update (#131)

Co-authored-by: Yani Guan <[email protected]>

Author: yaniguan

source/_posts/abacus_ai.md

@@ -13,7 +13,7 @@ Recently, doctoral student Sun Liang and researcher Chen Mohan from the Center f
 
 ### **Orbital Free Density Functional Theory and Kinetic Energy Density Functional**
 
-**Orbital Free Density Functional Theory (OFDFT)** is a highly efficient density functional theory calculation method, benefiting from its computational complexity of \( O(N) \) or \( O(N \ln N) \), where \( N \) is the number of atoms in the system. This enables it to handle systems with millions of atoms. In contrast, the commonly used Kohn–Sham DFT (KSDFT) has a computational complexity generally around \( O(N^3) \), which is limited to processing systems containing thousands of atoms at most. The OFDFT algorithm has been implemented in ABACUS. For more details, refer to the ABACUS online Chinese documentation: [https://mcresearch.github.io/abacus-user-guide](https://mcresearch.github.io/abacus-user-guide).
+**Orbital Free Density Functional Theory (OFDFT)** is a highly efficient density functional theory calculation method, benefiting from its computational complexity of $O(N)$ or $O(N \ln N)$, where $N$ is the number of atoms in the system. This enables it to handle systems with millions of atoms. In contrast, the commonly used Kohn–Sham DFT (KSDFT) has a computational complexity generally around $O(N^3)$, which is limited to processing systems containing thousands of atoms at most. The OFDFT algorithm has been implemented in ABACUS.
 
 The lower computational complexity of OFDFT stems from its treatment of the non-interacting kinetic energy as being dependent only on the electron density in the kinetic energy density functional (KEDF). As a result, it avoids the most time-consuming diagonalization of the Kohn–Sham density matrix. However, the total energy (including kinetic energy) is of the same order of magnitude as interaction energies in condensed matter and molecular systems. Therefore, the accuracy of the approximate kinetic energy functional significantly affects the precision of OFDFT calculations.
 
@@ -34,11 +34,10 @@ In recent years, researchers have begun exploring machine learning to construct
 
 Based on these requirements, we constructed the **MPN functional**, expressed as:
 
-\[
-\int w(|\mathbf{r} - \mathbf{r}'|) f(\rho(\mathbf{r})) \, \mathrm{d}\mathbf{r},
-\]
+$$\int w(|\mathbf{r} - \mathbf{r}'|) f(\rho(\mathbf{r})) \, \mathrm{d}\mathbf{r},$$
+
+where $w(|\mathbf{r} - \mathbf{r}'|)$ is the kernel describing nonlocal interactions, and $f(\rho(\mathbf{r}))$ is the function of the local electron density. In addition, the MPN functional incorporates penalties and constraints to ensure the three requirements mentioned above, thereby achieving numerical stability in calculations. Tests show that the MPN functional achieves high accuracy in describing simple metals and alloys.
 
-where \( w(|\mathbf{r} - \mathbf{r}'|) \) is the kernel describing nonlocal interactions, and \( f(\rho(\mathbf{r})) \) is the function of the local electron density. In addition, the MPN functional incorporates penalties and constraints to ensure the three requirements mentioned above, thereby achieving numerical stability in calculations. Tests show that the MPN functional achieves high accuracy in describing simple metals and alloys.
 
 However, we found that the MPN functional struggled to capture the bonding characteristics of semiconductors. This is because, in semiconductors, the charge density distribution differs significantly from that of simple metals: while simple metals exhibit a nearly uniform electron density, semiconductors possess distinct covalent bonding features and residual separated regions. To address this, we introduced a "multi-channel" architecture to better describe the electrons in semiconductors. 
 
@@ -48,9 +47,7 @@ However, we found that the MPN functional struggled to capture the bonding chara
 
 As shown in the figure, we scaled the kernel function in the MPN functional as:
 
-\[
-w_\lambda(r - r') = \lambda^3 w(\lambda(r - r')),
-\]
+$$w_\lambda(r - r') = \lambda^3 w(\lambda(r - r'))$$
 
 and used this to replace the kernel function in the MPN functional. This allowed the input electron density to be transformed into a new set of descriptors. Thus, the scaled kernel functions define a "channel." When \( \lambda > 1 \), the kernel function is compressed, enabling it to capture local electron information. Conversely, when \( \lambda < 1 \), the kernel function is stretched, making it capable of capturing long-range electron information. Finally, the descriptors from different channels are combined into a new vector, which is input into a neural network with a structure similar to that of the MPN functional to obtain the final kinetic energy density functional.
 
@@ -66,11 +63,12 @@ We named the new functionals **CPN\(_n\)**, where the subscript \(n\) represents
 
 The loss function for the CPN functional is the same as that used for the MPN functional:
 
-\[
+$$
 L = \frac{1}{N} \sum_r \left[ \left(\frac{F^\text{NN}_\theta - F^\text{KS}_\theta}{\overline{F^\text{KS}_\theta}}\right)^2 + \left(\frac{V^\text{MPN}_\theta - V^\text{KS}_\theta}{\overline{V^\text{KS}_\theta}}\right)^2 + \left[F^\text{NN}_\text{FEG} - \ln(e - 1)\right]^2 \right],
-\]
+$$
+
+where $N$ is the number of spatial grid points, and $\overline{F^\text{KS}_\theta}$ and $\overline{V^\text{KS}_\theta}$ are the averages of $F^\text{KS}_\theta$ and $V^\text{KS}_\theta$, respectively.
 
-where \(N\) is the number of spatial grid points, and \(\overline{F^\text{KS}_\theta}\) and \(\overline{V^\text{KS}_\theta}\) are the averages of \(F^\text{KS}_\theta\) and \(V^\text{KS}_\theta\), respectively.
 
 - The first term reinforces the functional with energy-related information, enhancing the numerical stability of the model.
 - The second term ensures corrections to the free electron gas (FEG) limit are not excessive, maintaining stability in calculations.
@@ -85,3 +83,10 @@ The figure above shows the energy-volume curve for Si in the diamond structure.
 <center><img src=https://dp-public.oss-cn-beijing.aliyuncs.com/community/abacus_ai/aba4.png# pic_center width="100%" height="100%" /></center>
 
 This section demonstrates the results obtained for the ground-state electron densities of Si in the diamond structure, GaAs in the zincblende structure, and systems from the training set. Firstly, all three CPN functionals successfully yield smooth electron densities. Secondly, with more channels included, the accuracy of the CPN functionals progressively improves, indicating that the multi-channel architecture effectively enhances the ability of the machine-learning-based functionals to describe semiconductors. Finally, describing covalent bonding remains a significant challenge in kinetic energy density functionals. As shown in the figure, even the HC functional, which is specifically designed for semiconductors, underestimates the electron density in covalent bond regions. However, whether in the training or testing set, **CPN\(_5\)** KEDF with five channels accurately captures and reconstructs covalent bonding structures. This demonstrates that the descriptors and multi-channel architecture effectively capture the characteristics of electron densities in semiconductors.
+
+Reference:
+[1] Sun L, Chen M. Machine learning based nonlocal kinetic energy density functional for simple metals and alloys[J]. Physical Review B, 2024, 109(11): 115135.
+[2] Sun L, Chen M. Multi-channel machine learning based nonlocal kinetic energy density functional for semiconductors[J]. Electronic Structure, 2024.
+[3] Wang L W, Teter M P. Kinetic-energy functional of the electron density[J]. Physical Review B, 1992, 45(23): 13196.
+[4] Wang Y A, Govind N, Carter E A. Orbital-free kinetic-energy density functionals with a density-dependent kerne[J]. Physical Review B, 1999, 60(24): 16350.
+[5] Huang C, Carter E A. Nonlocal orbital-free kinetic energy density functional for semiconductors[J]. Physical Review B, 2010, 81(4): 045206.

source/_posts/deeptb.md

@@ -54,3 +54,7 @@ DeePTB is currently open-sourced in the DeepModeling community. We welcome you t
 DeePTB Project Link: (https://github.com/deepmodeling/DeePTB)
 
 The dftio project is in the process of applying to be hosted in the DeepModeling community, so stay tuned for more details.
+
+Reference:
+[1] Q. Gu, Z. Zhouyin, S. K. Pandey, P. Zhang, L. Zhang, and W. E, Deep Learning Tight-Binding Approach for Large-Scale Electronic Simulations at Finite Temperatures with Ab Initio Accuracy, Nat Commun 15, 6772 (2024).
+[2] Z. Zhouyin, Z. Gan, S. K. Pandey, L. Zhang, and Q. Gu, Learning Local Equivariant Representations for Quantum Operators, arXiv:2407.06053.

source/_posts/dflow.md

@@ -10,7 +10,7 @@ From the development of software ecosystems in fields such as electronic structu
 
 AI advancements are driving a paradigm shift in scientific research, but the integration of scientific computing and AI faces challenges, such as the complex processes of efficient data generation and model training, and the management and scheduling of large-scale tasks. Traditional manual task management is inefficient, and script-based automation lacks reusability and maintainability. The rapid scalability of cloud computing offers new opportunities for scientific research, necessitating a new, user-friendly workflow framework that can effectively utilize cloud and high-performance computing resources, enabling seamless integration of algorithm design and practical application.
 
-In this context, the DeepModeling community initiated and gradually improved Dflow[1,2], a Python toolkit designed to help scientists build workflows. The core features of Dflow include:
+In this context, the DeepModeling community initiated and gradually improved Dflow, a Python toolkit designed to help scientists build workflows. The core features of Dflow include:
 
 1. Enabling complex process control and task scheduling. Dflow integrates Argo Workflows for reliable scheduling and task management, uses container technology to ensure environmental consistency and reproducibility, and employs Kubernetes technology to enhance workflow stability and observability, capable of handling workflows with thousands of concurrent nodes.
 

source/_posts/dp-CuSn.md

@@ -14,14 +14,14 @@ The findings were published in Computational Materials Science under the title "
 <!-- more -->
 
 ## Research Background
-Metallic materials and their alloys play a crucial role in various fields. The copper-tin (Cu-Sn) alloy, composed of copper and tin, exhibits excellent wear resistance, corrosion resistance, and high strength. This alloy is widely used in industries such as electronics, automation, chemical engineering, petroleum, and casting. Its unique structure and properties make it an ideal material for manufacturing high-performance components such as bearings, gears, and valves [1, 2]. Additionally, it is an ideal material for 3D printing, providing a solid foundation for advancements across multiple industrial sectors [3].
+Metallic materials and their alloys play a crucial role in various fields. The copper-tin (Cu-Sn) alloy, composed of copper and tin, exhibits excellent wear resistance, corrosion resistance, and high strength. This alloy is widely used in industries such as electronics, automation, chemical engineering, petroleum, and casting. Its unique structure and properties make it an ideal material for manufacturing high-performance components such as bearings, gears, and valves. Additionally, it is an ideal material for 3D printing, providing a solid foundation for advancements across multiple industrial sectors.
 
-Molecular modeling methods, especially Molecular Dynamics (MD) simulations, have rapidly advanced in studying the mechanical properties of materials, particularly in alloy systems. Zhang et al. [4], using first-principles calculations based on Density Functional Theory (DFT), investigated the effects of different tin contents on the structure, elasticity, electronic properties, and thermal performance of Cu-Sn alloys. Zhang [5] further studied the mechanical behavior and deformation mechanisms of Cu-Sn alloys under various influencing factors through tensile tests using MD simulations. The accuracy of MD simulations largely depends on the interatomic potential employed. However, traditional empirical potentials, such as the Lennard-Jones (L-J) potential [6], Embedded Atom Method (EAM) [7], and Modified Embedded Atom Method (MEAM) [8], are primarily developed based on experimental data and empirical rules, limiting their applicability and modeling scope [9]. Although these empirical potentials significantly enhance the efficiency of MD simulations, the accuracy of their results remains a topic of debate.
+Molecular modeling methods, especially Molecular Dynamics (MD) simulations, have rapidly advanced in studying the mechanical properties of materials, particularly in alloy systems. Zhang et al., using first-principles calculations based on Density Functional Theory (DFT), investigated the effects of different tin contents on the structure, elasticity, electronic properties, and thermal performance of Cu-Sn alloys. Zhang further studied the mechanical behavior and deformation mechanisms of Cu-Sn alloys under various influencing factors through tensile tests using MD simulations. The accuracy of MD simulations largely depends on the interatomic potential employed. However, traditional empirical potentials, such as the Lennard-Jones (L-J) potential, Embedded Atom Method (EAM), and Modified Embedded Atom Method (MEAM), are primarily developed based on experimental data and empirical rules, limiting their applicability and modeling scope. Although these empirical potentials significantly enhance the efficiency of MD simulations, the accuracy of their results remains a topic of debate.
 
 In this study, we constructed a Deep Potential (DP) model for the Cu-Sn system based on deep neural networks. An active learning strategy was adopted to thoroughly explore phase space and minimize manual intervention, thereby generating a reliable interatomic potential. With continuous training and optimization, the accuracy of the DP model's predictions improved significantly. The DP model for the Cu-Sn system accurately reproduces the results of first-principles calculations in predicting energy and mechanical properties.
 
 ## Results and Discussion
-First, we performed molecular dynamics (MD) simulations of phonon dispersion relations using the constructed DP potential model and compared the results with DFT calculations. As shown in Figure 4(a), the phonon dispersion curves obtained using the DP potential align well with the DFT results. The DP interatomic potential effectively reproduces the DFT data, indicating its ability to accurately describe the phonon behavior of the Cu₁₀Sn₃ structure. Figure 4(b) illustrates the phonon spectrum of the CuSn structure. The acoustic branches and most optical branches derived from the DP potential agree with the DFT results, with only the highest-frequency optical branch being slightly underestimated, a trend observed in previous studies [10]. These findings demonstrate that the DP model trained via deep neural networks achieves computational accuracy comparable to that of DFT methods. This model can be applied in MD simulations to further explore the structures and properties of Cu-Sn alloys.
+First, we performed molecular dynamics (MD) simulations of phonon dispersion relations using the constructed DP potential model and compared the results with DFT calculations. As shown in Figure 4(a), the phonon dispersion curves obtained using the DP potential align well with the DFT results. The DP interatomic potential effectively reproduces the DFT data, indicating its ability to accurately describe the phonon behavior of the Cu₁₀Sn₃ structure. Figure 4(b) illustrates the phonon spectrum of the CuSn structure. The acoustic branches and most optical branches derived from the DP potential agree with the DFT results, with only the highest-frequency optical branch being slightly underestimated, a trend observed in previous studies. These findings demonstrate that the DP model trained via deep neural networks achieves computational accuracy comparable to that of DFT methods. This model can be applied in MD simulations to further explore the structures and properties of Cu-Sn alloys.
 
 <center><img src=https://dp-public.oss-cn-beijing.aliyuncs.com/community/dp_cusn/dp1.png# pic_center width="100%" height="100%" /></center>