MatterGen: Universal MLIP Framework

• MatterGen is a universal machine-learned interatomic potential framework designed for atomistic simulations across all elements, temperatures, and pressures.
• It employs advanced graph neural network architectures, including M3GNet and E(3)-equivariant transformers, to process atomic graphs with radial and angular descriptors.
• MatterGen enables rapid, high-throughput materials discovery and fine-tuning for domain-specific applications with ab initio-level accuracy.

MatterSim is a universal machine-learned interatomic potential (MLIP) framework designed for atomistic simulation of materials spanning the entire periodic table, across wide temperature (0–5000 K) and pressure (0–1000 GPa) ranges. MatterSim incorporates graph neural network architectures (M3GNet style or E(3)-equivariant transformer backbones) and leverages active learning on millions of ab initio structures for rapid, accurate prediction of local energies, forces, stresses, and materials properties. The pre-trained foundation models enable direct deployment for static and dynamical atomistic simulations, while fine-tuning with domain-specific data achieves ab initio accuracy for system-specific workflows. MatterSim is widely benchmarked in high-throughput materials discovery, structural optimization, ionic transport studies, and catalyst screening, demonstrating performance on par with, or surpassing, competing universal MLIPs within its chemical coverage (Yang et al., 2024, Du et al., 14 Feb 2025, Hänseroth et al., 7 Nov 2025, Tahmasbi et al., 23 Dec 2025, Xu et al., 4 Dec 2025, Ito et al., 9 Sep 2025).

1. Model Architecture and Atomistic Representation

MatterSim builds on either M3GNet (rotationally and permutationally invariant graph neural networks) or E(3)-equivariant transformer architectures. Atomic environments are represented as periodic graphs $\mathcal{G}=(Z,\{r_i\},\{e_{ij}\},L)$ with nodes assigned atomic numbers $Z_i$, coordinates $r_i\in\mathbb{R}^3$, and optional scalar states, and edges $e_{ij}$ defined by a radial distance cutoff.

• Descriptor construction:
  • Radial basis expansions (Gaussian or Bessel) are applied to pairwise distances $r_{ij}$, $\phi_n(r_{ij})$, yielding descriptors $d_{ij}=[\phi_1(r_{ij}),..., \phi_{N_r}(r_{ij})]$.
  • Angular features ($g_{ijk}$) are optionally constructed from triplet angles using simple angular expansions $\psi_n(\theta_{jik})$.
  • For equivariant cases, angular information is explicitly encoded via spherical harmonics.
• Message-passing/network layers:
  • Node and edge features are updated in cascaded layers:

  $$m_{ij}^{(\ell)} = MLP_{edge}^{(\ell)}(h_i^{(\ell)}, h_j^{(\ell)}, e_{ij}^{(\ell)})$$

  $$h_i^{(\ell+1)} = h_i^{(\ell)} + \sum_{j\neq i} MLP_{node}^{(\ell)}(h_i^{(\ell)}, m_{ij}^{(\ell)})$$ - Typically, 4–6 layers are used in the MatterSim-Large model (Hänseroth et al., 7 Nov 2025). - No explicit vector or tensor features are stored in the invariant backbone; forces are gradients of the scalar energy.

• Energy decomposition and force consistency:

$$E(\{r_i\}) = \sum_{i}U(h_i^{(L)};\mathbf{w}), \quad F_i = -\nabla_{r_i}E$$

Each final node embedding $h_i^{(L)}$ is mapped to an atomic energy by a small MLP, summed to produce total potential energy. Forces and (where supported) stresses are exact derivatives of this energy.

2. Training Regimen and Foundation Model Construction

MatterSim's foundation models (e.g., v1.0.0-1M, v1.0.0-5M, MatterSim-Large) are pre-trained on large, diverse datasets:

• Data sources: Microsoft in-house DFT database (PBE, 0–5000 K, 0–1000 GPa) (Hänseroth et al., 7 Nov 2025), Materials Project crystals, Alexandria molecular database, structures sampled by classical MD (Yang et al., 2024).

• Active learning: Out-of-distribution (OOD) configurations are identified via ensemble uncertainty and added iteratively, spanning high-$T$, high-$P$, and off-equilibrium states. Final datasets reach up to 17 million structures across 89 elements (Yang et al., 2024).

• Training loss and hyperparameters:

  • Standard composite loss:

  $$L = w_E \sum_k (E_k^{pred} - E_k^{ref})^2 + w_F \frac{1}{3N}\sum_{k,i}\|F_{i,k}^{pred} - F_{i,k}^{ref}\|^2$$

  Energy-to-force weighting $w_F:w_E$ ranges from $0.5:1$ up to $150:1$ depending on task (Hänseroth et al., 7 Nov 2025). Adam optimizer, initial learning rate $10^{-3}$, batch sizes of 4–32, epochs 200–2500.

• Fine-tuning: The aMACEing Toolkit provides streamlined interfaces for system-specific fine-tuning (conversion, splitting, logging, evaluation, model export) with as few as 2,000 ab initio MD frames yielding near-quantum accuracy (Hänseroth et al., 7 Nov 2025).

3. Performance Benchmarks in Materials Modeling

Table: Typical Post-Fine-Tuning Performance Metrics (Hänseroth et al., 7 Nov 2025, Du et al., 14 Feb 2025)

Metric	MatterSim-Large (Pre-FT)	MatterSim-Large (Post-FT)	Best-case MLIP Avg.
Energy MAE	0.14–0.31 eV/atom	0.001–0.01 eV/atom	$\sim$1 meV/atom
Force RMSE	0.15–0.45 eV/Å	0.02–0.07 eV/Å	0.02–0.07 eV/Å
Li-ion Diffusion D	n/a	$1.19\times10^{-11}$ m²/s	DFT: $1.22\times10^{-11}$ m²/s
Bulk Modulus (GPa)	n/a	38.31 (Li$_3$YCl$_6$)	DFT: 37.29

MatterSim's fine-tuned models deliver ab initio-level accuracy for force (RMSE $<$ 0.07 eV/Å) and energy (MAE $\sim$1 meV/atom) predictions, with benchmarking studies showing performance comparable to MACE, GRACE, SevenNet, and ORB (Hänseroth et al., 7 Nov 2025, Du et al., 14 Feb 2025). On solid ion conductors, MatterSim achieves superior accuracy in predicting thermodynamic properties, elastic moduli, and ionic diffusivity (Du et al., 14 Feb 2025).

On zeolite frameworks, MatterSim reproduces experimental and PBE+D3 geometries and energetics, with Si–O bond length MAE $\sim$0.015 Å and energy RMSEs within 1.5 kJ mol⁻¹ of DFT across >200 topologies (Ito et al., 9 Sep 2025).

4. Application Domains and Limitations

MatterSim is widely applied for:

• Static relaxation and property prediction: lattices, phase diagrams, moduli, phonons, heat capacity, free energy (Yang et al., 2024).

• High-throughput screening: rapid evaluation of millions of candidate structures, relaxation of compositions spanning 89 elements (Yang et al., 2024).

• Dynamical simulations: stable NVT and NPT MD trajectories at $T$ up to 5000 K, $P$ up to 1000 GPa, with $>90\%$ success on diverse materials (Yang et al., 2024).

• Ion transport and diffusion: accurate, force-consistent MD for lithium, sodium, and mixed cation conductors (Du et al., 14 Feb 2025).

• Zeolite and catalysis benchmarking: competitive geometry and energetic fidelity in pure silica, aluminosilicate, and guest-containing frameworks (Ito et al., 9 Sep 2025).

• Structure exploration for supported nanoparticles: rapid sampling of configuration space and discovery of global minima without system-specific fitting, but with unreliable raw energy ranking (Xu et al., 4 Dec 2025).

Limitations:

• Large systematic energy errors and unreliable ranking in catalyst/nanoparticle landscapes unless fine-tuned (Xu et al., 4 Dec 2025).

• Systematic underperformance for Group 1 and 2 elements (alkali, alkaline-earth) in elemental EOS and minima-hopping benchmarks (errors $>$10%) (Tahmasbi et al., 23 Dec 2025).

• “Rugged” potential energy surfaces causing slightly higher failure rates in local optimization compared to smoother MLIPs (Tahmasbi et al., 23 Dec 2025).

• For production-level kinetics and thermodynamics, domain-specific fine-tuning or post-processing by DFT is recommended.

5. Implementation, Computational Efficiency, and Practical Guidelines

MatterSim is implemented for efficient GPU inference:

• Simulation cost:

  • MD (10,000 steps, 512 atoms, NVIDIA A100): $\sim$905 s
  • Fine-tuning (100 epochs, 2,000 frames): $\sim$342 min (Hänseroth et al., 7 Nov 2025)
  • Typical throughput: $\sim$150 k-atoms·step/s (MatterSim-1M), compared to 4,000 for specialized DP-UniAlCu (Xu et al., 4 Dec 2025)
• Integration: Export via the aMACEing Toolkit to LAMMPS or ASE; supported in the fairchem Python package and compatible with ASE’s “FIRE” optimizer (Hänseroth et al., 7 Nov 2025, Ito et al., 9 Sep 2025).
• Input/output: Accepts POSCAR, XYZ, and ASE-readable formats; outputs atom-wise energies, forces, and optional stress.
• Dispersion corrections: D3 appended at inference for compatibility with PBE+D3 training (Ito et al., 9 Sep 2025).
• Best practices: Employ pre-trained MatterSim-Large checkpoint, then fine-tune on $\sim$2,000 ab initio MD frames, reserving 10–30% for validation. For new element types or bonding environments, augment training data with targeted off-equilibrium samples (Hänseroth et al., 7 Nov 2025, Tahmasbi et al., 23 Dec 2025).

6. Comparative Analysis and Future Directions

MatterSim consistently ranks among the top universal MLIPs for accuracy in transition-metal and complex oxide systems (Tahmasbi et al., 23 Dec 2025, Hänseroth et al., 7 Nov 2025, Du et al., 14 Feb 2025). In high-throughput zeolite screening, it is competitive but eSEN-30M-OAM achieves slightly lower RMSE on all test sets (Ito et al., 9 Sep 2025). In supported nanoparticle exploration, MatterSim-1M demonstrates superior structure generation capability but unreliable energy rankings and higher computational cost compared to domain-tuned potentials (Xu et al., 4 Dec 2025).

Key strengths:

• Robust “foundation model” coverage across materials, temperatures, and pressures.
• Strict energy–force derivative consistency and physically conservative architecture.
• Ab initio fidelity upon fine-tuning, with reduction in training data requirements by up to 97%.

Open challenges:

• Network architecture and loss weighting require refinement for Group 1/2 (simple metal) systems.
• Smoother energy surfaces may aid optimization efficiency but not guarantee energetic fidelity.
• Augmented training on far-from-equilibrium, light-element, and low-dimensional structures suggested to improve universality.
• For quantitative ranking, MD kinetics, and energetics in catalytic systems, post-processing or fine-tuning remains necessary.

7. References and Availability

MatterSim is documented in (Yang et al., 2024), and its benchmarking and deployment are described in (Hänseroth et al., 7 Nov 2025, Tahmasbi et al., 23 Dec 2025, Du et al., 14 Feb 2025, Xu et al., 4 Dec 2025), and (Ito et al., 9 Sep 2025). The aMACEing Toolkit enables reproducible training workflows (Hänseroth et al., 7 Nov 2025). The full relaxation and benchmarking datasets are publicly available (see Zenodo: doi:10.5281/zenodo.17075635) (Ito et al., 9 Sep 2025). Researchers are advised to consult primary source papers for recent architecture, hyperparameter, and dataset updates.

MatterSim embodies the current consensus for universal MLIPs: large-scale, actively learned, graph-based foundation models enable rapid, accurate materials simulation and serve as extensible platforms for domain-specific fine-tuning and property regression in computational materials science.