Neuroevolution Potential (NEP/UNEP-v1)

Updated 2 June 2026

NEP/UNEP-v1 is a machine-learned interatomic potential framework that leverages systematically crafted local descriptors and compact neural networks optimized via evolutionary strategies.
It delivers near-DFT accuracy with empirical-potential-level efficiency across diverse chemistries, including alloys, oxides, semiconductors, and porous frameworks for large-scale MD.
Integrated with GPU-accelerated GPUMD, the model supports high-throughput simulations and on-the-fly active learning for uncertainty quantification and model updating.

The Neuroevolution Potential (NEP/UNEP-v1) is a machine-learned interatomic potential framework that couples systematically crafted local descriptors with compact neural networks, trained via black-box evolutionary optimization. Designed for deployment in large-scale atomistic simulations, especially within the GPU-accelerated GPUMD environment, NEP/UNEP-v1 delivers near-DFT accuracy while maintaining empirical-potential-level computational efficiency. This unified model is applicable across diverse chemistries—including pure elements, alloys, oxides, semiconductors, and porous frameworks—with high fidelity to both structural and thermal properties, even for million-atom and nanosecond timescale molecular dynamics (Ying et al., 2024, Song et al., 2023, Ying et al., 19 Jan 2025).

1. Mathematical Formulation and Descriptor Structure

NEP/UNEP-v1 represents the total potential energy $E$ of an $N$ -atom system as a sum of atomic energies $E_i$ : $E = \sum_{i=1}^N E_i$ Each site energy $E_i$ is modeled via a feed-forward neural network of fixed width, whose input is a descriptor vector $\mathbf{q}_i$ encoding the local environment of atom $i$ : $E_i = \mathbf{w}^e \cdot \tanh( W^u \mathbf{q}_i - \mathbf{b}^u ) - b^e$ where $W^u, \mathbf{b}^u, \mathbf{w}^e, b^e$ are species-dependent trainable weights and biases; $\tanh$ is used as the activation function (Wang et al., 15 Apr 2026, Song et al., 2023). For multi-element systems, the total model comprises separate neural submodels (optionally bagged in an ensemble) for each atomic species.

The descriptor vector $N$ 0 concatenates radial ( $N$ 1) and angular ( $N$ 2, with higher body-orders possible) symmetry functions. The canonical forms employed are: $N$ 3

$N$ 4

where $N$ 5 are Chebyshev or polynomial radial functions, $N$ 6 are Legendre polynomials, and $N$ 7 is a smooth cosine cutoff. For alloy and multicomponent problems, Chebyshev coefficients $N$ 8 are trained per element-pair; higher descriptor orders (e.g., up to five-body) and separate cutoffs for radial and angular channels are used in NEP4/UNEP-v1 (Song et al., 2023, Shuang et al., 2 Apr 2026).

All descriptors are invariant to global rotations, translations, and permutation of like atoms, and are normalized to unit variance over training data.

2. Training Methodology: Separable Natural Evolution Strategy (SNES)

NEP/UNEP-v1 employs a derivative-free optimization via a Separable Natural Evolution Strategy (SNES), which evolves a population of model parameter vectors. At each generation, candidate parameter sets are sampled from a multivariate Gaussian distribution, scored on a loss function, ranked, and used to update the Gaussian's mean and variance along the natural gradient:

Loss Function (for parameter vector $N$ 9):

$E_i$ 0

with typical weightings $E_i$ 1 for balancing global energy, atomic forces, and virial tensor errors (Ying et al., 2024, Song et al., 2023).

SNES Procedure: For each generation, sample a population of candidate parameters, evaluate the loss over a (possibly batched) training subset, rank and assign fitness utilities, and update the mean and variance via natural gradient steps. Typically, 30–100 offspring per generation and $E_i$ 2– $E_i$ 3 generations are employed for converged models, with mini-batch loss to expedite evaluation (Wang et al., 15 Apr 2026, Cao et al., 19 May 2025).

For some recent applications, analytic gradients and first-order optimizers (Adam) have been used for enhanced convergence (GNEP) (Huang et al., 1 Jul 2025).

3. Model Versions, Descriptor Advances, and Data Generation

The original NEP (e.g., NEP1) targeted single- and binary-atomic systems with type-averaged descriptors, while NEP2 introduced per-basis-function element-pair scaling to significantly enhance accuracy in multi-component alloys (Fan, 2021). NEP4/UNEP-v1 incorporates expanded descriptor sets (e.g., up to five-body terms, more Chebyshev channels), per-element network weights, and bagging/ensembling for uncertainty quantification (Song et al., 2023, Shuang et al., 2 Apr 2026).

Model training sets are built from extensive high-fidelity DFT databases. The unified 16-element metal potential (UNEP-v1) is trained entirely on unary and binary alloy data, with active learning and farthest-point sampling in descriptor space ensuring maximal chemical coverage. This technique enables generalization to arbitrary $E_i$ 4-component alloys and solid solutions without explicit $E_i$ 5 training data (Song et al., 2023, Cao et al., 19 May 2025, Shuang et al., 2 Apr 2026). For nonmetal systems (MOFs, oxides, etc.), similar descriptor choices and active-learning sampling strategies are employed (Ying et al., 2024, Xu et al., 25 May 2025, Zhang et al., 2024).

Tables of typical hyperparameters:

Parameter	Metals (UNEP-v1)	MOFs	Oxides
Radial cutoff $E_i$ 6	6.0 Å	6.0 Å	6.0 Å
Angular cutoff	5.0 Å	4.5 Å	5.0 Å
Radial channels	5 (×Chebyshev 9)	8–10	8–10
Angular channels	$E_i$ 7	8	2–4
Hidden layer size	80	40–64	40–100
Training length	$E_i$ 8 gens	$E_i$ 9– $E = \sum_{i=1}^N E_i$ 0	$E = \sum_{i=1}^N E_i$ 1 (Adam)
Batch size	$E = \sum_{i=1}^N E_i$ 2	500–1000	64

4. GPUMD Implementation and Computational Performance

NEP/UNEP-v1 is natively integrated in GPUMD, with all descriptor construction, neural network forward/backward passes, and force/virial/heat-current evaluation performed in CUDA kernels. Separate pre-allocated buffers store bead replicas, partial forces, and virials for PIMD workflows. GPUMD takes standard NEP model files, with element-specific settings included for all supported species (Ying et al., 2024, Zhou et al., 2024).

Performance is highly optimized for linear scaling and single- or multi-GPU deployment. Measured throughput routinely exceeds $E = \sum_{i=1}^N E_i$ 3– $E = \sum_{i=1}^N E_i$ 4 atom-step/s on modern A100, H100, or RTX 4090 hardware, enabling million-atom and multi-nanosecond molecular dynamics (MD) trajectories (Zhou et al., 2024, Cao et al., 19 May 2025, Shuang et al., 2 Apr 2026). The total model size per species is of order kilobytes; neighbor list and coordinate data dominate memory consumption (Shuang et al., 2 Apr 2026).

Relative to other state-of-the-art MLIPs (e.g., GAP, ACE, DP, GRACE), NEP/UNEP-v1 is typically one to two orders of magnitude faster at inference, with only a modest penalty over classical EAM-type potentials, but delivers DFT-quality accuracy for energies, forces, and virials across a wide variety of systems (Song et al., 2023, Zhou et al., 2024, Shuang et al., 2 Apr 2026).

5. Benchmarks, Accuracy, and Applications

Accuracy

Metals (UNEP-v1, 16 elements): Training RMSEs of 2–5 meV/atom (energy), 60–100 meV/Å (force), 0.2–0.4 GPa (virial); test RMSEs remain <25 meV/atom and 120 meV/Å for alloys and complex solid solutions (Song et al., 2023, Cao et al., 19 May 2025, Shuang et al., 2 Apr 2026).
MOFs/Water/Al: RMSEs of $E = \sum_{i=1}^N E_i$ 51.2 meV/atom (energy), 30–53 meV/Å (force), and 0.8–14 meV/atom (virial) have been achieved (Ying et al., 2024).
GaN, other semiconductors, oxides: Model and hyperparameter optimization gives force RMSEs $E = \sum_{i=1}^N E_i$ 650–100 meV/Å and energy RMSEs $E = \sum_{i=1}^N E_i$ 71 meV/atom (Chen et al., 8 Feb 2025, Gu et al., 15 Jan 2026, Zhang et al., 2024).

Large-Scale Applications

NEP/UNEP-v1 supports a range of applications:

Path-integral MD with nuclear quantum effects (LiH, MOFs, water, Al), capturing isotope effects and quantum corrections (Ying et al., 2024).
Heat transport simulations for pure and polycrystalline graphene, metals, and MOFs with system sizes up to 1.4 million atoms; accurate thermal conductivity predictions and transferability benchmarks (including D3 dispersion for van der Waals systems) (Zhou et al., 2024, Ying et al., 2023, Cao et al., 19 May 2025).
Hybrid MC/MD for chemical order and radiation damage in concentrated alloys and complex materials (Song et al., 2024, Song et al., 2023).
Structural and mechanical response for oxides (Al $E = \sum_{i=1}^N E_i$ 8O $E = \sum_{i=1}^N E_i$ 9, Ga $E_i$ 0O $E_i$ 1), cement gels, tobermorite, and Ca–Si–H systems, robust to polymorphism and amorphization (Xu et al., 25 May 2025, Zhang et al., 2024, Gu et al., 15 Jan 2026).
Autonomous active learning for dataset expansion in large or extrapolative cells, with D-optimality-driven selection and fragment embedding for scalable training data acquisition (Wang et al., 15 Apr 2026).

Transferability and Limitations

NEP/UNEP-v1 is demonstrated to transfer accurately from unary/binary training sets to arbitrary $E_i$ 2-component alloys and mixed-chemistry phases (Song et al., 2023, Ying et al., 19 Jan 2025). However, explicit long-range electrostatics, charge transfer, and out-of-domain chemistry require augmenting the framework with additional descriptors or coupling to charge-equilibration models.

6. Active Learning, Uncertainty Quantification, and Model Updates

Active learning in NEP/UNEP-v1 is based on D-optimality and ensemble uncertainty. During MD, atomic environments with extrapolation grade above threshold, detected via the D-optimality MaxVol criterion, are extracted, embedded in locally periodic fragments, and labeled with DFT for incremental retraining (Wang et al., 15 Apr 2026). For uncertainty quantification, bagging ensembles of NEP submodels are used; the variance across the ensemble informs model error and reliability (Shuang et al., 2 Apr 2026).

Automated retraining, fragment labeling, and model hot-swapping are directly supported in GPUMD, enabling seamless on-the-fly updates and adaptation to new environments with minimal computational overhead.

7. Impact and Outlook

The NEP/UNEP-v1 framework enables routine, high-fidelity atomistic simulations at scales and speeds previously inaccessible to DFT-based approaches and outperforms standard empirical models in both accuracy and transferability for alloys, oxides, and complex frameworks. Its design principles—local systematic descriptors, compact ANNs, and global evolutionary optimization—allow for rapid extension to new chemistries, automated active-learning deployment, and direct incorporation in multi-resolution methods.

Planned developments include further extension toward full periodic-table “foundation” NEPs, hybridization with charge and long-range descriptors, deeper architectures for strongly correlated materials, and workflow automation for self-guided data generation and model management (Song et al., 2023, Fan et al., 1 Mar 2026, Yan et al., 18 Mar 2026). This suggests NEP/UNEP-v1 remains a competitive standard in the current landscape of machine-learned potentials for large-scale molecular simulation.