathcal{L} = \ell(E, E^{DFT}) + \omega_F \ell(F, F^{DFT}) + \omega_\sigma \ell(\sigma, \sigma^{DFT})$$

with $\ell$ typically a Huber or mean squared error, and weights $(\omega_E, \omega_F, \omega_\sigma)$ chosen to balance energetic and dynamical fidelity ($\omega_F$ commonly in the range $[0.1, 1]$). An atomic reference–energy regularizer enforces correct dissociation limits for all elements:

$$\mathcal{L}_\text{tot} = \mathcal{L} + \lambda_0\sum_Z \left(E_0^Z - \bar{E}_0^Z\right)^2$$

• Optimization: Adam or AdamW optimizers with cosine decays or warm-up schedules, typical learning rates $10^{-3}$ to $10^{-5}$, batch sizes from 50 to 512, trained for 200–300 epochs with early stopping on validation sets (Yang et al., 2024, Du et al., 14 Feb 2025, Tahmasbi et al., 23 Dec 2025).

3. Quantitative Performance Benchmarks

MatterSim has been systematically benchmarked on diverse classes of materials, employing community-standard metrics:

• Bulk Elemental Systems (EOS and MH):
  • Equation-of-state (EOS) fits for SC, FCC, BCC, and DIA structures yield median equilibrium-volume error $|\Delta V_0| \approx 3.2\%$ and bulk modulus error $|\Delta B_0| \approx 8.5\%$ across 40 elements (Tahmasbi et al., 23 Dec 2025).
  • Transition metals: volume error typically $2–4\%$; alkali/alkaline earth metals up to $12\%$.
  • Minima Hopping (MH) structural recovery: recovery rate $R\approx0.78$ (95% global minima), pairwise ordering accuracy $\text{POA}\approx0.53$.
  • PES smoothness (instability $I$): $I\approx0.12$, corresponding to moderate relaxation robustness.
• Zeolite and Guest-Containing Frameworks:
  • Si–O bond MAE in pure zeolites: $0.013\,\text{Å}$ (DFT$\sim0.008\,\text{Å}$).
  • Energetics: RMSE of relative stabilities $1.49\,\text{kJ\,mol}^{-1}$ (DFT reference), consistently outperforming analytic IPs like GFN-FF (Ito et al., 9 Sep 2025).
  • Transition-metal/organic-cation frameworks: RMSE as low as $0.09–0.52\,\text{kJ\,mol}^{-1}$ per atom.
• Solid-State Ion Conductors:
  • Non-equilibrium structure force MAE: $24.4\,\text{meV/Å}$ (nearest competitor $>35\,\text{meV/Å}$).
  • Bulk/shear modulus MAE: $2–3\,\text{GPa}$, essentially identical to DFT and outperforming most other uMLIPs or classical force fields.
  • Li-ion diffusivity and activation energy: agreement within $<0.05\,\text{eV}$ of DeepMD/DFT, with predicted conductivities within $10–20\%$ across different levels of anion/cation disorder (Du et al., 14 Feb 2025).
• Supported Nanoparticle Catalysts:
  • Systematic binding energy deviations (MS-1M variant) up to $0.3\,\text{eV/atom}$ for certain surfaces/facets (cf. $0.02–0.07\,\text{eV/atom}$ for domain-specific DP or MACE).
  • Superior structural exploration: discovery of global DFT-validated minima unattainable by more specialized models, due to broader PES coverage (Xu et al., 4 Dec 2025).
  • MD cost: $\sim100–200\times$ more expensive than highly-optimized DP, but remains tractable for $<200$ atoms.

System	Metric	Value (MatterSim)	DFT (Reference)
Li₃YCl₆ (SSE)	Bulk modulus	38.31 GPa	37.29 GPa
	$\sigma_{300K}$	0.46 mS/cm	0.50 mS/cm
Si-O Zeolite	MAE (bond)	0.013 Å	0.008 Å
Elemental Fe (BCC)	$B_0$ error	–5.7%	–
Supported Cu NP	$\Delta E_b$	–0.3 eV/atom (max)	–

4. Physical Insights, Domain Generalization, and Limitations

MatterSim’s actively-learned, broadly representative training set enables strong generalization:

• Robustness: Inclusion of high-stress, high-temperature, and low-symmetry configurations ensures quantitatively reliable predictions across standard crystals, strained/defected phases, and chemically complex systems (e.g., aluminosilicates, guest-filled zeolites, multi-component SSEs) (Yang et al., 2024, Du et al., 14 Feb 2025, Ito et al., 9 Sep 2025).
• PES Smoothness/Exploration: Smooth potential energy surface (PES) enables efficient geometry relaxations and stable MD, but does not guarantee flawless polymorph ordering or rate of discovering true global minima (Tahmasbi et al., 23 Dec 2025). Structural discovery is highly competitive, but energetic accuracy can still show systematic biases for some substrates (e.g., Cu/Al₂O₃ nanoparticles).
• Chemical/structural transferability: Out-of-the-box, MatterSim is not tailored to any one system and thus displays consistent performance “zero-shot” on test structures far removed from its training set. This enables discovering unexpected configurations in new chemistries or nanostructures.

Limitations:

• Systematic energy offsets may appear for highly specialized or deeply underrepresented chemistries (e.g., nanoparticle–substrate interfaces without fine-tuning) (Xu et al., 4 Dec 2025).
• MD cost is nontrivial compared to domain-specific or highly parameter-efficient MLIPs, limiting applicability to sub-$\sim$1000-atom systems without additional compression or distillation.
• Absence of explicit charge, magnetic, or excited-state degrees of freedom in the current property decoder.
• Lack of explicit handling of long-range electrostatics restricts performance in e.g., polar solvents, highly ionic systems, or metallic interfaces.

5. Fine-Tuning, Customizability, and Computational Considerations

MatterSim is designed for continuous learning and flexible adaptation:

• Ensemble Uncertainty Quantification: Systematic estimation of prediction uncertainty (ensemble dispersion over atomic forces/energies) guides data selection and active re-training (Yang et al., 2024).
• Fine-tuning and transfer learning: MatterSim supports rapid fine-tuning to new levels of theory (e.g., rev-PBE0-D3 water structures or custom MD trajectories) with high data efficiency (successful adaptation using as little as 3% of target-labeled data).
• Distillation and hierarchical modeling: For large-scale or long-time MD, expensive universal models such as MatterSim can generate diverse training data, which are then distilled or used to initialize faster, system-tailored MLIPs (Xu et al., 4 Dec 2025).
• Hardware and scaling: Standard MD step rates for MatterSim are roughly 100–200× slower than for tailored DeepMD/DP models on equivalent hardware, rendering it best suited for structural search, rapid screening, or medium-scale MD (100–1000 atoms or $\sim$ns timescales) unless model reduction is applied.

6. Applications and Comparative Benchmarks

MatterSim’s demonstrated domains include:

• Materials Discovery: Screening equilibrium and metastable phases for new inorganic solids, prediction of ground-state structures, and guiding phase diagram construction via QHA (Yang et al., 2024).
• Lattice Dynamics and Thermomechanical Properties: Accurate predictions for phonon spectra, bulk/shear moduli, and temperature-dependent mechanical response (MAE in $B_0 < 3$ GPa).
• Ion-Conducting Materials: First-principles–level modeling of lithium/sodium-ion conductivity, disorder effects, and activation energies in modern SSEs (e.g., Li₆PS₅Cl, NaxLi₃–ₓYCl₆) (Du et al., 14 Feb 2025).
• Zeolites and Frameworks: Geometry and energetics near DFT accuracy for both pure-silica and substituted/aluminosilicate zeolites, even in the presence of guest cations and organic structure-directing agents (Ito et al., 9 Sep 2025).
• Heterogeneous Nanocatalysts: Identification of previously unattainable nanoparticle/substrate minima via exhaustive structure search, enabling data-efficient downstream fitting of domain-specific potentials (Xu et al., 4 Dec 2025).

A consistent conclusion across benchmarks is that MatterSim delivers high transferability, top-tier energy/force accuracy, and practical robustness across physically relevant parameter ranges, with remaining limitations in clock speed and residue energy bias in ultra-specialized materials regimes.

7. Prospects, Limitations, and Ongoing Development

MatterSim’s development roadmap includes:

• Integration of explicit electrostatics (Coulomb kernels, charge equilibration, Ewald-based message passing) to extend accuracy to ionic, polarizable, and surface-dominated systems.
• Expansion of pretraining sets to include surfaces, interfaces, amorphous and liquid phases, and to support transfer learning from hybrid-DFT and GW references (Yang et al., 2024).
• Multi-task and semi/self-supervised pretraining to further increase property diversity, and extension of predictive heads to targeted physical observables (e.g., polarizabilities, excited-state spectra).
• Systematic reduction in computational cost via model compression, sparse attention, and teacher–student distillation approaches, particularly for scale-up to $10^3$–$10^4$ atoms or multiscale MD.

This suggests that MatterSim is positioned as a zero-shot ML force field and property predictor, with high adaptability and strong physical credibility for both discovery and mechanistic studies, while still requiring ongoing innovation in efficiency and property breadth for niche materials and scaling to macroscale simulation. (Yang et al., 2024, Tahmasbi et al., 23 Dec 2025, Du et al., 14 Feb 2025, Ito et al., 9 Sep 2025, Xu et al., 4 Dec 2025)