NBHub | ABACUS+DeePKS Step-by-Step Practical Tutorial: Using the Perovskite System as an Example

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This Notebook will approach DeePKS from an application perspective, using the perovskite system as a case study. It systematically presents the complete process of DeePKS model training and deployment, including:

  1. Preparation of labeled data for the example system,
  2. Model training, and
  3. Result analysis.

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Tutorial Structure

Following a progression from simple to complex, this tutorial series is designed to guide readers step by step in learning DeePKS:

  • Single-element systems:

    • Start with energy label training for systems containing the same type of element.

  • Multi-label training for single-element systems:

    • Expand to training multiple labels (e.g., energy, forces, stress, and band structure) for single-element systems.

  • Real-world research systems:

    • Transition to complex research systems (e.g., those with diverse elemental compositions), incorporating multi-label training for energy, forces, stress, and band structure.

Learning Outcomes

Through this tutorial, readers will:

  • Gain a deep understanding of the DeePKS method,
  • Master how to apply it to actual model training and deployment, and
  • Equip themselves with essential skills to support future research.

Background

First-Principles Calculations Based on KS-DFT

First-principles calculations based on Kohn−Sham Density Functional Theory (KS-DFT) have become one of the most widely used quantum mechanical methods at the atomic and molecular scales in recent decades.

The accuracy of KS-DFT is determined by the precision of the unknown terms in the total energy—namely, the exchange-correlation functional. Among the various approximations of exchange-correlation functionals—such as LDA, GGA, meta-GGA, and hybrid functionals [1-2]—achieving a balance between accuracy and efficiency has always been a challenge.

  • The most commonly used functional, such as the PBE functional under the GGA approximation, performs well in terms of computational efficiency but often lacks accuracy for specific systems.
  • On the other hand, hybrid functionals like HSE06 offer higher accuracy but suffer from lower computational efficiency, making them impractical for handling large systems.

Opportunities with Artificial Intelligence

The rapid development of artificial intelligence (AI) has introduced new possibilities for representing and approximating high-dimensional complex functions. By leveraging deep learning models to bridge the gap between low- and high-accuracy functionals, it is now possible to achieve a good balance between efficiency and accuracy.

DeePKS Method

The DeePKS method is a deep learning-based functional correction approach developed to address this challenge [3-5]. Its key features are as follows:

  1. Objective:

    • DeePKS does not reconstruct the exchange-correlation functional itself.
    • Instead, it uses machine learning techniques to optimize low-accuracy functionals.

  2. How it Works:

    • DeePKS learns the differences in energy, forces, stress, and band structure labels between:
      • A baseline functional (e.g., PBE)
      • A target functional (e.g., HSE06)
    • This effectively combines the advantages of low- and high-accuracy calculations.

  3. Key Benefits:

    • Good balance between efficiency and accuracy.
    • Low computational cost:
      • Correction terms are computationally as inexpensive as low-accuracy functionals.
      • Far less expensive than high-accuracy functionals like HSE06.

Advantages in Practical Applications

  • The computational cost of correction terms in DeePKS is comparable to that of low-accuracy functionals.
  • This makes DeePKS significantly faster than high-accuracy functionals, giving it a notable edge in practical applications.

Integration with DFT Software

During DeePKS model training, the update of model parameters alternates with the self-consistent calculations of first-principles methods.
This requires DeePKS to seamlessly integrate with existing density functional theory software.

Reference:
1.Kohn W, Sham L J. Self-consistent equations including exchange and correlation effects[J]. Physical review, 1965, 140(4A): A1133.
2.Perdew J P, Burke K, Ernzerhof M. Generalized gradient approximation made simple[J]. Physical review letters, 1996, 77(18): 3865.
3.https://github.com/deepmodeling/deepks-kit/tree/develop
4.Chen Y, Zhang L, Wang H, et al. DeePKS: A comprehensive data-driven approach toward chemically accurate density functional theory[J]. Journal of Chemical Theory and Computation, 2020, 17(1): 170-181.
5.Ou Q, Tuo P, Li W, et al. DeePKS Model for Halide Perovskites with the Accuracy of a Hybrid Functional[J]. The Journal of Physical Chemistry C, 2023, 127(37): 18755-18764.
6.https://github.com/deepmodeling/abacus-develop
7.Li W, Ou Q, Chen Y, et al. DeePKS+ ABACUS as a Bridge between Expensive Quantum Mechanical Models and Machine Learning Potentials[J]. The Journal of Physical Chemistry A, 2022, 126(49): 9154-9164.