DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics

Han WangLinfeng ZhangJiequn HanWeinan E

article2017Computer Physics Communications1,930 citations

Introduces DeePMD-kit, an open-source software package that trains neural network potential energy models from first-principles data and interfaces directly with engines like LAMMPS to enable quantum-accurate molecular dynamics simulations at scale.

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Molecular simulations are vital for modeling materials and chemical processes, yet researchers routinely face a trade-off between computational accuracy and efficiency. High-accuracy quantum mechanical calculations, such as density functional theory, are computationally expensive and limited to small systems and short timescales. Conversely, empirical force fields allow large-scale simulations but often lack physical accuracy and transferability. To overcome these constraints, machine learning methods have emerged to represent potential energy surfaces accurately, but implementing these models into practical simulation workflows has historically required significant engineering effort.

The article demonstrates DeePMD-kit, an open-source software package designed to automate the training of deep learning potential energy models and streamline their deployment in molecular dynamics simulations.

DeePMD-kit bridges the machine learning framework TensorFlow with established molecular simulation software, specifically LAMMPS for classical dynamics and i-PI for path-integral simulations. The package transforms atomic coordinate data into symmetric descriptors using C++ modules integrated directly into TensorFlow. The authors tested and validated the software using a dataset of 40,000 frames from an ab initio liquid water simulation containing 64 molecules, training a deep neural network on 38,000 frames and evaluating it against 2,000 testing frames.

The findings show that DeePMD-kit successfully trained a 5-layer neural network model on a standard desktop CPU in 16 hours. On the held-out test dataset, the model achieved high accuracy, yielding relative errors of 4.3% in energy and 2.9% in atomic forces relative to the data standard deviation. When executed inside LAMMPS for a 200-picosecond molecular dynamics simulation, the trained model accurately reproduced key physical properties, including radial distribution functions and tetrahedral packing order parameters, in close agreement with the original quantum mechanical calculations.

These results indicate that DeePMD-kit significantly lowers the barrier to performing quantum-accurate simulations across large system sizes and extended timelines. By providing standardized data pipelines and native integration with major simulation engines, the package reduces the manual setup and software engineering overhead needed to deploy deep learning models in molecular modeling projects.

Organizations and research teams seeking quantum-level precision at reduced computational cost should consider adopting DeePMD-kit for potential energy surface modeling. Future software improvements outlined in the article will focus on adding parallel CPU multicore and GPU multithreading support for descriptor calculations during simulations.

A primary limitation of the current release is that descriptor evaluations during live molecular dynamics runs operate only in serial mode on CPUs, which constrains real-time simulation throughput. In addition, the predictive accuracy of the model depends heavily on the quality and scope of the underlying quantum mechanical training data.

Institute of Applied Physics and Computational Mathematics Princeton University convolutional neural networks deep learning python many-body potential energy representation DeePMD-kit molecular dynamics

arXiv: 1712.03641 deepmodeling/deepmd-kit

Paper: TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems, Martín Abadi et al. (2016). Understanding TensorFlow's dataflow architecture and automatic differentiation runtime provides the foundational deep learning framework that DeePMD-kit directly interfaces with for neural network training.
Paper: Neural Message Passing for Quantum Chemistry, Justin Gilmer et al. (2017). This work establishes how message passing neural networks accurately represent quantum chemical properties and molecular systems, motivating the deep learning potential representations implemented in DeePMD-kit.
Paper: Convolutional Networks on Graphs for Learning Molecular Fingerprints, David Duvenaud et al. (2015). This seminal text introduces differentiable, learned representations of molecular structures directly from graphs, which serves as a conceptual prerequisite for neural potential energy representations.

Paper: E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials, Simon Batzner et al. (2021). NequIP extends deep learning interatomic potentials by incorporating rigorous E(3)-equivariant graph neural networks for highly data-efficient molecular dynamics simulations.
Paper: Analyzing Learned Molecular Representations for Property Prediction, Kevin Yang et al. (2019). This work provides a systematic empirical analysis comparing learned graph-based representations against fixed molecular fingerprints across varied chemical spaces.

Cover for DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics

Abstract

Recent developments in many-body potential energy representation via deep learning have brought new hopes to addressing the accuracy-versus-efficiency dilemma in molecular simulations. Here we describe DeePMD-kit, a package written in Python/C++ that has been designed to minimize the effort required to build deep learning based representation of potential energy and force field and to perform molecular dynamics. Potential applications of DeePMD-kit span from finite molecules to extended systems and from metallic systems to chemically bonded systems. DeePMD-kit is interfaced with TensorFlow, one of the most popular deep learning frameworks, making the training process highly automatic and efficient. On the other end, DeePMD-kit is interfaced with high-performance classical molecular dynamics and quantum (path-integral) molecular dynamics packages, i.e., LAMMPS and the i-PI, respectively. Thus, upon training, the potential energy and force field models can be used to perform efficient molecular simulations for different purposes. As an example of the many potential applications of the package, we use DeePMD-kit to learn the interatomic potential energy and forces of a water model using data obtained from density functional theory. We demonstrate that the resulted molecular dynamics model reproduces accurately the structural information contained in the original model.

Topics

convolutional neural networks deep learning python

Keywords

many-body potential energy representation DeePMD-kit molecular dynamics deep neural network molecular simulations DFT water model atomic interactions

I Introduction
II Theory
III Software
III.1 Data preparation
III.2 Model training
III.3 Model testing
III.4 Molecular dynamics
IV Example
V Conclusion and future work
VI acknowledgments
References
A Deriviation of force and virial

Knowls

Knowl 1 — DeePMD Potential Energy Decomposition and Local Frame Atomic Descriptors
model/method
In the DeePMD method, the total potential energy $E$ of a system consisting of $N$ atoms at coordinates $\{\mathbf{R}_1, \dots, \mathbf{R}_N\}$ with $\mathbf{R}_i \in \mathbb{R}^3$ is decomposed into a sum of local atomic energy contributions:

$E = \sum_{i=1}^N E_i, \quad E_i = E_{s(i)}(\mathbf{R}_i, \{\mathbf{R}_j \mid j \in N_{R_c}(i)\})$

where $s(i)$ denotes the chemical species of atom $i$ , and $N_{R_c}(i) = \{j \mid |\mathbf{R}_{ij}| = |\mathbf{R}_i - \mathbf{R}_j| \le R_c, j \ne i\}$ is the set of neighbor atoms within a cutoff radius $R_c$ .

To preserve translational, rotational, and permutational symmetries:
1. Translational symmetry is preserved by using relative displacement vectors $\mathbf{R}_{ij} = \mathbf{R}_i - \mathbf{R}_j = x^0_{ij}\mathbf{e}^0_x + y^0_{ij}\mathbf{e}^0_y + z^0_{ij}\mathbf{e}^0_z$ in the global laboratory frame $\{\mathbf{e}^0_x, \mathbf{e}^0_y, \mathbf{e}^0_z\}$ .
2. Rotational symmetry is preserved by constructing a local coordinate frame $\{\mathbf{e}_{i1}, \mathbf{e}_{i2}, \mathbf{e}_{i3}\}$ using two reference neighbor atoms $a(i), b(i) \in N_{R_c}(i)$ chosen according to predefined rules:
$\mathbf{e}_{i1} = \mathbf{e}(\mathbf{R}_{ia(i)})$

$\mathbf{e}_{i2} = \mathbf{e}\left(\mathbf{R}_{ib(i)} - (\mathbf{R}_{ib(i)} \cdot \mathbf{e}_{i1})\mathbf{e}_{i1}\right)$

$\mathbf{e}_{i3} = \mathbf{e}_{i1} \times \mathbf{e}_{i2}$

where $\mathbf{e}(\mathbf{R}) = \mathbf{R}/|\mathbf{R}|$ . The local coordinates $(x_{ij}, y_{ij}, z_{ij})$ are obtained via the rotation matrix $\mathcal{R}(\mathbf{R}_{ia(i)}, \mathbf{R}_{ib(i)}) = [\mathbf{e}_{i1}, \mathbf{e}_{i2}, \mathbf{e}_{i3}]$ :

$(x_{ij}, y_{ij}, z_{ij}) = (x^0_{ij}, y^0_{ij}, z^0_{ij}) \cdot \mathcal{R}(\mathbf{R}_{ia(i)}, \mathbf{R}_{ib(i)})$
1. Atomic descriptors for atom $i$ given neighbor $j$ are defined as:
$\{D_{ij}^\alpha\} = \begin{cases} \left\{ \frac{1}{R_{ij}}, \frac{x_{ij}}{R_{ij}}, \frac{y_{ij}}{R_{ij}}, \frac{z_{ij}}{R_{ij}} \right\}, & \text{full information } (\alpha = 0,1,2,3) \\ \left\{ \frac{1}{R_{ij}} \right\}, & \text{radial-only information } (\alpha = 0) \end{cases}$
1. Permutational symmetry is enforced by sorting neighbor indices $j$ in the descriptor vector $\mathbf{D}_i$ first by chemical species and then by descending inverse distance $1/R_{ij}$ within each species.
Knowl 2 — Deep Neural Network Architecture for Atomic Potential Energy
model/method
The atomic potential energy $E_{s(i)}$ for an atom $i$ of chemical species $s(i)$ is parameterized as a function of its descriptor vector $\mathbf{D}_i$ via a feedforward deep neural network (DNN) $\mathcal{N}_{s(i)}$ :

$E_{s(i)} = \mathcal{N}_{s(i)}(\mathbf{D}_i) = \mathcal{L}_{s(i)}^{\mathrm{out}} \circ \mathcal{L}_{s(i)}^{N_h} \circ \mathcal{L}_{s(i)}^{N_h-1} \circ \dots \circ \mathcal{L}_{s(i)}^1(\mathbf{D}_i)$

where $N_h$ is the number of hidden layers, and $\circ$ denotes function composition.

Each hidden layer $p \in \{1, \dots, N_h\}$ maps the activations $\mathbf{d}_i^{p-1} \in \mathbb{R}^{M_{p-1}}$ from layer $p-1$ (with $\mathbf{d}_i^0 = \mathbf{D}_i$ ) to $\mathbf{d}_i^p \in \mathbb{R}^{M_p}$ using a linear transformation followed by an element-wise hyperbolic tangent activation function $\phi(x) = \tanh(x)$ :

$\mathbf{d}_i^p = \mathcal{L}_{s(i)}^p(\mathbf{d}_i^{p-1}) = \phi\left(\mathbf{W}_{s(i)}^p \mathbf{d}_i^{p-1} + \mathbf{b}_{s(i)}^p\right)$

where $\mathbf{W}_{s(i)}^p \in \mathbb{R}^{M_p \times M_{p-1}}$ is the weight matrix and $\mathbf{b}_{s(i)}^p \in \mathbb{R}^{M_p}$ is the bias vector.

The final layer $\mathcal{L}_{s(i)}^{\mathrm{out}}$ is a linear output mapping:

$E_{s(i)} = \mathcal{L}_{s(i)}^{\mathrm{out}}(\mathbf{d}_i^{N_h}) = \mathbf{W}_{s(i)}^{\mathrm{out}} \mathbf{d}_i^{N_h} + b_{s(i)}^{\mathrm{out}}$

where $\mathbf{W}_{s(i)}^{\mathrm{out}} \in \mathbb{R}^{1 \times M_{N_h}}$ is the output weight vector and $b_{s(i)}^{\mathrm{out}} \in \mathbb{R}$ is the output scalar bias.
Knowl 3 — Analytical Interatomic Force Formulation in DeePMD
equation
The total interatomic force $\mathbf{F}_i$ acting on atom $i$ is calculated analytically by taking the negative gradient of the total potential energy $E = \sum_j E_j = \sum_j \mathcal{N}_{s(j)}(\mathbf{D}_j)$ with respect to atomic position $\mathbf{R}_i$ :

$\mathbf{F}_i = -\frac{\partial E}{\partial \mathbf{R}_i} = -\sum_{j \in N(i), \alpha} \frac{\partial \mathcal{N}_{s(i)}}{\partial D_{ij}^\alpha} \frac{\partial D_{ij}^\alpha}{\partial \mathbf{R}_i} - \sum_{j \ne i} \sum_{k \in N(j), \alpha} \delta_{i, a(j)} \frac{\partial \mathcal{N}_{s(j)}}{\partial D_{jk}^\alpha} \frac{\partial D_{jk}^\alpha}{\partial \mathbf{R}_i} - \sum_{j \ne i} \sum_{k \in N(j), \alpha} \delta_{i, b(j)} \frac{\partial \mathcal{N}_{s(j)}}{\partial D_{jk}^\alpha} \frac{\partial D_{jk}^\alpha}{\partial \mathbf{R}_i} - \sum_{j \ne i} \sum_{k \in \tilde{N}(j), \alpha} \delta_{i, k} \frac{\partial \mathcal{N}_{s(j)}}{\partial D_{jk}^\alpha} \frac{\partial D_{jk}^\alpha}{\partial \mathbf{R}_i}$

where:
- $N(j)$ is the neighbor index set of atom $j$ ;
- $a(j)$ and $b(j)$ denote the two reference neighbor atoms chosen to define the local frame of atom $j$ ;
- $\tilde{N}(j) = N(j) \setminus \{a(j), b(j)\}$ is the neighbor set excluding the local frame axis atoms;
- $\delta_{i, k}$ is the Kronecker delta;
- $\mathcal{N}_{s(j)}$ is the atomic neural network function for chemical species $s(j)$ ;
- $D_{jk}^\alpha$ is the $\alpha$ -th descriptor component of neighbor $k$ in the local coordinate frame of atom $j$ .
The four summation terms account respectively for: (1) direct dependence of atom $i$ 's own descriptors on $\mathbf{R}_i$ ; (2) indirect dependence when atom $i$ serves as the first axis atom $a(j)$ of another atom $j$ ; (3) indirect dependence when atom $i$ serves as the second axis atom $b(j)$ of another atom $j$ ; and (4) indirect dependence when atom $i$ is a non-axis neighbor $k \in \tilde{N}(j)$ of atom $j$ .
Knowl 4 — Analytical Virial Tensor Formulation in DeePMD
equation
The virial tensor $\Xi$ of a system governed by the DeePMD potential is derived from the relation $\Xi = -\frac{1}{2} \sum_i \mathbf{R}_i \otimes \mathbf{F}_i = \frac{1}{2} \sum_{i \ne j} \mathbf{R}_{ij} \otimes \frac{\partial E}{\partial \mathbf{R}_{ij}}$ , yielding the analytical expression:

$\Xi = \frac{1}{2} \sum_{i \ne j} \mathbf{R}_{ij} \otimes \sum_\alpha \frac{\partial \mathcal{N}_{s(i)}}{\partial D_{ij}^\alpha} \frac{\partial D_{ij}^\alpha}{\partial \mathbf{R}_{ij}} + \frac{1}{2} \sum_{i \ne j} \delta_{j, a(i)} \mathbf{R}_{ij} \otimes \sum_{q, \alpha} \frac{\partial \mathcal{N}_{s(i)}}{\partial D_{iq}^\alpha} \frac{\partial D_{iq}^\alpha}{\partial \mathbf{R}_{ij}} + \frac{1}{2} \sum_{i \ne j} \delta_{j, b(i)} \mathbf{R}_{ij} \otimes \sum_{q, \alpha} \frac{\partial \mathcal{N}_{s(i)}}{\partial D_{iq}^\alpha} \frac{\partial D_{iq}^\alpha}{\partial \mathbf{R}_{ij}}$

where $\mathbf{R}_{ij} = \mathbf{R}_i - \mathbf{R}_j$ is the interatomic vector, $a(i)$ and $b(i)$ are the neighbor atoms defining the local coordinate frame for atom $i$ , $\mathcal{N}_{s(i)}$ is the neural network evaluating atomic energy $E_i$ , and $D_{iq}^\alpha$ denotes the $\alpha$ -th component of the descriptor for neighbor atom $q$ of atom $i$ .
Knowl 5 — Multi-Task Loss Function and Dynamic Prefactor Weighting Scheme
model/method
The trainable neural network parameters $\{\mathbf{W}_s^p, \mathbf{b}_s^p\}$ are optimized by minimizing a composite loss function $L(p_e, p_f, p_\xi)$ over each training batch:

$L(p_e, p_f, p_\xi) = \frac{p_e}{N} \Delta E^2 + \frac{p_f}{3N} \sum_{i=1}^N |\Delta \mathbf{F}_i|^2 + \frac{p_\xi}{9N} \|\Delta \Xi\|^2$

where $N$ is the number of atoms in a frame, $\Delta E^2 = \frac{1}{S_b} \sum_{k=1}^{S_b} |E^k - E(\mathbf{R}_1^k, \dots, \mathbf{R}_N^k)|^2$ is the mean squared error in total potential energy over a batch of $S_b$ frames, $|\Delta \mathbf{F}_i|^2$ is the squared error in atomic force vector components, and $\|\Delta \Xi\|^2$ is the Frobenius squared norm of the error in the $3 \times 3$ virial tensor.

To balance optimization across energy, force, and virial targets during training, the weighting prefactors $p \in \{p_e, p_f, p_\xi\}$ dynamically vary with the training step $t$ according to the current learning rate $r_l(t)$ :

$p(t) = p^{\mathrm{limit}} \left(1 - \frac{r_l(t)}{r_l^0}\right) + p^{\mathrm{start}} \left(\frac{r_l(t)}{r_l^0}\right)$

where $p^{\mathrm{start}}$ and $p^{\mathrm{limit}}$ are user-defined starting and limiting prefactor values, and the learning rate decays exponentially:

$r_l(t) = r_l^0 \times d_r^{t / d_s}$

where $r_l^0$ is the initial learning rate, $d_r < 1$ is the decay rate, and $d_s$ is the decay step interval.
Knowl 6 — DeePMD-kit Software Architecture and Molecular Dynamics Interfaces
model/method
DeePMD-kit is organized into three software components:
1. Core C++ Library and Custom TensorFlow Operators: Implements atomic descriptor computation, local-to-global frame transformations, descriptor derivatives $\partial D_{jk}^\alpha / \partial \mathbf{R}_i$ , and analytic chain rules for forces and virial tensors as custom C++ operators integrated directly into TensorFlow. The neural network gradient $\partial E_{s(i)} / \partial D_{jk}^\alpha$ is evaluated via TensorFlow's automatic differentiation (tf.gradients).
2. Python Training and Model Management Pipeline: Provides Python programs dp_train (reads training configurations from a JSON file and minimizes the multi-task loss with the Adam stochastic gradient descent optimizer), dp_frz (exports and freezes model weights and computational graphs into a standalone Protobuf file graph.pb), and dp_test (evaluates model generalization and tests for overfitting on independent datasets).
3. Molecular Dynamics Engine Interfaces:
  - LAMMPS: Integrated via a custom pair_style deepmd graph.pb pair style in C++, allowing direct evaluation of energies, atomic forces, and virial tensors during classical MD simulations.
  - i-PI: Integrated via a client program dp_ipi communicating with the i-PI server over UNIX domain sockets or TCP/IP sockets to compute potential energy and forces across multiple path-integral replicas in parallel for quantum path-integral molecular dynamics.
Knowl 7 — Cyclic Multi-System Batch Training Procedure
algorithm
When training a DeePMD model on heterogeneous datasets containing $S_s$ distinct physical systems $\{\Omega_1, \dots, \Omega_{S_s}\}$ with differing numbers of atoms or chemical compositions, DeePMD-kit executes training over systems in a cyclic manner without replacement.
Input: Training systems { $\Omega_1, \dots, \Omega_{S_s}$ }, batch size $S_b$ , total optimization steps $N_{\text{stop}}$
Output: Trained model parameters { $\mathbf{W}_s^p, \mathbf{b}_s^p$ }
$t \leftarrow 0$
while $t < N_{\text{stop}}$ do
    for $k \leftarrow 1$ to $S_s$ do
         $n_{\text{batches}} \leftarrow \lfloor |\Omega_k| / S_b \rfloor$
        Partition $\Omega_k$ into $n_{\text{batches}}$ batches randomly without replacement
        for each batch $B$ in the partition of $\Omega_k$ do
            Compute learning rate $r_l(t) \leftarrow r_l^0 \times d_r^{t / d_s}$
            Compute loss prefactors $p_e(t), p_f(t), p_\xi(t)$
            Forward propagate batch $B$ through custom descriptor and DNN operators
            Evaluate loss $L(p_e(t), p_f(t), p_\xi(t))$ on $B$
            Compute parameter gradients via backpropagation
            Update parameters using Adam optimizer
             $t \leftarrow t + 1$
            if $t \ge N_{\text{stop}}$ then
                break
Knowl 8 — DeePMD-kit RAW Data Format Specification
definition
DeePMD-kit defines the RAW data protocol to standardize molecular configuration and label inputs across diverse ab initio and simulation packages. Each system folder contains plain text files where each line corresponds to a single simulation frame:
- coord.raw: Contains $3N$ floating-point numbers per line, representing Cartesian coordinates $(x_1, y_1, z_1, \dots, x_N, y_N, z_N)$ of all atoms in the laboratory frame, in units of $\text{\AA}$ .
- box.raw: Contains 9 floating-point numbers per line, specifying the $3 \times 3$ simulation cell box tensor components $(h_{xx}, h_{xy}, h_{xz}, h_{yx}, h_{yy}, h_{yz}, h_{zx}, h_{zy}, h_{zz})$ .
- energy.raw: Contains 1 floating-point scalar per line, representing the total system potential energy in units of $\text{eV}$ .
- force.raw: Contains $3N$ floating-point numbers per line, representing the atomic forces $(F_{1x}, F_{1y}, F_{1z}, \dots, F_{Nx}, F_{Ny}, F_{Nz})$ in units of $\text{eV/\AA}$ .
- virial.raw: Contains 9 floating-point numbers per line, representing the 9 components of the system virial tensor in units of $\text{eV}$ .
- type.raw: A single line containing $N$ integers separated by spaces, specifying the chemical species index of each atom in identical order across all frames.
Missing label files (such as absence of virial data) are handled by setting their respective loss prefactor ( $p_e, p_f$ , or $p_\xi$ ) to zero. For computational efficiency during training, RAW text files are converted into NumPy binary array files (.npy) prior to execution.
Knowl 9 — Empirical Accuracy and Structural Property Validation on Bulk Liquid Water
empirical result
The DeePMD-kit implementation was evaluated on a periodic bulk liquid water system of 64 molecules (192 atoms, cubic box length $12.4447 \ \text{\AA}$ ) using a dataset generated from a 20 ps NVT AIMD trajectory at 330 K with the PBE0+TS exchange-correlation functional (0.5 fs timestep, 40,000 frames total; 38,000 training, 2,000 testing).

Training Setup:
- Network architecture: 5 hidden layers with sizes $(240, 120, 60, 30, 10)$ ;
- Cutoff radius $R_c = 6.0 \ \text{\AA}$ (full radial and angular coordinates for the 16 nearest oxygen and 32 nearest hydrogen neighbors; radial-only coordinates for all other neighbors);
- Optimization: Adam optimizer for $10^6$ steps with batch size 4, initial learning rate $r_l^0 = 0.001$ , decay rate $d_r = 0.95$ per $d_s = 5000$ steps;
- Loss prefactors: $p_e^{\mathrm{start}} = 0.02, p_e^{\mathrm{limit}} = 8$ , $p_f^{\mathrm{start}} = 1000, p_f^{\mathrm{limit}} = 1$ , and $p_v = 0$ .
- Hardware: Intel Core i7-3770 CPU with 32 GB RAM, 4 OpenMP threads; total wall-clock training time was 16 hours.
Results:
- Initial random parameters produced testing RMS errors of $3.7 \times 10^2 \ \text{eV}$ for total energy and $8.4 \times 10^{-1} \ \text{eV/\AA}$ for forces.
- Converged testing RMS errors reached $2.8 \times 10^{-2} \ \text{eV}$ for energy and $2.4 \times 10^{-2} \ \text{eV/\AA}$ for force.
- Relative to the dataset standard deviations ( $6.5 \times 10^{-1} \ \text{eV}$ for energy and $8.1 \times 10^{-1} \ \text{eV/\AA}$ for force), the relative testing errors were 4.3% for energy and 2.9% for force.
- A 200 ps NVT classical MD simulation in LAMMPS using the trained frozen DeePMD model reproduced the reference PBE0+TS DFT radial distribution functions ( $g_{\mathrm{OO}}(r)$ , $g_{\mathrm{OH}}(r)$ , $g_{\mathrm{HH}}(r)$ ) and the tetrahedral packing parameter $q$ distribution with high fidelity.
Knowl 10 — Hardware and Parallelization Limitations in Descriptor Computation
limitation
In the initial release of DeePMD-kit:
1. CPU-Only Implementation of Descriptors: The C++ operators for constructing atomic chemical environment descriptors are implemented solely on CPU architectures, without GPU execution support.
2. Serial Molecular Dynamics Evaluation: While descriptor evaluation is parallelized across frames during model training using OpenMP multi-threading, the evaluation of descriptors, energies, forces, and virials during active MD simulations (such as inside the LAMMPS pair style or i-PI client) runs strictly serially on a single core and does not utilize CPU multicore or GPU multithreading parallelism.

Coverage note — None was omitted; all primary contributions of the paper—including the mathematical formulations for descriptors, energies, forces, and virials, the DeePMD-kit software architecture, the RAW data format specification, the cyclic multi-system training algorithm, the empirical validation on liquid water, and the descriptor parallelization limitations—are fully covered.

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33.For this example, the raw data and the JSON parameter files for training and MD simulation are provided in the online package. More details on how to use them are explained in the manual.

Citation

MLA

Wang, H., et al. “DeePMD-kit: A Deep Learning Package for Many-body Potential Energy Representation and Molecular Dynamics”. Computer Physics Communications, vol. 228, 2018, pp. 178–84, https://doi.org/10.1016/j.cpc.2018.03.016.

APA

Wang, H., Zhang, L., Han, J., & E, W. (2018). DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics. Computer Physics Communications, 228, 178–184. https://doi.org/10.1016/j.cpc.2018.03.016

Chicago

Wang, H., L. Zhang, J. Han, and W. E. 2018. “DeePMD-kit: A Deep Learning Package for Many-body Potential Energy Representation and Molecular Dynamics”. Computer Physics Communications 228: 178–84. https://doi.org/10.1016/j.cpc.2018.03.016.

Harvard

Wang, H. et al. (2018) “DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics”, Computer Physics Communications, 228, pp. 178–184. Available at: https://doi.org/10.1016/j.cpc.2018.03.016.

Vancouver

1. Wang H, Zhang L, Han J, E W (2018) DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics. Computer Physics Communications 228:178–184

BibTeX

@article{Wang_2018, title={DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics}, volume={228}, ISSN={0010-4655}, url={http://dx.doi.org/10.1016/j.cpc.2018.03.016}, DOI={10.1016/j.cpc.2018.03.016}, journal={Computer Physics Communications}, publisher={Elsevier BV}, author={Wang, Han and Zhang, Linfeng and Han, Jiequn and E, Weinan}, year={2018}, month=July, pages={178–184} }

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DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics

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Table of Contents

Knowls

Knowl 1 — DeePMD Potential Energy Decomposition and Local Frame Atomic Descriptors

Knowl 2 — Deep Neural Network Architecture for Atomic Potential Energy

Knowl 3 — Analytical Interatomic Force Formulation in DeePMD

Knowl 4 — Analytical Virial Tensor Formulation in DeePMD

Knowl 5 — Multi-Task Loss Function and Dynamic Prefactor Weighting Scheme

Knowl 6 — DeePMD-kit Software Architecture and Molecular Dynamics Interfaces

Knowl 7 — Cyclic Multi-System Batch Training Procedure

Knowl 8 — DeePMD-kit RAW Data Format Specification

Knowl 9 — Empirical Accuracy and Structural Property Validation on Bulk Liquid Water

Knowl 10 — Hardware and Parallelization Limitations in Descriptor Computation

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