MatterSim-MT: Multi-task Materials Model

• MatterSim-MT is a multi-task foundation model that uses extensive DFT-labeled data to predict energies, forces, stresses, and electronic properties across 89 elements.
• It employs a GeoMFormer-based equivariant transformer with coupled invariant and vector streams to effectively model periodic materials graphs.
• The model supports advanced simulation regimes such as redox battery behavior, ferroelectric dynamics, and polar phonon analysis with competitive accuracy.

MatterSim-MT is a multi-task foundation model for in silico materials characterization. In its explicitly named form, it denotes the 2026 model pretrained on over 35 million first-principles-labeled structures covering 89 elements, temperatures up to 5000 K, and pressures up to 1000 GPa, with joint prediction of energies, forces, stresses, Bader charges, magnetic moments, Born effective charges, and dielectric matrices (Yang et al., 8 May 2026). It extends the earlier MatterSim program, which established a universal atomistic model across elements, temperatures, and pressures as a machine-learning force field and fine-tunable backbone (Yang et al., 2024). In a separate but related usage, “MatterSim-MT” can also denote MatterSim as instantiated inside the MatterTune framework, where MatterSim-v1 is exposed through standardized data, trainer, property, and application abstractions rather than through a separately named architecture (Kong et al., 14 Apr 2025).

1. Origins, lineage, and terminological scope

MatterSim originated as a deep learning atomistic model trained on ~17M DFT-PBE(+U) structures, designed to serve as a universal machine-learning force field across the first 89 elements, configurations from 0 to 5000 K, and pressures up to 1000 GPa (Yang et al., 2024). That earlier formulation supported zero-shot molecular dynamics, structure relaxation, quasi-harmonic thermodynamics, and direct structure-to-property fine-tuning. Its implementation included an M3GNet-based MatterSim, used as the default zero-shot MLFF because of good accuracy and high inference speed, and a Graphormer-based MatterSim, which was larger and more accurate but slower and heavier in memory.

MatterSim-MT generalizes that program from a force-field-centered universal model to a multi-task foundation model. Its defining change is not only larger pretraining data—≈35 million structures for energies, forces, and stresses—but also auxiliary supervision for electronic-response and local-state observables: 172,488 structures for Bader charges, 284,195 structures for magnetic moments, and 3,051 structures for Born effective charges and dielectric matrices (Yang et al., 8 May 2026). The result is a single model that serves both as a potential-energy-surface model and as a predictor of quantities that are not captured by potential energy surfaces alone.

The term also has a narrower software meaning in the MatterTune literature. MatterTune does not introduce a separately named “MatterSim-MT” architecture; rather, it integrates MatterSim-v1 as a backbone within a modular fine-tuning platform. In that context, “MatterSim-MT” denotes MatterSim as implemented and used inside MatterTune, including its trainers, property heads, ASE calculator, and feature-extraction tooling (Kong et al., 14 Apr 2025).

2. Representation, backbone architecture, and task heads

MatterSim-MT operates on a periodic materials graph

$$\mathcal{G} = (\boldsymbol{Z},\boldsymbol{V},\boldsymbol{R},[\boldsymbol{L}, \boldsymbol{S}]),$$

where $\boldsymbol{Z}$ denotes atomic numbers and per-atom features, $\boldsymbol{R}$ atomic Cartesian coordinates, $\boldsymbol{V}$ relative displacement vectors, $\boldsymbol{L}$ the lattice matrix, and $\boldsymbol{S}$ global scalar state variables (Yang et al., 8 May 2026). Nodes are atoms, edges connect pairs within a cutoff radius $r_c = 5.0~\text{\AA}$, and periodic boundary conditions are handled by a multi-graph construction in which the unit cell is replicated up to pbc_expanded_num_cell_per_direction = 5 in each direction. A smooth cutoff mask $m_{ij}$ vanishes continuously at the cutoff.

The backbone is a GeoMFormer-based equivariant transformer with two coupled streams: an invariant stream of scalar atom features $x_i$ and an equivariant stream of vector features $e_i$ (Yang et al., 8 May 2026). The embedding stage augments atomic-number embeddings with radial Gaussian basis information and directional geometry. Each transformer block contains invariant self-attention, equivariant self-attention, invariant cross-attention, equivariant cross-attention, and feed-forward or gated update modules. Periodic images reuse keys and values from their parent atoms to maintain consistency under the multi-graph expansion.

Several model sizes are reported: 1M, 10M, 220M, and 1.3B parameters, with atom embedding sizes from 128 to 1536, 2 to 9 transformer blocks, and 8 to 32 attention heads (Yang et al., 8 May 2026). All simulations in the main text use the 10M-parameter model as the best balance between cost and accuracy.

Task heads act on the final invariant and equivariant features. Energy is obtained by pooling per-atom outputs, forces are obtained as negative gradients of energy with respect to positions, and stress uses a separate global head (Yang et al., 8 May 2026). Bader charges and magnetic moments are produced as per-atom scalars. Born effective charges and dielectric tensors use ETGNN-inspired tensor constructions. In the precursor MatterSim, forces and stresses were likewise tied to the energy model in the M3GNet-based variant through

$\boldsymbol{Z}$0

which is central to the model’s energy-conserving behavior in molecular dynamics (Yang et al., 2024).

3. Pretraining corpus, active data generation, and optimization

The main MatterSim-MT pretraining dataset contains ≈35 million structures labeled with total energy, per-atom forces, and stress tensor (Yang et al., 8 May 2026). These labels were generated with VASP and PAW pseudopotentials at the PBE GGA level, using a plane-wave cutoff of 520 eV and energy convergence of $\boldsymbol{Z}$1. Hubbard $\boldsymbol{Z}$2 corrections were applied for 3d, 4d, and 5d transition metals in oxides and fluorides.

The data-generation strategy inherits the “materials explorer” program of MatterSim-v1. A ground-state explorer samples equilibrium and near-equilibrium structures, while an off-equilibrium explorer runs NPT MD with an older M3GNet-based MatterSim-v1 model under pressures 0, 200, 500, 800, and 1000 GPa and temperatures 300, 1000, 2000, and 5000 K for 10 ps each (Yang et al., 8 May 2026). The earlier MatterSim work described the broader active-learning loop explicitly: an ensemble of 5 models with different random seeds estimates force uncertainty, high-uncertainty configurations are recomputed by DFT, and the model is retrained until benchmark performance saturates (Yang et al., 2024).

Auxiliary supervision extends the property space beyond the potential energy surface. MatterSim-MT is additionally trained on 172,488 periodic structures with Bader charges from AFLOW, 284,195 ferromagnetic structures with magnetic moments from MPTrj, and 3,051 dynamically stable crystals from PhononDB with Born effective charges and dielectric matrices (Yang et al., 8 May 2026).

The multi-task training objective is

$\boldsymbol{Z}$3

with mean absolute error as the loss function, $\boldsymbol{Z}$4, $\boldsymbol{Z}$5, and $\boldsymbol{Z}$6 for magnetic moments, Bader charges, Born effective charges, and dielectric matrices, respectively (Yang et al., 8 May 2026). Optimization uses AdamW with maximum learning rate $\boldsymbol{Z}$7, batch size 1024, linear warmup for 1 epoch, linear decay to 0 over 23 epochs, and EMA 0.99.

4. Learned property space and simulation regimes beyond a PES

MatterSim-MT jointly predicts mechanical, thermodynamic, and electronic-response quantities. Its held-out validation errors are summarized below (Yang et al., 8 May 2026).

Property	Output type	Validation MAE
Magnetic moments	Per-atom scalar	0.064 $\boldsymbol{Z}$8
Bader charges	Per-atom scalar	0.0233 e
Born effective charges	Per-atom tensor	0.0756 e
Dielectric matrices	Per-crystal tensor	0.2478

This joint property space enables simulation modes that standard ML force fields do not support directly. For polar phonons, MatterSim-MT predicts both force constants and the quantities needed for non-analytical corrections. In 3C-SiC, the model is used to relax the structure, compute finite-displacement forces, predict Born effective charges $\boldsymbol{Z}$9 and $\boldsymbol{R}$0, and add the non-analytical correction

$\boldsymbol{R}$1

to obtain pressure-dependent LO-TO splitting (Yang et al., 8 May 2026). At zero pressure it predicts lattice constant $\boldsymbol{R}$2 Å, $\boldsymbol{R}$3, $\boldsymbol{R}$4, $\boldsymbol{R}$5, $\boldsymbol{R}$6, and LO-TO splitting $\boldsymbol{R}$7, compared with 5.20 THz from PBE and 5.29 THz from experiment.

For ferroelectric dynamics, MatterSim-MT supplies both the zero-field potential energy and the Born effective charges needed to couple an external electric field to structural motion. In BaTiO$\boldsymbol{R}$8, the electric enthalpy is written as

$\boldsymbol{R}$9

and the field-induced atomic force is

$\boldsymbol{V}$0

The reported MD setup uses NVT at 100, 200, and 300 K with a Nosé-Hoover thermostat, time step 2 fs, and a sinusoidal electric field with $\boldsymbol{V}$1 and period $\boldsymbol{V}$2; hysteresis loops are averaged over 5 cycles (Yang et al., 8 May 2026).

For redox-active battery materials, the model combines structural dynamics with local charges and local magnetic moments. In Li$\boldsymbol{V}$3Mn$\boldsymbol{V}$4O$\boldsymbol{V}$5, the reported protocol constructs a $\boldsymbol{V}$6 supercell derived from LiCoO$\boldsymbol{V}$7, replaces Co with Mn, randomly replaces 30 Mn with Li, relaxes the structure, runs NVT MD at 1000 K with timestep 1 fs, and removes one Li every 5 ps until complete delithiation over ≈900 ps (Yang et al., 8 May 2026). The simulation tracks the crossover from Mn-centered redox to oxygen dimer formation and near-zero Bader charges on O$\boldsymbol{V}$8 molecules at high delithiation, indicating anionic redox.

5. Accuracy, robustness at extreme conditions, and scaling behavior

MatterSim-MT-10M is benchmarked against universal MLFFs including M3GNet, CHGNet, MACE-MP-0, SevenNet, ORB-v2, and OMat24 on high-temperature and high-pressure datasets (Yang et al., 8 May 2026). On MPF-TP it reports MAEs of 0.042 eV/atom for energy, 0.530 eV/Å for forces, and 1.368 GPa for stress; OMat24 reports 0.126, 0.233, and 2.408, while ORB-v2 reports 0.267, 0.613, and 10.699. On Random-TP, MatterSim-MT-10M reports 0.259 eV/atom, 1.200 eV/Å, and 2.715 GPa. On Extended-TP it reports 0.054 eV/atom, 0.780 eV/Å, and 3.274 GPa. On the HEX high-pressure elemental benchmark it reports 0.106 eV/atom, 0.118 eV/Å, and 8.54 GPa.

The same model is evaluated for lattice dynamics and quasi-harmonic thermodynamics. On PhononDB-based benchmarks, the maximum phonon frequency MAE is 1.016 THz, the phonon group velocity MAE is 22.9 km/s, and the $\boldsymbol{V}$9 error for QHA Gibbs free energies over 300–900 K is 18.5 meV/atom (Yang et al., 8 May 2026). These benchmarks align with a thermodynamic emphasis already present in the precursor MatterSim, which reported a max phonon frequency MAE of 0.87 THz, average phonon frequency MAE of 0.76 THz, bulk modulus MAE of ~2.47 GPa at 0 K, and an integrated Gibbs free-energy MAE of approximately 6.5 meV/atom versus PBE over 0–1000 K (Yang et al., 2024).

Scaling behavior is explicit. Validation loss decreases with more training data, larger models continue to benefit from more data, and the 1.3B-parameter model shows further improvement although it is not used for simulations because of cost (Yang et al., 8 May 2026). The reported pattern is that small models saturate quickly as dataset size grows, whereas larger models retain monotonic gains up to the full 35M dataset.

6. Fine-tuning, MatterTune deployment, and limitations

A principal use case is fine-tuning from PBE(+U) pretraining to a higher level of theory. For liquid water at rev-PBE0-D3, MatterSim-MT is fine-tuned on only 60 high-level configurations, while a comparison model is trained from scratch on 900 configurations (Yang et al., 8 May 2026). The fine-tuning protocol discards and reinitializes the pretrained task head, uses different learning rates for head and backbone—$\boldsymbol{L}$0 and $\boldsymbol{L}$1—and trains with AdamW and a stepLR schedule with step size 8 epochs over 200 epochs using energy-plus-force loss with $\boldsymbol{L}$2. The resulting diffusion coefficient at 300 K is $\boldsymbol{L}$3 for Finetune-60, compared with $\boldsymbol{L}$4 for the untuned PBE-level MatterSim-MT and 0.187–0.24 from experiment.

MatterSim also appears as a backbone in MatterTune, a framework organized into model, data, trainer, and application subsystems (Kong et al., 14 Apr 2025). In that environment, MatterSim-v1 has 4.55M parameters, a pretraining dataset size of 17M atomic structures, and a pretraining objective of energy, forces, and stress. MatterTune standardizes structures as ASE Atoms, requires each backbone to implement model_forward(batch) and atoms_to_data(atoms_list), and maps model outputs to property schemas such as Energy, Forces, and Stress. The shared trainer is built on PyTorch Lightning, and the application layer exposes ASE calculators, property predictors, and feature extractors.

The MatterTune results clarify one practical niche of MatterSim as an energy-conserving, compact backbone. In a few-shot ambient water experiment, MatterSim-V1-1M achieved energy MAE 1.21 meV/atom and force MAE 38.37 meV/Å on a 900-sample dataset, and energy MAE 1.20 meV/atom and force MAE 40.65 meV/Å on a 30-sample repeated dataset (Kong et al., 14 Apr 2025). Using only the 30-sample fine-tuned models, the study ran 200 ps MD at 298 K for a 192-atom water cell with ASE and reported that MatterSim-V1-1M and EquiformerV2 produced oxygen–oxygen radial distribution functions that fit experimental curves well, whereas JMP-S and ORB-v2 showed clear problems despite competitive or lower force MAE. The same integration reproduced Matbench Discovery results for MatterSim-V1-5M with MatterTune values of F1 0.842, DAF 5.255, Precision 0.876, Accuracy 0.949, MAE (stability) 0.024, and $\boldsymbol{L}$5 0.848.

The limitations are explicit. MatterSim-MT covers 89 elements, but some chemically difficult cases are excluded because off-equilibrium DFT calculations often failed to converge (Yang et al., 8 May 2026). Its native level of theory is PBE(+U), so band gaps, some redox energetics, and van der Waals-sensitive systems inherit the limitations of that baseline unless fine-tuned. The explicitly learned property scope comprises energy, forces, stress, Bader charges, magnetic moments, Born charges, and dielectric tensors; band gaps, excitations, and electron-phonon couplings are not directly learned. Tensor heads use ETGNN-style constructions that encourage physically reasonable symmetry, but the model does not explicitly enforce all constraints, such as acoustic sum rules or exact charge neutrality of Born charges, unless such constraints are added as loss terms (Yang et al., 8 May 2026). The earlier MatterSim work also noted that long-range electrostatics and polarization are not modeled explicitly in the force-field formulation, and that surfaces, interfaces, polymers, ionic liquids, and related systems remain under-represented relative to bulk crystals (Yang et al., 2024).