# ænet-gpr
**Efficient Data Augmentation for ANN Potential Training Using GPR Surrogate Models**
`aenet-gpr` is a Python package that enables scalable and cost-efficient training of artificial neural network (ANN) potentials by leveraging Gaussian Process Regression (GPR) as a surrogate model.
It automates data augmentation to:
- Reduce the number of expensive DFT calculations
- Lower ANN training overhead particularly critical for complex and heterogeneous interface systems
- Maintain high accuracy comparable to the demanding direct force training
📄 Reference:
[In Won Yeu, Alexander Urban, Nongnuch Artrith et al., “Scalable Training of Neural Network Potentials for Complex Interfaces Through Data Augmentation”, *npj Computational Materials* 11, 156 (2025)](https://doi.org/10.1038/s41524-025-01651-0)
📬 Contact:
- In Won Yeu (iy2185@columbia.edu)
- Nongnuch Artrith (n.artrith@uu.nl)
## 🔁 Workflow Overview
<p align="center">
<img src="doc/source/images/0_flowchart.png" width="700">
</p>
1. **Data Grouping**
- Split the initial DFT database into homogeneous subsets (same composition and number of atoms)
2. **Train**
- Construct local GPR models using structure, energy, and atomic force data of each subset
3. **Test**
- Predict and evaluate target properties with the trained GPR models
4. **Augment**
- Perturb reference structures and generate new data
- Tag with GPR-predicted energies to expand the training dataset
✅ Outputs are saved in [XCrysDen Structure Format (XSF)](http://ann.atomistic.net/documentation/#structural-energy-reference-data), fully compatible with the [ænet package](https://github.com/atomisticnet/aenet-PyTorch) for indirect force training (**GPR-ANN**).
## 🔑 Key Features
- GPR-based prediction of energies and atomic forces with uncertainty estimates
- Supports various descriptors including Cartesian and SOAP
- Applicable to periodic and non-periodic systems
- Batch-based kernel computation for speed and memory efficiency
- Accepts multiple input formats (e.g., XSF, VASP OUTCAR, etc.)
- Fully controlled through a single input file (`train.in`)
- Compatible with various GPR applications such as GPR-NEB, GPR-ANN, and ASE-Calculator
## 📦 Installation
**Requirements:**
- Python with PyTorch (to be installed separately, see below)
- Other dependencies (`numpy`, `ASE`, `DScribe`) are automatically installed when installing `aenet-gpr`
### 1. Install PyTorch
Refer to [official guide](https://pytorch.org/get-started/locally) and install compatible versions depending on availablity of GPU and CUDA:
- With CUDA (optional for GPU support):
`$ pip install torch torchvision torchaudio --index-url https://download.pytorch.org/whl/cu118`
- CPU-only:
`$ pip install torch torchvision torchaudio --index-url https://download.pytorch.org/whl/cpu`
### 2. Install ænet-gpr
- Installation using pip
`$ pip install aenet-gpr`
## 📘 Tutorial
Find interactive notebooks `*.ipynb` in the `./tutorial/` folder, or run directly on Google Colab:
### GPR tutorials for various systems
- [GPR Tutorial: H₂](https://colab.research.google.com/github/atomisticnet/aenet-gpr/blob/main/tutorial/tutorial_1_H2.ipynb)
- [GPR Tutorial: EC–EC](https://colab.research.google.com/github/atomisticnet/aenet-gpr/blob/main/tutorial/tutorial_2_EC-EC.ipynb)
- [GPR Tutorial: Li–EC](https://colab.research.google.com/github/atomisticnet/aenet-gpr/blob/main/tutorial/tutorial_3_Li-EC.ipynb)
### GPR applications for accelerating atomistic simulations
- [GPR-ANN: accelerating ANN potential training through GPR data augmentation](https://colab.research.google.com/github/atomisticnet/aenet-gpr/blob/main/tutorial/tutorial_python_GPR-ANN.ipynb)
- [GPR-NEB: accelerating NEB through GPR surrogate model](https://colab.research.google.com/github/atomisticnet/aenet-gpr/blob/main/tutorial/tutorial_python_GPR-NEB.ipynb)
- [GPR-ASE: ASE GPRCalculator](https://colab.research.google.com/github/atomisticnet/aenet-gpr/blob/main/tutorial/tutorial_python_ASE-GPRCalculator.ipynb)
The `./example/` directory includes example input and output data files.
## 📂 Input Files
### 1. Structure–Energy–Force Data
By default, input data is provided in `.xsf` format.
#### Example: aenet XSF format (non-periodic)
The first comment line should specify **total energy** of a structure. Each line following the keyword `ATOMS` contains **atomic symbol**, **three Cartesian coordinates**, and the three components of **atomic forces**. The length, energy, and force units are Å, eV, and eV/Å.
```
# total energy = -0.0970905812353288 eV
ATOMS
H -0.91666666666667 0.00000000000000 0.00000000000000 0.32660398877491 0.00000000000000 0.00000000000000
H 0.91666666666667 0.00000000000000 0.00000000000000 -0.32660398877491 0.00000000000000 0.00000000000000
```
#### Example: aenet XSF format (periodic)
```
# total energy = -16688.9969866290994105 eV
CRYSTAL
PRIMVEC
10.31700000000000 0.00000000000000 0.00000000000000
0.00000000000000 10.31700000000000 0.00000000000000
0.00000000000000 0.00000000000000 32.00000000000000
PRIMCOORD
46 1
Li -0.02691046000000 0.02680527000000 10.32468480000000 -0.01367780493112 -0.01466501222916 0.08701630310868
Li -0.04431013000000 3.46713645000000 10.25290534000000 0.06865473174602 -0.00786890285541 0.15426435842600
Li 0.02355300000000 6.82569825000000 10.31803445000000 0.00877419275000 0.03943267659765 0.14805797440506
...
```
Other formats such as **VASP OUTCAR** (with a line of `File_format vasp-out` in `train.in` below) are also supported as long as they can be read through [ASE](https://wiki.fysik.dtu.dk/ase/ase/io/io.html).
### 2. Configuration File
#### Example: `train.in` (comments are provided to guide the keyword meanings)
```
# File path
Train_file ./example/3_Li-EC/train_set/file_*.xsf
Test_file ./example/3_Li-EC/test_set/file_*.xsf
# Train model save (default: False)
Train_model_save False # True-> train data and trained GPR model are saved in "data_dict.pt" and "calc_dict.pt"
# File format (default: xsf)
File_format xsf # Other DFT output files, which can be read via ASE such as "vasp-out" "aims-output" "espresso-out", are also supported
# Uncertainty estimation (default: True)
Get_variance True # False -> only energy and forces are evaluated without uncertainty estimate
# Descriptor (default: cartesian coordinates)
Descriptor cart # cart or soap
# Kernel parameter (default: Squared exponential)
scale 0.4 # default: 0.4
weight 1.0 # default: 1.0
# Data process (default: batch, 25)
data_process batch # batch (memory cost up, time cost down) or iterative (no-batch: memory down, time up)
batch_size 25
# Flags for xsf file writing (default: False)
Train_write False # True -> xsf files for reference training set are written under "./train_xsf/" directory
Test_write False # True -> xsf files for reference test set are written under "./test_xsf/" directory
Additional_write False # True -> additional xsf files are written under "./additional_xsf/" directory; False -> Augmentation step is not executed
# Data augmentation parameter (default: 0.055, 25)
Disp_length 0.05
Num_copy 20 # [num_copy] multiples of reference training data are augmented
```
## 🚀 Usage Example
With the `train.in` file and datasets prepared, simply run:
`$ python -m aenet_gpr ./train.in > train.out`
The **Train–Test–Augment** steps will be executed sequentially. Augmented data will be saved in the `./additional_xsf/` directory.
## 🖥️ Running on an HPC system (SLURM)
To run `aenet_gpr` on an HPC cluster using SLURM, use a batch script like the following:
```
#!/bin/bash
#SBATCH --job-name=aenet-job
#SBATCH --nodes=1
#SBATCH --tasks-per-node=8
#SBATCH --cpus-per-task=4
#SBATCH --time=1:00:00
module load anaconda3
source activate aenet-env
ulimit -s unlimited
python -m aenet_gpr ./train.in > train.out
```
## ⚙️ Tuning Tips
### 1. Accuracy – Descriptor and Kernel Scale Parameter
- Descriptor: **Cartesian**, **SOAP**, and others supported by [DScribe](https://singroup.github.io/dscribe/latest/index.html)
- Default kernel: **Squared Exponential (sqexp)**
- Kernel parameters: **scale** and **weight**
<p align="center">
<img src="doc/source/images/0_kernel.png" width="300">
</p>
Following figure shows energy prediction errors of the `./example/3_Li-EC/` example with different kernel parameters and descriptors.
<p align="center">
<img src="doc/source/images/3_Li-EC_accuracy.png" width="1000">
</p>
When using the **Cartesian descriptor** (gray circles), the error decreases as the `scale` parameter increases, and it converges at `scale = 3.0`. When using the **periodic SOAP descriptor** (for details, see [DScribe documentation](https://singroup.github.io/dscribe/latest/tutorials/descriptors/soap.html)), the error is significantly reduced by one order of magnitude compared to the **Cartesian descriptor**.
As demonstrated in the examples for the `./example/2_EC-EC/` (results available in the `example` directory), non-periodic systems can be well-represented using **non-periodic Cartesian descriptors**, while periodic systems are expected to yield better accuracy when using **periodic SOAP descriptors**.
For the example of **SOAP descriptor** here, eight uniformly distributed points in the Li slab Rectangular cuboid were used as `centers` argument for **SOAP**.
The corresponding `train.in` input arguments are
```
Descriptor soap
soap_r_cut 5.0
soap_n_max 6
soap_l_max 4
soap_centers [[2.20113706670393, 2.328998192856251, 6.952547732109352], [2.20113706670393, 2.328998192856251, 11.895790642109352], [2.20113706670393, 6.760484232856251, 6.952547732109352], [2.20113706670393, 6.760484232856251, 11.895790642109352], [6.63924050670393, 2.328998192856251, 6.952547732109352], [6.63924050670393, 2.328998192856251, 11.895790642109352], [6.63924050670393, 6.760484232856251, 6.952547732109352], [6.63924050670393, 6.760484232856251, 11.895790642109352]]
soap_n_jobs 4
scale 2.0
weight 1.0
```
### 2. Efficiency – Data Processing Mode
- `data_process iterative`: Computing kernels data-by-data involves `n_data × n_data` sequential kernel evaluations, minimizing the memory overhead but significantly increasing computational time.
- `data_process batch`: **aenet-gpr** supports batch processing by grouping the data process into a specific size (`batch_size 25`), which significantly reduces train and evaluation time while keeping memory usage efficient.
Below, we provide a benchmark comparing the required time and memory for different batch sizes on the `./example/3_Li-EC/` example.
<p align="center">
<img src="doc/source/images/3_Li-EC_cost.png" width="1000">
</p>
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"description": "# \u00e6net-gpr\n**Efficient Data Augmentation for ANN Potential Training Using GPR Surrogate Models**\n\n`aenet-gpr` is a Python package that enables scalable and cost-efficient training of artificial neural network (ANN) potentials by leveraging Gaussian Process Regression (GPR) as a surrogate model. \nIt automates data augmentation to:\n\n- Reduce the number of expensive DFT calculations \n- Lower ANN training overhead particularly critical for complex and heterogeneous interface systems \n- Maintain high accuracy comparable to the demanding direct force training\n\n\ud83d\udcc4 Reference: \n[In Won Yeu, Alexander Urban, Nongnuch Artrith et al., \u201cScalable Training of Neural Network Potentials for Complex Interfaces Through Data Augmentation\u201d, *npj Computational Materials* 11, 156 (2025)](https://doi.org/10.1038/s41524-025-01651-0)\n\n\ud83d\udcec Contact: \n- In Won Yeu (iy2185@columbia.edu) \n- Nongnuch Artrith (n.artrith@uu.nl)\n\n## \ud83d\udd01 Workflow Overview\n\n<p align=\"center\">\n<img src=\"doc/source/images/0_flowchart.png\" width=\"700\">\n</p>\n\n1. **Data Grouping** \n - Split the initial DFT database into homogeneous subsets (same composition and number of atoms)\n\n2. **Train** \n - Construct local GPR models using structure, energy, and atomic force data of each subset\n\n3. **Test** \n - Predict and evaluate target properties with the trained GPR models\n\n4. **Augment** \n - Perturb reference structures and generate new data \n - Tag with GPR-predicted energies to expand the training dataset\n\n\u2705 Outputs are saved in [XCrysDen Structure Format (XSF)](http://ann.atomistic.net/documentation/#structural-energy-reference-data), fully compatible with the [\u00e6net package](https://github.com/atomisticnet/aenet-PyTorch) for indirect force training (**GPR-ANN**).\n\n## \ud83d\udd11 Key Features\n\n- GPR-based prediction of energies and atomic forces with uncertainty estimates \n- Supports various descriptors including Cartesian and SOAP \n- Applicable to periodic and non-periodic systems \n- Batch-based kernel computation for speed and memory efficiency \n- Accepts multiple input formats (e.g., XSF, VASP OUTCAR, etc.) \n- Fully controlled through a single input file (`train.in`)\n- Compatible with various GPR applications such as GPR-NEB, GPR-ANN, and ASE-Calculator\n\n## \ud83d\udce6 Installation\n\n**Requirements:**\n\n- Python with PyTorch (to be installed separately, see below)\n- Other dependencies (`numpy`, `ASE`, `DScribe`) are automatically installed when installing `aenet-gpr`\n\n### 1. Install PyTorch\n\nRefer to [official guide](https://pytorch.org/get-started/locally) and install compatible versions depending on availablity of GPU and CUDA:\n\n - With CUDA (optional for GPU support):\n\n `$ pip install torch torchvision torchaudio --index-url https://download.pytorch.org/whl/cu118`\n\n - CPU-only:\n \n `$ pip install torch torchvision torchaudio --index-url https://download.pytorch.org/whl/cpu`\n\n\n### 2. Install \u00e6net-gpr\n \n - Installation using pip\n\n `$ pip install aenet-gpr`\n\n## \ud83d\udcd8 Tutorial\n\nFind interactive notebooks `*.ipynb` in the `./tutorial/` folder, or run directly on Google Colab:\n\n### GPR tutorials for various systems\n\n- [GPR Tutorial: H\u2082](https://colab.research.google.com/github/atomisticnet/aenet-gpr/blob/main/tutorial/tutorial_1_H2.ipynb) \n- [GPR Tutorial: EC\u2013EC](https://colab.research.google.com/github/atomisticnet/aenet-gpr/blob/main/tutorial/tutorial_2_EC-EC.ipynb) \n- [GPR Tutorial: Li\u2013EC](https://colab.research.google.com/github/atomisticnet/aenet-gpr/blob/main/tutorial/tutorial_3_Li-EC.ipynb)\n\n### GPR applications for accelerating atomistic simulations\n\n- [GPR-ANN: accelerating ANN potential training through GPR data augmentation](https://colab.research.google.com/github/atomisticnet/aenet-gpr/blob/main/tutorial/tutorial_python_GPR-ANN.ipynb)\n- [GPR-NEB: accelerating NEB through GPR surrogate model](https://colab.research.google.com/github/atomisticnet/aenet-gpr/blob/main/tutorial/tutorial_python_GPR-NEB.ipynb)\n- [GPR-ASE: ASE GPRCalculator](https://colab.research.google.com/github/atomisticnet/aenet-gpr/blob/main/tutorial/tutorial_python_ASE-GPRCalculator.ipynb)\n\nThe `./example/` directory includes example input and output data files.\n\n## \ud83d\udcc2 Input Files\n\n### 1. Structure\u2013Energy\u2013Force Data\n\nBy default, input data is provided in `.xsf` format. \n\n#### Example: aenet XSF format (non-periodic)\nThe first comment line should specify **total energy** of a structure. Each line following the keyword `ATOMS` contains **atomic symbol**, **three Cartesian coordinates**, and the three components of **atomic forces**. The length, energy, and force units are \u00c5, eV, and eV/\u00c5.\n```\n# total energy = -0.0970905812353288 eV\n\nATOMS\nH -0.91666666666667 0.00000000000000 0.00000000000000 0.32660398877491 0.00000000000000 0.00000000000000\nH 0.91666666666667 0.00000000000000 0.00000000000000 -0.32660398877491 0.00000000000000 0.00000000000000\n```\n\n#### Example: aenet XSF format (periodic)\n```\n# total energy = -16688.9969866290994105 eV\n\nCRYSTAL\nPRIMVEC\n 10.31700000000000 0.00000000000000 0.00000000000000\n 0.00000000000000 10.31700000000000 0.00000000000000\n 0.00000000000000 0.00000000000000 32.00000000000000\nPRIMCOORD\n 46 1\nLi -0.02691046000000 0.02680527000000 10.32468480000000 -0.01367780493112 -0.01466501222916 0.08701630310868\nLi -0.04431013000000 3.46713645000000 10.25290534000000 0.06865473174602 -0.00786890285541 0.15426435842600\nLi 0.02355300000000 6.82569825000000 10.31803445000000 0.00877419275000 0.03943267659765 0.14805797440506\n...\n```\n\nOther formats such as **VASP OUTCAR** (with a line of `File_format vasp-out` in `train.in` below) are also supported as long as they can be read through [ASE](https://wiki.fysik.dtu.dk/ase/ase/io/io.html).\n\n### 2. Configuration File\n\n#### Example: `train.in` (comments are provided to guide the keyword meanings)\n```\n# File path\nTrain_file ./example/3_Li-EC/train_set/file_*.xsf\nTest_file ./example/3_Li-EC/test_set/file_*.xsf\n\n# Train model save (default: False)\nTrain_model_save False # True-> train data and trained GPR model are saved in \"data_dict.pt\" and \"calc_dict.pt\"\n\n# File format (default: xsf)\nFile_format xsf # Other DFT output files, which can be read via ASE such as \"vasp-out\" \"aims-output\" \"espresso-out\", are also supported\n\n# Uncertainty estimation (default: True)\nGet_variance True # False -> only energy and forces are evaluated without uncertainty estimate\n\n# Descriptor (default: cartesian coordinates)\nDescriptor cart # cart or soap\n\n# Kernel parameter (default: Squared exponential)\nscale 0.4 # default: 0.4\nweight 1.0 # default: 1.0\n\n# Data process (default: batch, 25)\ndata_process batch # batch (memory cost up, time cost down) or iterative (no-batch: memory down, time up)\nbatch_size 25\n\n# Flags for xsf file writing (default: False)\nTrain_write False # True -> xsf files for reference training set are written under \"./train_xsf/\" directory\nTest_write False # True -> xsf files for reference test set are written under \"./test_xsf/\" directory\nAdditional_write False # True -> additional xsf files are written under \"./additional_xsf/\" directory; False -> Augmentation step is not executed\n\n# Data augmentation parameter (default: 0.055, 25)\nDisp_length 0.05\nNum_copy 20 # [num_copy] multiples of reference training data are augmented\n```\n\n## \ud83d\ude80 Usage Example\n\nWith the `train.in` file and datasets prepared, simply run:\n\n`$ python -m aenet_gpr ./train.in > train.out`\n\nThe **Train\u2013Test\u2013Augment** steps will be executed sequentially. Augmented data will be saved in the `./additional_xsf/` directory.\n\n## \ud83d\udda5\ufe0f Running on an HPC system (SLURM)\n\nTo run `aenet_gpr` on an HPC cluster using SLURM, use a batch script like the following:\n\n```\n#!/bin/bash\n#SBATCH --job-name=aenet-job\n#SBATCH --nodes=1\n#SBATCH --tasks-per-node=8\n#SBATCH --cpus-per-task=4\n#SBATCH --time=1:00:00\n\nmodule load anaconda3\nsource activate aenet-env\n\nulimit -s unlimited\npython -m aenet_gpr ./train.in > train.out\n```\n\n## \u2699\ufe0f Tuning Tips\n\n### 1. Accuracy \u2013 Descriptor and Kernel Scale Parameter\n\n- Descriptor: **Cartesian**, **SOAP**, and others supported by [DScribe](https://singroup.github.io/dscribe/latest/index.html)\n- Default kernel: **Squared Exponential (sqexp)**\n- Kernel parameters: **scale** and **weight**\n\n<p align=\"center\">\n<img src=\"doc/source/images/0_kernel.png\" width=\"300\">\n</p>\n\nFollowing figure shows energy prediction errors of the `./example/3_Li-EC/` example with different kernel parameters and descriptors.\n\n<p align=\"center\">\n<img src=\"doc/source/images/3_Li-EC_accuracy.png\" width=\"1000\">\n</p>\n\nWhen using the **Cartesian descriptor** (gray circles), the error decreases as the `scale` parameter increases, and it converges at `scale = 3.0`. When using the **periodic SOAP descriptor** (for details, see [DScribe documentation](https://singroup.github.io/dscribe/latest/tutorials/descriptors/soap.html)), the error is significantly reduced by one order of magnitude compared to the **Cartesian descriptor**. \n\nAs demonstrated in the examples for the `./example/2_EC-EC/` (results available in the `example` directory), non-periodic systems can be well-represented using **non-periodic Cartesian descriptors**, while periodic systems are expected to yield better accuracy when using **periodic SOAP descriptors**. \n\nFor the example of **SOAP descriptor** here, eight uniformly distributed points in the Li slab Rectangular cuboid were used as `centers` argument for **SOAP**. \n\nThe corresponding `train.in` input arguments are\n```\nDescriptor soap\nsoap_r_cut 5.0\nsoap_n_max 6\nsoap_l_max 4\nsoap_centers [[2.20113706670393, 2.328998192856251, 6.952547732109352], [2.20113706670393, 2.328998192856251, 11.895790642109352], [2.20113706670393, 6.760484232856251, 6.952547732109352], [2.20113706670393, 6.760484232856251, 11.895790642109352], [6.63924050670393, 2.328998192856251, 6.952547732109352], [6.63924050670393, 2.328998192856251, 11.895790642109352], [6.63924050670393, 6.760484232856251, 6.952547732109352], [6.63924050670393, 6.760484232856251, 11.895790642109352]]\nsoap_n_jobs 4 \n \nscale 2.0 \nweight 1.0\n```\n\n### 2. Efficiency \u2013 Data Processing Mode\n\n- `data_process iterative`: Computing kernels data-by-data involves `n_data \u00d7 n_data` sequential kernel evaluations, minimizing the memory overhead but significantly increasing computational time. \n\n- `data_process batch`: **aenet-gpr** supports batch processing by grouping the data process into a specific size (`batch_size 25`), which significantly reduces train and evaluation time while keeping memory usage efficient.\n\nBelow, we provide a benchmark comparing the required time and memory for different batch sizes on the `./example/3_Li-EC/` example.\n\n<p align=\"center\">\n<img src=\"doc/source/images/3_Li-EC_cost.png\" width=\"1000\">\n</p>\n",
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