---
license: cc-by-nc-4.0
pretty_name: HPG-Diff
language:
- en
tags:
- topology-optimization
- diffusion-models
- physics-guided
- structural-design
dataset_info:
- features:
  - name: image
    dtype: image
  - name: load
    dtype:
      array3_d:
        shape:
        - 64
        - 64
        - 2
        dtype: float64
  - name: pf
    dtype:
      array3_d:
        shape:
        - 64
        - 64
        - 3
        dtype: float64
  - name: disp
    dtype:
      array3_d:
        shape:
        - 64
        - 64
        - 1
        dtype: float64
  - name: psl
    dtype: image
  - name: summary
    struct:
    - name: y_loads
      sequence: float64
    - name: BC_conf
      sequence:
      - name: '0'
        sequence: int64
      - name: '1'
        dtype: int64
    - name: VF
      dtype: float64
    - name: load_nodes
      sequence: float64
    - name: BC_conf_x
      dtype: string
    - name: BC_conf_y
      dtype: string
    - name: load_coord
      dtype:
        array2_d:
          shape:
          - null
          - 2
          dtype: float64
    - name: x_loads
      sequence: float64
  - name: id
    dtype: string
  splits:
  - name: train
    num_bytes: 7784070952
    num_examples: 30000
  download_size: 3647646831
  dataset_size: 7784070952
  config_name: train
- features:
  - name: bc
    dtype:
      array3_d:
        shape:
        - 64
        - 64
        - 2
        dtype: float32
  - name: load
    dtype:
      array3_d:
        shape:
        - 64
        - 64
        - 2
        dtype: float64
  - name: pf
    dtype:
      array3_d:
        shape:
        - 64
        - 64
        - 3
        dtype: float64
  - name: disp
    dtype:
      array3_d:
        shape:
        - 64
        - 64
        - 1
        dtype: float64
  - name: psl
    dtype: image
  - name: compliance
    sequence: float64
  - name: summary
    struct:
    - name: y_loads
      sequence: float64
    - name: BC_conf
      sequence:
      - name: '0'
        sequence: int64
      - name: '1'
        dtype: int64
    - name: VF
      dtype: float64
    - name: load_nodes
      sequence: float64
    - name: BC_conf_x
      dtype: string
    - name: BC_conf_y
      dtype: string
    - name: load_coord
      dtype:
        array2_d:
          shape:
          - null
          - 2
          dtype: float64
    - name: x_loads
      sequence: float64
  - name: id
    dtype: string
  splits:
  - name: test_level_1
    num_bytes: 581208700
    num_examples: 1800
  - name: test_level_2
    num_bytes: 316289133
    num_examples: 1000
  download_size: 340573399
  dataset_size: 897497833
  config_name: test
configs:
- config_name: train
  default: true
  data_files:
  - split: train
    path: data/train-*
- config_name: test
  data_files:
  - split: test_level_1
    path: data/test_level_1-*
  - split: test_level_2
    path: data/test_level_2-*
---

# HPG-Diff

The dataset for **HPG-Diff: Hierarchical Physics-Guided Diffusion with Differentiable Connectivity Constraints for Topology Optimization**, published in *Applied Soft Computing*, 2026.

HPG-Diff uses displacement, principal stress lines, and strain energy density to guide topology generation. This dataset provides the structural examples, conditioning fields, and benchmark reference values used for training and evaluation.

[Paper](https://doi.org/10.1016/j.asoc.2026.115899) · [Code](https://github.com/JinboYang94/HPG-Diff)

## Datasets

| Configuration | Split | Examples | Description |
|---|---|---:|---|
| `train` | `train` | 30,000 | Training topologies with conditioning physics fields |
| `test` | `test_level_1` | 1,800 | In-distribution boundary conditions |
| `test` | `test_level_2` | 1,000 | Out-of-distribution boundary conditions |

The examples use a 64 × 64 grid. Training and evaluation have separate configurations because their fields differ.

## Data Format

| Field | Shape / type | Description |
|---|---|---|
| `id` | string | Sample identifier |
| `image` | image, training only | Target topology |
| `load` | 64 × 64 × 2 | Load field |
| `pf` | 64 × 64 × 3 | Physical-field tensor used by the model |
| `disp` | 64 × 64 × 1 | Displacement field |
| `psl` | RGB image | Principal stress line representation |
| `summary` | structured record | Loads, supports, coordinates, and volume fraction |
| `bc` | 64 × 64 × 2, test only | Boundary-condition field |
| `compliance` | list of numbers, test only | Reference compliance values used by the evaluation code |

## Usage

```python
from datasets import load_dataset

train = load_dataset("scottyjb/HPGDiff", "train", split="train")
test_1 = load_dataset("scottyjb/HPGDiff", "test", split="test_level_1")
test_2 = load_dataset("scottyjb/HPGDiff", "test", split="test_level_2")
```

The training and evaluation scripts are available in the [code repository](https://github.com/JinboYang94/HPG-Diff).

## Data Source

The SIMP topology examples come from [TopoDiff](https://decode.mit.edu/projects/topodiff/) by François Mazé and Faez Ahmed. HPG-Diff supplements them with displacement and principal stress line features.

## Citation

```bibtex
@article{yang2026hpgdiff,
  title   = {{HPG-Diff}: Hierarchical physics-guided diffusion with differentiable connectivity constraints for topology optimization},
  author  = {Yang, Jinbo and Yuan, Mingyue and Zhang, Boyuan and Kitamura, Yoshifumi and Jing, Shikai},
  journal = {Applied Soft Computing},
  volume  = {202},
  pages   = {115899},
  year    = {2026},
  doi     = {10.1016/j.asoc.2026.115899}
}
```

The `compliance` field in each test row contains the complete reference vector for that split. Evaluation reads it from the first row and matches values by the original row order; keep that order when computing compliance metrics.

## License

This dataset is released under [CC BY-NC 4.0](https://creativecommons.org/licenses/by-nc/4.0/). Source materials retain their original licenses.