Organizations: School of Materials Science and Engineering & State Key Laboratory of Advanced Refractories & State Key Laboratory of Advanced Special Steels, Shanghai University, Shanghai, 200444, P. R. China.
The core of molecular dynamics simulation fundamentally lies in the interatomic potential. Traditional empirical potentials lack accuracy, while first-principles methods are computationally prohibitive. Machine learning interatomic potentials (MLIPs) promise near-quantum accuracy at linear cost, but existing models still face challenges in efficiency and stability. We presents Machine Learning Advances Neural Network (MLANet), an efficient and robust graph neural network framework. MLANet introduces a dual-path dynamic attention mechanism for geometry-aware message passing and a multi-perspective pooling strategy to construct comprehensive system representations. This design enables highly accurate modeling of atomic environments while achieving exceptional computational efficiency, making high-fidelity simulations more accessible. Tested across a wide range of datasets spanning diverse systems, including organic molecules (e.g., QM7, MD17), periodic inorganic materials (e.g., Li-containing crystals), two-dimensional materials (e.g., bilayer graphene, black phosphorus), surface catalytic reactions (e.g., formate decomposition), and charged systems, MLANet maintains competitive prediction accuracy while its computational cost is markedly lower than mainstream equivariant models, and it enables stable long-time molecular dynamics simulations. MLANet provides an efficient and practical tool for large-scale, high-accuracy atomic simulations.
Figures & tables
Figure 1: The architecture of MLANet. a Overall Model Architecture. b Internal Structure of MLANet. c Message Passing Layer of MLANet.
Figure 2: Learning Curves and Model Efficiency of MLANet on QM7. a Histogram of molecular masses in the QM7 dataset, b histogram of atomization energies. c Log–log learning curve of energy prediction MAE versus training set size, d memory usage and training time per epoch for MLANet with maximum rotation order lmax∈{1,2,3} .
Figure 3: Learning curves and computational efficiency for MLANet on the lithium-containing subset of Mptrj. a, b, c Log-log plots show the scaling of energy, force, and stress prediction errors (MAE) with training set size for MLANet variants with maximum rotation order lmax∈{1,2,3} . d The panel compares memory usage and training speed per epoch across model variants.
Figure 4: Exfoliation of phosphorene. a, b Exfoliation curves of black phosphorene predicted by the MLANet model without ( a ) and with ( b ) the long‑range interaction term (red lines), compared with DFT + MBD reference data (black dashed lines). c, d Exfoliation curves of Hittorf’s phosphorus (P2/c and P2/n structures) predicted by the MLANet model including the long‑range interaction term compared with DFT + MBD reference data points The plots show the energy evolution with interlayer distance.
Method
MAE [kcal/mol]
AttentiveFP [ 44 ]
66.2 (2.8)
DMPNN [ 45 ]
105.8 (13.2)
DTNN [ 46 ]
8.2 (3.9)
GraphConv [ 47 ]
118.9 (20.2)
GROVER (base) [ 48 ]
72.5 (5.9)
MPNN [ 49 ]
113.0 (17.2)
Table 1: Results on the QM7 datasets. Boldface indicates the best performance. Errors shown in parentheses are obtained as the standard deviations from ten-fold cross validation.
SchNet [ 20 ]
DimeNet++ [ 55 ]
PaiNN [ 56 ]
NequIP [ 27 ]
DetaNet [ 41 ]
EnviroDetaNet [ 57 ]
MLANet
Dipole Moment (D/Å)
0.0790
0.0246
0.0102
0.0124
0.0087
0.0069
0.0188
Polarizability ( a03 )
-
-
0.1536
0.1925
0.1374
0.0657
0.1745
Table 2: Model performance (MAE) on the QM9S dataset.
Figure 5: Performance comparison of force prediction accuracy (MAE), MD stability, and computational speed for small molecule systems. Metrics are normalized to their maximum values for visualization. See Table. S3 in the SI for numerical data. Speed tests used a single NVIDIA V100 GPU.
AIREBO [ 59 ]
Reaxff [ 60 ]
GAP2020 [ 61 ]
LCBOP [ 62 ]
DP [ 63 ]
NEP [ 64 ]
REBO-ILP [ 65 , 66 ]
NequIP [ 27 ]
hNN [ 67 ]
MLANet
Slinding Energy (meV/atom)
1.1
0.7
2.5
0.9
0.6
0.7
1.0
0.4
0.4
0.5
Binding Energy (meV/atom)
17.7
16.0
10.3
7.4
3.5
2.6
1.6
1.2
0.8
1.3
Table 3: RMSE values of binding energies and sliding energies for the potentials against reference DFT calculations in bilayer graphene.
Figure 6: Comparison of MLANet predictions and DFT calculations. a AB, AA, and SP stacking configurations, whose positions are marked on the MLANet potential energy surface plot. b Binding energy curves of AB-stacked bilayer graphene from DFT (blue) and MLANet (orange). c, d Rigid-sliding potential energy surfaces of bilayer graphene from MLANet and DFT at a separation of 3.2 Å. e, f Rigid-sliding potential energy surfaces of bilayer graphene from MLANet and DFT at a separation of 3.4 Å. g, h Rigid-sliding potential energy surfaces of bilayer graphene from MLANet and DFT at a separation of 3.6 Å. i, j Flexible-sliding potential energy surfaces of bilayer graphene from MLANet and DFT at a separation of 3.2 Å. The energy zero for both DFT and MLANet is set to the total energy of AB-stacked bilayer graphene. k Energy scan curves along the AA-to-SP direction under four conditions from panel j , where the curves and data points represent predictions from MLANet and DFT, respectively.
Dataset
Metric
NequIP [ 27 ]
MACE [ 28 ]
Mattersim [ 68 ]
Grace [ 69 ]
AlphaNet [ 70 ]
MLANet
Formate Decomposition
Force MAE (meV/Å)
47.3
54.1
46.8
53.9
42.5
44.9
Energy MAE (meV/atom)
0.50
0.31
0.45
0.48
0.23
2.31
Table 4: Results on the Formate Decomposition datasets.
BPNN [ 71 ]
ACE [ 72 ]
REANN [ 73 ]
DeePMD [ 74 ]
NequIP [ 27 ]
MACE [ 28 ]
CACE [ 75 ]
CAMP [ 58 ]
MLANet
Energy
2.3
1.7
0.8
2.1
0.94
0.63
0.59
0.59
0.47
Forces
120
99
53
92
45
36
47
34
60
Table 5: Model performance on the water dataset. RMSEs of energy and forces are in the units of meV/atom and meV/Å, respectively.
Dataset
Metric
4G-HDNNP [ 42 ]
Maruf’s NequIP [ 78 ]
ReaxNet [ 79 ]
MLANet
C 10 H 2 /C 10 H 3+
Force RMSE (eV/Å)
0.078
0.071
0.023
0.074
Ag 3+/−
Force RMSE (eV/Å)
0.033
-
0.005
0.024
Na 8/9 Cl 8+
Force RMSE (eV/Å)
0.032
2.145
0.028
0.012
Table 6: Results on the different charge-state datasets
We introduce implicit machine learning force fields (I-MLFFs), which replace explicit stacks of neural network layers with self-consistent fixed-point equations. In molecular simulations, this formulation enables intermediate representations to be reused across successive timesteps, thereby warm-starting force evaluation. The resulting models effectively combine the computational footprint of a shallow, single-layer MLFF with the representational capacity and accuracy of a deep neural network. Our approach unlocks architecture-agnostic efficiency gains that are inaccessible when force prediction and trajectory integration are considered separately. We demonstrate this across three major classes of graph neural networks: invariant, equivariant Cartesian tensor, and SO(3)-equivariant spherical-tensor architectures. Each yields a two- to five-fold reduction in compute and memory footprint. Crucially, these gains are achieved while retaining full atomistic resolution and the original integration timestep, avoiding spatial or temporal coarse graining. Our contribution therefore advances the scaling frontier of quantum-mechanically faithful molecular simulation, enabling longer trajectories and larger atomistic systems within fixed GPU memory and compute budgets, and thereby opening access to new insights across biomolecular and material systems.
Johannes Maeß, Leon Werner, J. Thorben Frank +5
BIFOLD, Berlin, Germany. · Machine Learning Group, TU Berlin, Berlin, Germany. · Department of Artificial Intelligence, Korea University, Seoul, South Korea. +1
Foundation MLIPs demonstrate broad applicability across diverse material systems and have emerged as a powerful and transformative paradigm in chemical and computational materials science. Equivariant MLIPs achieve state-of-the-art accuracy in a wide range of benchmarks by incorporating equivariant inductive bias. However, the reliance on tensor products and high-degree representations makes them computationally costly. This raises a fundamental question: as quantum mechanical-based datasets continue to expand, can we develop a more compact model to thoroughly exploit high-dimensional atomic interactions? In this work, we present MatRIS (Materials Representation and Interaction Simulation), an invariant MLIP that introduces attention-based modeling of three-body interactions. MatRIS leverages a novel separable attention mechanism with linear complexity O(N), enabling both scalability and expressiveness. MatRIS delivers accuracy comparable to that of leading equivariant models on a wide range of popular benchmarks (Matbench-Discovery, MatPES, MDR phonon, Molecular dataset, etc). Taking Matbench-Discovery as an example, MatRIS achieves an F1 score of up to 0.847 and attains comparable accuracy at a lower training cost. The work indicates that our carefully designed invariant models can match or exceed the accuracy of equivariant models at a fraction of the cost, shedding light on the development of accurate and efficient MLIPs.
Yuanchang Zhou, Siyu Hu, Xiangyu Zhang +3
State Key Lab of Processors, Institute of Computing Technology, Chinese Academy of Sciences · University of Chinese Academy of Sciences · School of Advanced Interdisciplinary Sciences, UCAS
Machine learning interatomic potentials (MLIPs) have become a hallmark of AI for scientific simulation. While efforts on new architectures and datasets have led to increasingly accurate and general models, the choice of optimizer for training has largely remained unexplored, defaulting to Adam and its variants in the community. Here, we implement and systematically compare a class of recently proposed matrix-structured optimizers, including Muon, SOAP, and the hybrid SOAP-Muon, for training NequIP and Allegro MLIP models. We find that these optimizers can substantially outperform Adam in both convergence speed and final accuracy. SOAP and SOAP-Muon emerge as robust and consistently strong methods, while Muon only provides partial gains relative to Adam. The improvements are particularly pronounced under partial force supervision. Our results indicate that optimizer choice is an overlooked yet impactful design axis for MLIPs.
Gil Harari, Yoel Zimmermann, Ola Tangen Kulseng +4
John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA · Robert Bosch LLC Research and Technology Center, Watertown, MA, USA