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Developed by AdvanceSoft Corp. (2020-2022)

NeuralMD

Advance /Advance / NeuralMD
This is a software for molecular dynamics calculations based on Neural Network
Potential. Create a molecular force field using the results of first-principle calculations
exported by Quantum ESPRESSO*1 as training data. Using this force field, moleculardynamics calculations are implemented in LAMMPS*2.

Neural Network Potential Features- Faster than first-principles calculations and Higher precision than existing moleculardynamics calculations- Capable of handling systems with no existing force field, such as unknown materials andunknown added elements- Achieve systematic simulations without relying on researchers' intuition or experience

TheorySymmetric Function

In Neural Network Potential, the system's totalenergy E_(tot ) is expressed as the sum of theeach atomic energies：
𝐸𝑡𝑜𝑡 = ∑𝑖 ∈ {all atoms}

Representation of the geometric structure ofother atoms, which are in the vicinity of thefocused atom (i). It contains information such as

𝐸𝑖bond distances (r) and bond angles (θ).

Each atomic energy E_i is computed by a neuralnetwork：
𝐸𝑖 = 𝐸𝑁𝑁 ( 𝐺𝑖,1 , 𝐺𝑖,2 , 𝐺𝑖,3 , ⋯ )The input data to the neural network, called
symmetry functions G_i, and the weighted
Behler function and Chebyshev polynomial areavailable in this product*3,4.

𝑖𝜃𝑟Neural Network

In the final layer, the bias and perceptron
representing the standard atomic energy andchemical shift, respectively.

Advance/NeuralMD Distinctive Features1.

Single Atom Neural Network Potential

2.

Δ - Neural Network Potential

3.

Enhanced force field using the Metropolis method

4.

Operation from Advance/NanoLabo (GUI)5.

Self-learning Hybrid Monte Carlo method*1 Quantum ESPRESSO is a general-purpose open-source application for first-principles calculation, distributed under the GPL license. (https://www.quantum-espresso.org)*2 LAMMPS is a general-purpose open-source application for classical molecular dynamics simulation, distributed under the GPL license. (https://lammps.sandia.gov)*3 “wACSF—Weighted atom-centered symmetry functions as descriptors in machine learning potential”, M.Gastegger, et al., JCP 148 (2018) 241709*4 “Efficient and accurate machine-learning interpolation of atomic energies in compositions with many species”, N.Artrith, et al., Phys. Rev. B 96 (2017) 014112*5 “Density functional theory based neural network force fields from energy decompositions”, Y. Huang, et al., Phys. Rev. B 99 (2019) 064103

Features
1. Single Atom Neural Network Potential
In density functional theory calculations, the Single Atom Neural Network Potential *1 (SANNP)
algorithm is available, which outputs the energy of each atom directly as training data. For systems
with small electrical polarization, the convergence of the learning process is better than that of HighDimensional Neural Network Potential*2 (HDNNP), which uses the total energy as training data.
Moreover, since the Hirshfeld charge of each atom can be output simultaneously, it is also possible
to deal with long-range Coulomb interactions (3G-HDNNP＊2 applied).
*1 “Density functional theory based neural network force fields from energy decompositions”, Y.Huang, et al., Phys. Rev. B 99 (2019) 064103*2“A fourth-generation high-dimensional neural network potential with accurate electrostatics including non-local charge transfer”, T.W.Ko et al, Nat. Comm. 12 (2021) 398

2. Δ - Neural Network Potential
Δ-Neural Network Potential*3 (Δ-NNP) is a method developed originally by our company, which
expresses the total energy 𝐸𝑡𝑜𝑡 as the sum of the energy 𝐸𝐶 calculated by the classical force field
and the energy 𝐸𝑁𝑁𝑃 calculated by Neural Network Potential. The neural network's training data will
not be the energy 𝐸𝐷𝐹𝑇 itself as calculated by first principles, it will be the difference between the firstprinciples and classical force field energies 𝐸𝐷𝐹𝑇 − 𝐸𝐶 . We call it Δ-NNP due to the use of differentials.
For the classical force field, we use a Lennard-Jones-like two-body function:
1𝐴𝐵𝐶𝐷
𝐸𝐶 = ∑ 12 + 10 + 8 + 6
2
𝑟𝑖𝑗
𝑟𝑖𝑗
𝑟𝑖𝑗 𝑟𝑖𝑗𝑖, 𝑗

For inorganic materials, while the two-body function serves as the zeroth approximation of thepotential terrain, the approach is to use Neural Network Potential to supplement the surplus thatcannot be expressed by the two-body function. Consequently, the convergence of the learning
process will be improved, and a stable force field can be created even with a small amount of trainingdata.

*3 http://case.advancesoft.jp/NeuralMD/LGPS-conductivity/index.html

3. Enhanced force field using the Metropolis method
Perform Monte Carlo calculations using the Metropolis method with a pre-created Neural Network
Potential. By utilizing the distribution of symmetric functions, only the unknown structures are
extracted from the generated structures and added to the training

data. Through this process,teacher data can be efficiently reconstructed and re-trained into a more accurate force field. For
structure generation in the Metropolis method, besides translational shifts of atomic coordinates, it
is also possible to consider elemental and vacancy position swapping operations.

4. Operation from Advance/NanoLabo
All processes, starting from the creation of training data, neuralnetwork training and force field generation, to the execution ofmolecular dynamics calculations, are operated from theAdvance/NanoLabo screen. The grand project (right figure)allows you to proceed with your tasks while managing a large
number of training data, etc. In addition, in creating training
data, first-principles calculations can be distributed acrossmultiple computational resources (e.g., compute servers, cloud,etc.).

5. Self-learning Hybrid Monte Carlo method
The self-learning Hybrid Monte Carlo method is a first-principles Monte Carlo algorithm developedby the Japan Atomic Energy Agency*1. By applying the Neural Network Potential molecular dynamics
trajectory as the proposed structure in the Monte Carlo method, efficient sampling of the structure
can be achieved while first-principle accuracy is guaranteed for the Monte Carlo calculation itself. At
the same time as the Monte Carlo calculations are performed, training of the Neural Network Potential
is carried out in parallel, using the results of the first-principles calculations computed for eachstructure. As a result, when the method is executed, a Neural Network force field specific to the target
system is automatically generated.
*1“Self-learning hybrid Monte Carlo: A first-principles approach”, Y.Nagai, et al., Phys. Rev. B 102 (2020) 041124

Advance / NeuralMD Pro
Advance/NeuralMD Pro supports training neural networks and molecular dynamics calculations onGPUs. It can also be used in conjunction with MPI parallelism to support machines with multiple GPUs
and/or multiple machine nodes with GPUs. It is designed to keep both GPU and CPU utilization high at
all times by launching two to four MPI processes per GPU device. High computation cost symmetryfunction and force calculations are GPUized (bottom left).

Speed comparison of molecular dynamics calculations on Intel Xeon
Platinum 72 cores (CPU) and NVIDIA V100 1-8 devices (GPU). Plot of
relative speeds with CPU speed set to 1. The target is an LGPS
supercell (20,000 atoms). Mat3ra (https://mat3ra.com) was used as
the computing resource.

How-to-use
A. Manual force-field creation
1. Create a sample structure

Sample structures for creating force fields can be created by the user usingAdvance/NanoLabo or others. Using multiple sample structures at the same time, itis possible to create a single force field.

2. Generate random structures
Based on the sample structures, it automatically generates numerous structureswith randomly displaced atomic coordinates. It also outputs a script to run firstprinciple calculations at once for all the generated structures.

3. First-principles calculations with Quantum ESPRESSO
Execute the generated script to implement the first-principles calculations.
The calculation is processed using Quantum ESPRESSO, which has been modified byus, and outputs the energy for each atom.

4. Neural network learning (optimization)
The energy of each atom calculated by Quantum ESPRESSO is used as the training
data to optimize the neural network. For the optimization calculation, we will use thetools provided by our company. After calculating, outputs the neural network
information as a force field file that can be used in LAMMPS.

5. Molecular Dynamics Calculations with LAMMPS
Using the created force field file, molecular dynamics calculations will beimplemented. For calculation, we will use LAMMPS, which we have added thefunctions of Neural Network Potential.

B. Use of Self-learning Hybrid Monte Carlo Method
Users do not need to create their own training data; simply prepare a Quantum
ESPRESSO input file and automatically generate a force field by executing a single selflearning Hybrid Monte Carlo calculation command.
Using Advance/NanoLabo (GUI), simply press the button on the screen.
The process, which used to take weeks to a month or more for manual force fieldcreation, can be completed in half a day to a few days.

Licensing
License TypeOSLicense Type

Windows*1

Node Lock (Remote Desktop available)

Linux

Floating

License Price*1 Advance/NeuralMD Pro is not available in Windows.

Annual

ProductAnnual

Permanent

Permanent(Business /National Institute)(Academic)(Business / NationalInstitute)

Advance/NeuralMD

500,000JPY*3250,000JPY*31,500,000JPY*3750,000JPY*3Advance/NeuralMD Pro*2900,000JPY*3450,000JPY*32,700,000JPY*31,350,000JPY*3(Academic)*2 Advance/NeuralMD Pro can train neural networks and perform molecular dynamics on GPUs.
*3 Purchasing Advance/NanoLabo at the same time, 20% discount will be given from the list price.

Trial LicenseFree trial licenses are available for one month per person.

CasesIonic conductivity of Li10GeP2S12

Li-ion Conductivity Calculation by Δ-NNP
By applying Δ-NNP to a Li ion conductor,
Li10GeP2S12, the ionic conductivity (σ) is
calculated. The first-principle MD cannot
have a large model size and can only besimulated in the high temperature region
where ions move violently. On the otherhand, using Neural Network Potential, thesimulation is possible even at room
temperature, and the experimental valuesof ion conductivity are well reproduced.

*1 A.Marcolongo, ea al., https://arxiv.org/abs/1910.10090*2 Ryoji Kanno, Electrochemistry, 85(9), 591–596 (2017)

Higher accuracy than existing molecular force fields
Neural Network Potential is applied to GaN crystals and compared with the Tersoff force field* 3. For
the training data, 500 structures generated by classical molecular dynamics calculations between
300K and 6000K are used. As for the potential energy and the forces acting on the atoms, the resultsof the DFT calculation are well reproduced, and show a higher accuracy than existing force fields
such as Tersoff.
*3 Many-body Molecular Force Field https://lammps.sandia.gov/doc/pair_tersoff.html
Potential
energy vs. Volume
Translated with
www.DeepL.com/Translator(free version)*4Verify the forces acting on atoms*4 For the NNP training data, GaN crystals withvarious lattice constants are used.

RMSE(Tersoff): 1.05 eV/Å, RSME(NNP): 0.19 eV/Å

AdvanceSoft Corporation
Please contact us first if you would like more information. Demonstrations are also possible.
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