SELTO Dataset

A Benchmark Dataset for Deep Learning for 3D Topology Optimization

This dataset represents voxelized 3D topology optimization problems and solutions. The solutions have been generated in cooperation with the Ariane Group and Synera using the  Altair OptiStruct implementation of SIMP within the Synera software. The SELTO dataset consists of four different 3D datasets for topology optimization, called disc simple, disc complex, sphere simple and sphere complex. Each of these datasets is further split into a training and a validation subset.

The following paper provides full documentation and examples:

Dittmer, S., Erzmann, D., Harms, H., Maass, P., SELTO: Sample-Efficient Learned Topology Optimization (2022) https://arxiv.org/abs/2209.05098.

The Python library DL4TO (https://github.com/dl4to/dl4to) can be used to download and access all SELTO dataset subsets.
Each TAR.GZ file container consists of multiple enumerated pairs of CSV files. Each pair describes a unique topology optimization problem and contains an associated ground truth solution. Each problem-solution pair consists of two files, where one contains voxel-wise information and the other file contains scalar information. For example, the i-th sample is stored in the files i.csv and i_info.csv, where i.csv contains all voxel-wise information and i_info.csv contains all scalar information. We define all spatially varying quantities at the center of the voxels, rather than on the vertices or surfaces. This allows for a shape-consistent tensor representation.

For the i-th sample, the columns of i_info.csv correspond to the following scalar information:

• E - Young's modulus [Pa]
• ν - Poisson's ratio [-]
• σ_ys - a yield stress [Pa]
• h - discretization size of the voxel grid [m]

The columns of i.csv correspond to the following voxel-wise information:

• x, y, z - the indices that state the location of the voxel within the voxel mesh
• Ω_design - design space information for each voxel. This is a ternary variable that indicates the type of density constraint on the voxel. 0 and 1 indicate that the density is fixed at 0 or 1, respectively. -1 indicates the absence of constraints, i.e., the density in that voxel can be freely optimized
• Ω_dirichlet_x, Ω_dirichlet_y, Ω_dirichlet_z - homogeneous Dirichlet boundary conditions for each voxel. These are binary variables that define whether the voxel is subject to homogeneous Dirichlet boundary constraints in the respective dimension
• F_x, F_y, F_z - floating point variables that define the three spacial components of external forces applied to each voxel. All forces are body forces given in [N/m^3]
• density - defines the binary voxel-wise density of the ground truth solution to the topology optimization problem

How to Import the Dataset

with DL4TO: With the Python library DL4TO (https://github.com/dl4to/dl4to) it is straightforward to download and access the dataset as a customized PyTorch torch.utils.data.Dataset object. As shown in the tutorial this can be done via:

from dl4to.datasets import SELTODataset

dataset = SELTODataset(root=root, name=name, train=train)

Here, root is the path where the dataset should be saved. name is the name of the SELTO subset and can be one of "disc_simple", "disc_complex", "sphere_simple" and "sphere_complex". train is a boolean that indicates whether the corresponding training or validation subset should be loaded. See here for further documentation on the SELTODataset class.

without DL4TO: After downloading and unzipping, any of the i.csv files can be manually imported into Python as a Pandas dataframe object:

import pandas as pd

root = ...
file_path = f'{root}/{i}.csv'
columns = ['x', 'y', 'z', 'Ω_design','Ω_dirichlet_x', 'Ω_dirichlet_y', 'Ω_dirichlet_z', 'F_x', 'F_y', 'F_z', 'density']
df = pd.read_csv(file_path, names=columns)

Similarly, we can import a i_info.csv file via:

file_path = f'{root}/{i}_info.csv'
info_column_names = ['E', 'ν', 'σ_ys', 'h']
df_info = pd.read_csv(file_path,  names=info_columns)

We can extract PyTorch tensors from the Pandas dataframe df using the following function:

import torch

def get_torch_tensors_from_dataframe(df, dtype=torch.float32):
    shape = df[['x', 'y', 'z']].iloc[-1].values.astype(int) + 1
    voxels = [df['x'].values, df['y'].values, df['z'].values]

    Ω_design = torch.zeros(1, *shape, dtype=int)
    Ω_design[:, voxels[0], voxels[1], voxels[2]] = torch.from_numpy(data['Ω_design'].values.astype(int))

    Ω_Dirichlet = torch.zeros(3, *shape, dtype=dtype)
    Ω_Dirichlet[0, voxels[0], voxels[1], voxels[2]] = torch.tensor(df['Ω_dirichlet_x'].values, dtype=dtype)
    Ω_Dirichlet[1, voxels[0], voxels[1], voxels[2]] = torch.tensor(df['Ω_dirichlet_y'].values, dtype=dtype)
    Ω_Dirichlet[2, voxels[0], voxels[1], voxels[2]] = torch.tensor(df['Ω_dirichlet_z'].values, dtype=dtype)

    F = torch.zeros(3, *shape, dtype=dtype)
    F[0, voxels[0], voxels[1], voxels[2]] = torch.tensor(df['F_x'].values, dtype=dtype)
    F[1, voxels[0], voxels[1], voxels[2]] = torch.tensor(df['F_y'].values, dtype=dtype)
    F[2, voxels[0], voxels[1], voxels[2]] = torch.tensor(df['F_z'].values, dtype=dtype)

    density = torch.zeros(1, *shape, dtype=dtype)
    density[:, voxels[0], voxels[1], voxels[2]] = torch.tensor(df['density'].values, dtype=dtype)

    return Ω_design, Ω_Dirichlet, F, density