Transient Simulation Datasets Using Allen-Cahn and Eriksson-Johnson Equations

These datasets contain low- and high-resolution numerical simulations of transient initial-boundary-value problems based on the Allen-Cahn and Eriksson-Johnson equations. These data were used in the paper, "PC-SRGAN: Physically Consistent Super-Resolution Generative Adversarial Network for General Transient Simulations", which proposes a physics-informed super-resolution model to reconstruct fine-resolution solutions from coarse simulations. 

Structure

Each of these datasets is split into training, validation and test subsets, each of which has two folders: one for low and another for the high-resolution simulations. Each simulation instance is a folder named after its parameters. Inside that lowest-level folder, each sample is a numpy file (.npy) of a 1-channel image (filename denotes the time point of the simulation). All four of these datasets have a file (index-val-mapping.csv) in their root directory, which provides the mapping of parameters (as seen in the lowest-level folder names) and their actual values.

Dataset statistics

• Allen-Cahn with Periodic boundary
  ‣ Training: 55,062 samples
  ‣ Validation: 9,065 samples
  ‣ Test: 7,973 samples
  ‣ Total: 72,100 samples

• Allen-Cahn with Periodic boundary (x4)
  ‣ Training: 27,662 samples
  ‣ Validation: 4,506 samples
  ‣ Test: 3,882 samples
  ‣ Total: 36,050 samples

• Allen-Cahn with Neumann boundary
  ‣ Training: 15,732 samples
  ‣ Validation: 2,590 samples
  ‣ Test: 2,278 samples
  ‣ Total: 20,600 samples

• Eriksson-Johnson with Dirichlet boundary
  ‣ Training: 51,875 samples
  ‣ Validation: 8,494 samples
  ‣ Test: 7,352 samples
  ‣ Total: 67,721 samples

The dataset marked "x4" is for 4 times super-resolution (8x8 => 32x32), whereas the rest are for 8 times super-resolution (8x8 => 64x64). These data can be used to benchmark super-resolution methods for physics-based simulations. Refer to the paper for details.

Version history

• Version 1: Released all three x8 datasets.
• Version 2: Added the x4 dataset, with no change to earlier datasets.