Machine-Learned Force Fields for Realistic Physics

<p>Machine-Learned Force Fields (ML FFs) provide near-<i>ab initio</i> accuracy for large realistic system sizes and dynamical simulation time-scales greatly exceeding those accessible to Density Functional Theory (DFT). Use ML FFs in QuantumATK to generate realistic complex structures of novel crystal and amorphous materials, alloys, interfaces, and multilayer stacks, simulate thermal and mechanical properties, diffusion and surface processes. Benefit from the pre-trained ML FF library or develop new ML FFs using automated and efficient training and simulation workflows.</p>

Machine-Learned Force Fields (ML FFs) provide near-ab initio accuracy for large realistic system sizes and dynamical simulation time-scales greatly exceeding those accessible to Density Functional Theory (DFT). Use ML FFs in QuantumATK to generate realistic complex structures of novel crystal and amorphous materials, alloys, interfaces, and multilayer stacks, simulate thermal and mechanical properties, diffusion and surface processes. Benefit from the pre-trained ML FF library or develop new ML FFs using automated and efficient training and simulation workflows.

The QuantumATK simulation engines enable atomic-scale modeling using multiple simulation methods in one platform [1]: state-of-the-art density functional theory (DFT) with plane wave or LCAO basis sets, semi-empirical methods, conventional FFs (built-in database of 300 potentials) and ML FFs. All simulation engines share a common infrastructure for material property, molecular dynamics (MD), nudged elastic band (NEB), geometry optimization, and other simulations.

ML FFs for Dynamical Simulations of Large-Scale Realistic Systems

  • ML FFs are 1000 to 10,000x faster than DFT, thus enabling dynamical modeling of realistic novel and complex systems containing even 100,000+ atoms, instead of small model 100-atom systems.
  • ML FFs provide near-ab initio accuracy for multi-element materials, heterogeneous systems like interfaces, and systems far from equilibrium, including amorphous materials, phase transitions, or chemical reactions.
  • ML FFs are often easier to develop than conventional FFs using the automated workflows available in QuantumATK. Accurate conventional FFs for such complex systems would require much more extensive and complicated development processes.

Application Examples of Machine-Learned Force Fields

Structure Generation of Amorphous Materials

Generate amorphous structures for PCRAM, ReRAM, and FeRAM novel memories, solar cells, and other applications. In this example, 80ps ML FF-MD generated am- SiO2 structure of 600 atoms in 11 minutes, whereas it took 10 days to generate 72-atom structure with DFT-MD on 16 cores. Structural parameters obtained with ML FFs are in good agreement with DFT and experimental results.

Simulation of Interfaces and Multilayer Stacks

Build and optimize complex crystalline and amorphous interfaces and multilayer stack structures for semiconductor development applications, such as high-k metal gate (HKMG) (using Multilayer builder GUI) and MRAM magnetic tunnel junction engineering. This example shows a generated structure of a nearly defect-free c-Si|am-SiO2|am-HfO2|am-Ti2N HKMG stack.

Simulation of Glassy Amorphous Materials

Generate glassy amorphous materials with impurities for optoelectronic applications. In this example, ML FF - MD is used to simulate a large-scale 120,000 atom size sodium silicate glass with Na impurities, (Na2O)2(SiO2)40000,, at 2500K.

Crystallization & Amorphization Processes

Study ns-long crystallization and amorphization processes with ML FF - MD in large-scale systems for, e.g., PCRAM novel memory applications. This example depicts crystallization of 2520-atom phase change alloy material Ge2Sb2Te5.

Thermal Property Simulations

Simulate thermal conductance using ML FFs with ns-long reverse non-equilibrium MD (RNEMD) simulations for developing PCRAM and evaluating self-heating and heat dissipation in devices. Examples include simulating thermal conductance in bulk Ge2Sb2Te5 (2300 atoms), Ge2Sb2Te5|Si (882 atoms), and Si|GaAs (864 atoms) interfaces, monolayer MoS2 (108,000 atoms). Calculated values are in good agreement with experimental and DFT results where available.

Surface Process Modeling

Simulate thermal ALD and ALE processes using specifically trained ML FFs with MD. This example shows the simulation of the thermal ALD process: HfCl4 deposition on an HfO2 surface of 4.5 nm2 area. Precursor adsorption energies are consistent with DFT results. Obtained sticking coefficient and coverage values can be used as parameters for feature scale models to optimize the yield of ALD.

Built-in Library of Ready-to-Use Machine-Learned Force Fields

QuantumATK offers Moment Tensor Potentials (MTPs), which provide high robust accuracy with lower computational cost compared to other ML Force Fields [2,3].  Benefit from the pre-trained ready-to-use high-quality MTP library (check [4,5] for the list of materials) or develop MTPs for new materials, interfaces and surface processes by using automatic generation workflows described below.

Automated Efficient Generation of Machine-Learned Force Fields

Basic Workflow

  • Automatically generate training configurations (based on random displacements for crystal structures)
  • Compute training data, such as energy, forces and stress, with DFT
  • Perform machine learning, i.e., fitting to the training data
  • Validate generated ML FFs and optimize hyperparameters
  • Use ML FFs for production simulations, such as MD, force bias Monte Carlo, nudged elastic band and geometry optimization 
  • Benefit from OpenMP, massively-parallel MPI, and hybrid parallelization

Advanced Active Learning Workflow

  • Improve initial ML FFs generated with the basic workflow by actively adding training configurations and DFT training data during MD simulations
  • Automatic iterative process is based on specified threshold values for configuration extrapolation
  • Recommended for
    • amorphous systems
    • interfaces
    • systems at high temperatures 
    • surface process modeling

Templates & GUI

  • Use automatic training tools and GUI templates [6] for:
  • Inspect automatically generated training configurations using Trajectory Analyzer GUI
  • Validate generated ML FFs by comparing calculated values with available experimental and DFT data for: 
    • Radial/angular distribution function (RDF and ADF)
    • Elastic constants
    • Neutron scattering factor
    • Chemical composition profile 
    • X-ray scattering

QuantumATK Advantages

  • Automated user-friendly generation of training data, tailored for specific applications 
    • Ensures minimal amount of training data and time needed 
    • No computationally expensive ab initio MD is needed in most cases
    • Provides good quality accurate ML FFs for complex systems
  • Single interface for different simulation engines
    • Easily switch between training with DFT-LCAO and DFT-PW
    • Combine ML FFs with conventional FFs, DFT or Semi-empirical calculators to further improve accuracy in specific applications


Value of Machine-Learned FFs

  1. Why is it not possible to run all needed simulations using DFT instead?
    ML FFs are 1000 to 10 000x faster than DFT and can often be almost as accurate. Dynamical simulations with ML FFs reduce simulation time from days to minutes, from years to hours, thus enabling dynamical modeling of realistic novel and complex systems containing 1,000 - 100 000 atoms and more.
  2. Why is it not possible to run all needed simulations using efficient conventional force field libraries instead?
    - It is possible to use conventional FFs for selected materials only, and the possibility to combine them to describe, for example, interfaces between different materials is very limited and inaccurate.
    - Conventional FFs are often not very accurate far from equilibrium, which is needed to describe amorphous materials, phase transitions, or chemical reactions.
  3. Do I need to use machine learning? What about fitting a new conventional force field?
    Conventional FFs work well for relatively simple materials, but fitting accurate conventional force fields for complex materials has been shown to be very difficult, in fact near impossible for multi-element materials or heterogeneous systems like interfaces (in particular between metals and semiconductors)
  4. What is the largest number of atoms that can be simulated with ML FFs?
    QuantumATK team has simulated 100,000 atom systems with ns long MD simulations. Larger systems can be also simulated with ML-FFs, depending on available computational resources. 

Machine-Learned FFs in QuantumATK

  1. How did QuantumATK implement Moment Tensor Potential (MTP) ML FFs?
    QuantumATK team implemented MTPs in-house, i.e., not the original MTP package from literature [2,3]. QuantumATK team expects similar efficiency for QuantumATK and original implementations, however, no explicit efficiency comparisons were done, as they also depend on the MD simulation engine.
  2. How long does it take to generate ML FFs with QuantumATK?
    In case of having 2-4 cluster nodes (32-72 cores available), obtain a good quality ML FF for:
    - Crystal structures (1-3 elements) in 1-2 days, depending on the complexity of the material
    - Interfaces and amorphous materials, including Active Learning MD, in 1-2 weeks, depending on the complexity
    - More complex systems (e.g, more than 3 elements, various interfaces or special applications like ALD), in several weeks
    In all cases, the most time-consuming part is generating training configurations and calculating training data with DFT. Fitting to the training data can be done in a few hours or max a day. Generated training configurations could be re-used when developing ML FFs for similar materials (e.g., different stoichiometry, common elements).
  3. What software can be used to run MD simulations with pre-trained or generated ML FFs?
    Only QuantumATK software can be used to run MD simulations with these ML FFs. QuantumATK offers high-performance massively-parallel state-of-the-art MD simulation methods.
  4. How are ML FFs licensed in QuantumATK?
    - Base license: Run calculations with ML FFs you fitted yourself
    - Elite license: Fit your own ML FF or access the built-in ML FF library
  5. What are QuantumATK advantages for Machine-Learned FFs over competing solutions?
    - QuantumATK provides a user-friendly, automatic and efficient generation of curated training data instead of manual flows
    - Essential for good quality ML FFs and to minimize the training time and data, i.e., 10-100x reduction in the amount of DFT reference data
    - The unique, automated QuantumATK protocols are tailored for specific applications, such as molecular surface deposition or interfaces
    - ML FF models (NNP, GAP, etc.) in competing solutions are less accurate or slower than the MTP model used in QuantumATK [2,3]
    - QuantumATK has demonstrated highly accurate and efficient ML FFs for complex materials, such as amorphous alloys, interfaces with multiple materials involved, and molecular surface deposition, not just simple materials
  6. Why generation of training configurations does not include ab initio MD simulations?
    Generation of training configurations with ab initio MD is a very computationally expensive process. From QuantumATK team's experience,  this often results in a lot more DFT calculations than needed, because subsequent snapshots from MD simulations are typically very correlated and similar. QuantumATK primarily validated this by using the training protocol which uses random displacements and strain for crystal structures. It provides good description of crystal properties, such as lattice constants, phonons, and elastic constants up to moderate temperatures without adding snapshots from ab initio MD simulations. For amorphous or other more complex structures, however, it can sometimes be beneficial to include ab initio MD training data, too.


[1] S. Smidstrup, T. Markussen, P. Vancraeyveld, J. Wellendorf, J. Schneider, T. Gunst, B. Vershichel, D. Stradi, P. A. Khomyakov, U. G. Vej-Hansen, M.-E. Lee, S. T. Chill, F. Rasmussen, G. Penazzi, F. Corsetti, A. Ojanpera, K. Jensen, M. L. N. Palsgaard, U. Martinez, A. Blom, M. Brandbyge, and K. Stokbro, "QuantumATK: An integrated platform of electronic and atomic-scale modelling tools", J. Phys.: Condens. Matter 32, 015901 (2020). arXiv: 1905.02794v2.

[2] A. V. Shapeev, "Moment tensor potentials: a class of systematically improvable interatomic potentials", Multi-scale Model. & Simul. 14, 1153 (2016).

[3] Y. Zuo, C. Chen, X. Li, Z. Deng, Y. Chen, J. Behler, G. Csányi, A. V. Shapeev, A. P. Thompson, M. A. Wood, and S. Ping Ong, "Performance and cost assessment of machine learning interatomic potentials"J.  Phys. Chem. A 124, 731 (2020).

[4] ML FF features:

[5] Materials in the pre-trained ready-to-use ML FF library:

[6] Tutorial on automatic ML FF training tools and GUI templates: 

Useful Resources

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