OutisLi/DPA4-MatPES-v20260628

DPA4-MatPES

DPA4-MatPES provides a series of DPA4 / SeZM machine-learning interatomic potentials trained on the MatPES R2SCAN 2025.2 dataset. The models are SO(3)-equivariant and conservative, and span the full periodic table. They are intended for inorganic materials within the chemical space covered by MatPES R2SCAN.

Overview

General information:

Item	Value
Architecture	DPA4 / SeZM
Backend	PyTorch only
Precision	float32
Elements	Full periodic table (H–Og)
Cutoff radius	6.0 Å
Training data	MatPES R2SCAN 2025.2 (347,889 frames)
Validation data	MatPES R2SCAN 2025.2 (19,328 frames)
Trained with	DeePMD-kit 3.2.0, PyTorch 2.11 / CUDA 12.8

Model variants:

Model	Parameters
DPA4-Mini	655,504 (0.655 M)
DPA4-Neo	1,125,372 (1.125 M)
DPA4-Air	5,148,611 (5.149 M)

Released files:

File	Description
DPA4-Mini-MatPES-v20260628.pt	DPA4-Mini checkpoint.
DPA4-Mini-MatPES-v20260628.json	DPA4-Mini training configuration.
DPA4-Neo-MatPES-v20260628.pt	DPA4-Neo checkpoint.
DPA4-Neo-MatPES-v20260628.json	DPA4-Neo training configuration.
DPA4-Air-MatPES-v20260628.pt	DPA4-Air checkpoint.
DPA4-Air-MatPES-v20260628.json	DPA4-Air training configuration.

The models predict atomic energies, from which forces and virials are obtained by differentiation:

$\qquad \mathbf{F}_i = -\frac{\partial E}{\partial \mathbf{r}_i}$

The descriptor propagates vector and higher-order angular (SO(3)-equivariant) features through message passing and reads out only the final l = 0 scalar to the energy fitting network. The architecture is described in the DeePMD-kit DPA4 documentation.

Model architecture

Names in parentheses are the corresponding DeePMD-kit configuration keys. The complete configurations, including the full type_map, are given in the released input files.

Network dimensions

Parameter	DPA4-Mini	DPA4-Neo	DPA4-Air	Description
Feature channels (channels)	32	32	64	Total channels per (l, m) coefficient.
Focus streams (n_focus)	1	2	1	Parallel focus streams inside the SO(2) convolution.
Interaction blocks (n_blocks)	2	2	3	Number of message-passing blocks.
SO(2) layers per block (so2_layers)	3	3	4	Number of SO(2) mixing layers per block.
FFN blocks (ffn_blocks)	1	1	1	Number of FFN sublayers per interaction block.
Environment seeding (use_env_seed)	True	True	True	Seed the initial node state with local-environment information via environment-matrix FiLM conditioning.

Radial basis and angular resolution

Parameter	DPA4-Mini	DPA4-Neo	DPA4-Air	Description
Radial basis (basis_type)	bessel	bessel	bessel	Radial basis type (bessel or gaussian).
Radial functions (n_radial)	16	16	16	Number of radial basis functions.
Max angular degree (lmax)	2	3	3	Maximum degree of the equivariant representation.
Max SO(2) order (mmax)	1	1	1	Maximum SO(2) order.

Equivariant interaction

Parameter	DPA4-Mini	DPA4-Neo	DPA4-Air	Description
Radial degree mixer (radial_so2_mode)	degree_channel	degree_channel	degree_channel	Dynamic radial degree-mixer mode in the SO(2) convolution; degree_channel uses a per-channel cross-degree radial kernel.
Mixer rank (radial_so2_rank)	1	1	1	Low-rank factorization rank for the degree_channel kernel (0 = full per-channel kernel).
Attention heads (n_atten_head)	1	1	1	Heads aggregating messages in the SO(2) convolution (0 = envelope-weighted scatter-sum).
SO(3) message branch (message_node_so3)	True	True	True	Enable the post-aggregation SO(3) Wigner-D grid-net branch (message as query, node state as context).
Normalization placement (sandwich_norm)	[false, true, true, false]	[false, true, true, false]	[false, true, true, false]	Pre/post-norm switches for residual branches, ordered [so2_pre, so2_post, ffn_pre, ffn_post].

Feed-forward and read-out

Parameter	DPA4-Mini	DPA4-Neo	DPA4-Air	Description
Activation (activation_function)	silu	silu	silu	Base activation for helper MLPs, the SO(2) gated path, and the output FFN.
GLU (glu_activation)	True	True	True	Base GLU switch for the FFN (e.g. SiLU → SwiGLU).
FFN width (ffn_neurons)	0 (auto)	0 (auto)	0 (auto)	Hidden width for block and output FFNs; 0 resolves the width from channels.
FFN SO(3) grid (ffn_so3_grid)	True	True	True	Use the Wigner-D SO(3) grid in the block-internal FFN.
Grid-branch routing (grid_branch)	[0, 0, 1]	[0, 0, 1]	[0, 0, 1]	Scalar-routed polynomial product branches per grid path, ordered [node_wise, message_node, ffn].
SO(3) read-out (so3_readout)	mlp	mlp	mlp	Read-out mode for the final l=0 descriptor; mlp folds l>0 geometry into l=0 via a point-wise SO(3) grid MLP.
Fitting hidden width (fitting_net.neuron)	[0] (auto)	[0] (auto)	[0] (auto)	Fitting-net hidden-layer widths; 0 is an auto-width placeholder resolved from the descriptor width.

Cut-off and model size

Parameter	DPA4-Mini	DPA4-Neo	DPA4-Air	Description
Cut-off radius (rcut)	6.0 Å	6.0 Å	6.0 Å	Neighbor cut-off radius.
Total parameters	655,504 (0.655 M)	1,125,372 (1.125 M)	5,148,611 (5.149 M)	Trainable parameter count.

Precision and compilation

Parameter	Value	Description
Compute precision (precision)	float32	Precision of the descriptor parameters.
Mixed precision (use_amp)	True	Automatic mixed precision with bfloat16 on CUDA during training.
TF32 matmul (enable_tf32)	True	TF32 matmul precision for CUDA training forwards (eval-time TF32 is controlled separately).
Compiled path (use_compile)	True	Use the compiled DPA4/SeZM training path.

Training

The models were trained with the conservative energy objective using dp --pt train.

Setting	DPA4-Mini	DPA4-Neo	DPA4-Air
Epochs	300	250	200
Batch size	filter:12000	filter:3000	filter:2000
Learning rate	WSD schedule, start_lr = 1e-3 → stop_lr = 1e-6	WSD schedule, start_lr = 5e-4 → stop_lr = 1e-6	WSD schedule, start_lr = 3.5e-4 → stop_lr = 1e-6
Decay phase	cosine decay over 65% of the schedule	cosine decay over 65% of the schedule	cosine decay over 65% of the schedule
Optimizer	HybridMuon (weight_decay = 0.001)	HybridMuon (weight_decay = 0.001)	HybridMuon (weight_decay = 0.001)
Loss	MAE energy loss with prefactors pref_e = 20, pref_f = 20, pref_v = 5	MAE energy loss with prefactors pref_e = 20, pref_f = 20, pref_v = 5	MAE energy loss with prefactors pref_e = 20, pref_f = 20, pref_v = 5

Validation

Errors are reported on the MatPES R2SCAN validation set.

Model	Energy MAE/atom	Energy RMSE/atom	Force MAE	Force RMSE	Stress MAE	Stress RMSE	Training hoursᵃ
DPA4-Mini	21.99 meV	55.18 meV	110.23 meV/Å	259.77 meV/Å	3.830 meV/ų	8.236 meV/ų	9.9
DPA4-Neo	17.70 meV	52.91 meV	95.91 meV/Å	225.23 meV/Å	3.167 meV/ų	7.047 meV/ų	14.6
DPA4-Air	15.34 meV	50.95 meV	93.27 meV/Å	225.06 meV/Å	2.968 meV/ų	6.608 meV/ų	19.5

• ᵃ Training hours are measured on a single NVIDIA H20 GPU.

Usage

DPA4/SeZM is a PyTorch-only model and uses the .pt2 (AOTInductor) export path; the TorchScript freeze path does not apply. Usage follows the DeePMD-kit DPA4 documentation.

Installation

DPA4/SeZM is available in the DeePMD-kit main branch (version 3.2.0). Install the latest code together with PyTorch 2.11 and CUDA 12.8:

pip install torch
pip install git+https://github.com/deepmodeling/deepmd-kit

For offline or backend-specific installation, see the DeePMD-kit installation guide. The compiled inference path (DP_COMPILE_INFER) additionally requires torch >= 2.11 and CUDA >= 12.6.

Evaluate a checkpoint

Run dp test on a released checkpoint with data in the standard or mixed-type DeePMD-kit data format. Replace <Mini|Neo|Air> with the selected model variant:

dp --pt test -m DPA4-<Mini|Neo|Air>-MatPES-v20260628.pt -s /path/to/test/system -n 1000

Freeze to .pt2 for deployment

dp --pt freeze -c DPA4-<Mini|Neo|Air>-MatPES-v20260628.pt -o frozen_model

The PyTorch backend detects DPA4/SeZM and writes frozen_model.pt2. The .pt2 is an AOTInductor archive and is target-specific: it depends on the host CPU/GPU, the GPU compute capability, and the libtorch version. Freeze on the target machine rather than reusing a .pt2 across different hardware.

Inference precision is fixed at freeze time. The .pt2 is a forward-only AOTInductor package, so the SO(2)-rotation kernel and matmul precision are compiled into the graph at export and are not re-evaluated when the file is later loaded by ASE or LAMMPS. Set the relevant environment variables before running dp --pt freeze:

Variable	Default	Effect
DP_TF32_INFER	0 (highest)	float32 matmul precision: 0 highest, 1 high, 2 medium. Keep 0 for MD and other PES-smoothness-sensitive workflows.
DP_TRITON_INFER	off	Fused Triton SO(2) rotation kernel (CUDA). Retains full float32 accumulation, so it is safe for MD.

Accepted boolean values: 1/true/yes/on and 0/false/no/off.

Run in LAMMPS

The frozen .pt2 is used through pair_style deepmd. A minimal setup:

units           metal
atom_style      atomic
atom_modify     map yes

neighbor        2.0 bin
read_data       system.lmp

pair_style      deepmd frozen_model.pt2
pair_coeff      * * O H

atom_modify map yes is required: .pt2 graph inference relies on an explicit ghost/periodic-image to local-atom map, and the model fails fast if the map is absent. The element names after pair_coeff * * bind LAMMPS atom types to entries of the model's type_map in order (here types 1 and 2 to O and H); if omitted, the mapping falls back to the type_map stored in the .pt2 metadata.

Multi-GPU (MPI) inference uses the same .pt2. Launch one MPI rank per GPU and make every target device visible:

CUDA_VISIBLE_DEVICES=0,1,2,3 mpirun -np 4 lmp -in in.lammps

Run with ASE

from ase.io import read
from deepmd.calculator import DP

atoms = read("structure.cif")
atoms.calc = DP(model="frozen_model.pt2")

energy = atoms.get_potential_energy()
forces = atoms.get_forces()
stress = atoms.get_stress()

Adjust the energy bias for a new system

DFT energy labels differ between datasets by an arbitrary per-element constant. Before evaluating or simulating a system whose energy reference differs from MatPES R2SCAN, the per-element energy bias can be refit to that system without retraining any network weights, which often improves energy accuracy:

dp --pt change-bias DPA4-<Mini|Neo|Air>-MatPES-v20260628.pt -s /path/to/system

This updates only the energy shift and writes an adjusted checkpoint; the descriptor and fitting-net weights are unchanged.

Fine-tune on a downstream dataset

The released checkpoints serve as pretrained initializations. Start from the corresponding released input file, keep the model section (descriptor and fitting net) unchanged, replace type_map and the training/validation data with the downstream dataset, and use a small learning rate (e.g. start_lr = 1e-4):

dp --pt train input_finetune.json --finetune DPA4-<Mini|Neo|Air>-MatPES-v20260628.pt

DPA4/SeZM also supports LoRA adapters for single-task fine-tuning; the best checkpoints fold the LoRA deltas back into the base weights, producing a plain DPA4/SeZM checkpoint suitable for deployment.

Intended use and limitations

• Intended for energy, force, and stress prediction of inorganic materials within the chemistry and configuration space covered by MatPES R2SCAN. Accuracy outside this domain should be validated before use.
• PyTorch backend only; export is .pt2 (AOTInductor), and model compression is not supported.
• Multi-GPU (MPI) LAMMPS inference applies to the plain energy model; ZBL zone bridging and spin models run on a single MPI rank.

Citation

If you use these models, please cite the DPA4 paper, DeePMD-kit, and the MatPES R2SCAN dataset.

@article{li2026dpa4,
  title   = {{DPA4}: Pushing the Accuracy-Cost Frontier of Interatomic
             Potentials with {EMFA} {SO(2)} Convolution},
  author  = {Li, Tiancheng and Li, Wentao and Peng, Anyang and Xue, Jianming
             and Zhang, Linfeng and Zhang, Duo and Wang, Han},
  journal = {arXiv preprint arXiv:2606.02419},
  year    = {2026},
  doi     = {10.48550/arXiv.2606.02419},
  url     = {https://arxiv.org/abs/2606.02419}
}

@article{Wang_ComputPhysCommun_2018_v228_p178,
  author    = {Wang, Han and Zhang, Linfeng and Han, Jiequn and E, Weinan},
  title     = {{DeePMD-kit: A deep learning package for many-body potential
               energy representation and molecular dynamics}},
  journal   = {Comput. Phys. Comm.},
  volume    = {228},
  pages     = {178--184},
  year      = {2018},
  doi       = {10.1016/j.cpc.2018.03.016}
}

@article{Zeng_JChemPhys_2023_v159_p054801,
  author    = {Jinzhe Zeng and Duo Zhang and Denghui Lu and Pinghui Mo and Zeyu
               Li and Yixiao Chen and Mari{\'a}n Rynik and Li'ang Huang and Ziyao
               Li and Shaochen Shi and Yingze Wang and Haotian Ye and Ping Tuo
               and Jiabin Yang and Ye Ding and Yifan Li and Davide Tisi and Qiyu
               Zeng and Han Bao and Yu Xia and Jiameng Huang and Koki Muraoka and
               Yibo Wang and Junhan Chang and Fengbo Yuan and Sigbj{\o}rn
               L{\o}land Bore and Chun Cai and Yinnian Lin and Bo Wang and Jiayan
               Xu and Jia-Xin Zhu and Chenxing Luo and Yuzhi Zhang and Rhys E A
               Goodall and Wenshuo Liang and Anurag Kumar Singh and Sikai Yao and
               Jingchao Zhang and Renata Wentzcovitch and Jiequn Han and Jie Liu
               and Weile Jia and Darrin M York and Weinan E and Roberto Car and
               Linfeng Zhang and Han Wang},
  title     = {{DeePMD-kit v2: A software package for deep potential models}},
  journal   = {J. Chem. Phys.},
  volume    = {159},
  issue     = {5},
  pages     = {054801},
  year      = {2023},
  doi       = {10.1063/5.0155600}
}

@article{Zeng_JChemTheoryComput_2025_v21_p4375,
  author    = {Jinzhe Zeng and Duo Zhang and Anyang Peng and Xiangyu Zhang and
               Sensen He and Yan Wang and Xinzijian Liu and Hangrui Bi and Yifan
               Li and Chun Cai and Chengqian Zhang and Yiming Du and Jia-Xin Zhu
               and Pinghui Mo and Zhengtao Huang and Qiyu Zeng and Shaochen Shi
               and Xuejian Qin and Zhaoxi Yu and Chenxing Luo and Ye Ding and
               Yun-Pei Liu and Ruosong Shi and Zhenyu Wang and Sigbj{\o}rn
               L{\o}land Bore and Junhan Chang and Zhe Deng and Zhaohan Ding and
               Siyuan Han and Wanrun Jiang and Guolin Ke and Zhaoqing Liu and
               Denghui Lu and Koki Muraoka and Hananeh Oliaei and Anurag Kumar
               Singh and Haohui Que and Weihong Xu and Zhangmancang Xu and
               Yong-Bin Zhuang and Jiayu Dai and Timothy J. Giese and Weile Jia
               and Ben Xu and Darrin M. York and Linfeng Zhang and Han Wang},
  title     = {{DeePMD-kit v3: A Multiple-Backend Framework for Machine Learning
               Potentials}},
  journal   = {J. Chem. Theory Comput.},
  volume    = {21},
  number    = {9},
  pages     = {4375--4385},
  year      = {2025},
  doi       = {10.1021/acs.jctc.5c00340}
}

@article{Kaplan_arXiv_2025_2503_04070,
  title         = {A Foundational Potential Energy Surface Dataset for Materials},
  author        = {Kaplan, Aaron D. and Liu, Runze and Qi, Ji and Ko, Tsz Wai
                   and Deng, Bowen and Riebesell, Janosh and Ceder, Gerbrand
                   and Persson, Kristin A. and Ong, Shyue Ping},
  journal       = {arXiv preprint arXiv:2503.04070},
  year          = {2025},
  doi           = {10.48550/arXiv.2503.04070},
  url           = {https://arxiv.org/abs/2503.04070}
}