Dataset Card for InverseBench

• Dataset Card for InverseBench
  • Data for linear inverse scattering
  • Data for MRI
  • Data for black hole imaging
  • Data for full waveform inversion
  • Data for Navier-Stokes equation
  • Acknowledgement

Our data can be downloaded from CaltechData.

Data for linear inverse scattering

• Generated using the online simulator CytoPacq[1].
• License: Creative Commons BY-NC-SA 4.0
• Configuration used to generate data:
  • VOI: 42x42x12
  • Cover the whole CCD data: unchecked.
  • Subpixel precision 1x.
  • Type of phantom: HL60 nucleus (static)
  • Position: random
  • Amount: uniformly random number from 1 to 6.
  • Optical System: default value
  • Acquisition Device: default value
• Data post-processing:
  • We crop each image to shape 128x128.
  • Samples in test and val are selected so that their cosine similarity is less than 0.6 w.r.t the most similar sample in training set.

Data Split	Number of Entries	Value range (min,max)	Unit
Train	10,000	(0, 1.0)	F/m
Test	100	(0, 1.0)	F/m
Validation	10	(0, 1.0)	F/m

We use three samples from the validation set to tune hyperparameters for each algorithm and 100 test samples for reporting the results.

Data for MRI

• The multi-coil raw $k$-space data from the fastMRI knee dataset [2].
• We exclude the first and last 5 slices of each volume for training and validation as they do not contain much anatomical information and resize all images down to $320\times 320$ following the preprocessing procedure of the prior work [3].

Data split	Number of entries
Train	25,012
Test	96
Validation	6

We use six samples from the validation set to tune hyperparameters for each algorithm and 96 test samples for reporting the results.

Data for black hole imaging

• Training dataset is from GRMHD (50k).
• Synthetic test dataset from a different pretrained diffusion model.

Data split	Number of entries	Value range (min, max)
Train	50,000	(0, 1)
Test	100	(0, 1)
Validation	5	(0, 1)

We use five samples from the validation set to tune hyperparameters for each algorithm and 100 test samples for reporting the results.

Data for full waveform inversion

• Adapted from the velocity map part of CurveFault dataset in OpenFWI by Deng, Chengyuan, et al. 2022 [1].
• License: Creative Commons BY-NC-SA 4.0
• Data adaptation by us: we resize the original velocity map from resolution 70x70 to 128x128 with bilinear interpolation and anti-aliasing.

Data split	Number of entries	Statistics (min,max)	Unit
Train	50,000	1.50/4.50	km/s
Test	100	1.50/4.50	km/s
Validation	10	1.50/4.50	km/s

We use one validation sample from the validation set to tune hyperparameters for each algorithm and 10 test samples for reporting the results due to the computational cost of the simulation.

Data for Navier-Stokes equation

• We create a dataset of non-trivial initial vorticity fields by first sampling from a Gaussian random field and then evolving the 2D Navier-Stokes equation for five time units.
• The equation setup follows [5,6]. We set the Reynolds number to 200 and spatial resolution to 128\times\128.

Data split	Number of entries	Statistics (min,max)
Train	20,480	(-10, 10)
Test	100	(-10, 10)
Validation	10	(-10, 10)

We use one validation sample from the validation set to tune hyperparameters for each algorithm and 10 test samples for reporting the results due to the computational cost of the simulation.

Acknowledgement

• We thank Ben Prather, Abhishek Joshi, Vedant Dhruv, C.K. Chan, and Charles Gammie for the synthetic blackhole images GRMHD Dataset used here, generated under NSF grant AST 20-34306.

[1]: Wiesner D, Svoboda D, Maška M, Kozubek M. CytoPacq: A web-interface for simulating multi-dimensional cell imaging. Bioinformatics, Oxford University Press, 2019. ISSN 1367-4803. 2019. doi:10.1093/bioinformatics/btz417.

[2]: Zbontar, Jure, et al. "fastMRI: An open dataset and benchmarks for accelerated MRI." arXiv preprint arXiv:1811.08839 (2018).

[3]: Jalal, Ajil, et al. "Robust compressed sensing mri with deep generative priors." Advances in Neural Information Processing Systems 34 (2021): 14938-14954.

[4]: Deng, Chengyuan, et al. "OpenFWI: Large-scale multi-structural benchmark datasets for full waveform inversion." Advances in Neural Information Processing Systems 35 (2022): 6007-6020.

[5]: Iglesias, Marco A., Kody JH Law, and Andrew M. Stuart. "Ensemble Kalman methods for inverse problems." Inverse Problems 29.4 (2013): 045001.

[6]: Li, Zongyi, et al. "Physics-informed neural operator for learning partial differential equations." ACM/JMS Journal of Data Science 1.3 (2024): 1-27.