PosteriorBench datasets

PosteriorBench provides physical fields and reference posterior ensembles for evaluating scientific inverse solvers. The five tasks are Poisson, Darcy flow, light transport (LTMI), carbon capture and storage (CCS), and stochastic risk quantification (SRQ). It includes training data as well as posterior cases for evaluation of generated posterior distributions.

Our benchmark paper is accepted at NeurIPS 2026! Check out the paper and code.

Dataset overview

Dataset directory	Training examples	Validation cases	Test cases	Spatial grid
Poisson	50,000	10	90	128 × 128
Darcy	50,000	10	90	128 × 128
LTMI	100,000	10	90	64 × 64
CCS	12,000	8	80	64 × 200
RiskQuantification	100,000	10	90	128 × 128

Each task's full posterior dataset is stored as a DatasetDict with validation and test splits. Each posterior case contains 100 reference samples and their weights, except SRQ, which contains 1,000.

For loading and development checks, pilot/ provides a smaller subset of the full data: two training examples and one validation case per task. Its posterior datasets contain only the validation split. Each pilot posterior case retains its complete reference ensemble.

Each task directory in the full collection includes metadata.json and an individual *croissant.json file.

The training datasets and reference posteriors are stored separately:

PosteriorBench_hf/
├── PDEFieldDataset_hf/     # For training
│   ├── Poisson/
│   ├── Darcy/
│   ├── LTMI/
│   ├── CCS/
│   └── RiskQuantification/
├── PosteriorDataset_hf/    # For evaluation
│   ├── Poisson/
│   ├── Darcy/
│   ├── LTMI/
│   ├── CCS/
│   └── RiskQuantification/
└── pilot/
    ├── PDEFieldDataset_hf/
    └── PosteriorDataset_hf/

Field conventions

The following shapes describe one training example in the stored representation:

Task	Stored fields	Meaning
Poisson	a: [128,128]; u: [128,128]	Forcing field f and solution field phi
Darcy	data: [2,128,128]	Normalized permeability and solution, in channel order [a,u]
LTMI	a: [2,64,64]; u: [2,64,64]	Two extinction-coefficient fields and two response channels
CCS	a: [1,64,200]; u: [1,64,200]	Condition and dynamics fields
SRQ	a: [128,128]	First-exit risk probability field; u = a

Posterior records include a_ref, u_ref, posterior_samples_a, posterior_samples_u, posterior_weights, and task-specific metadata. The a_ref field is the generating target field for a case, while the posterior sample arrays contain alternative reference realizations. Channel dimensions and observation conventions differ between tasks. Use the task metadata and benchmark's task adapters to interpret sparse observations and sensor locations. For SRQ, the spatial axes are remaining time and initial state; observations are given by metadata.sensor_coords and metadata.observation_values.

Usage

For loading, training, and evaluation, please follow the instructions in the PosteriorBench GitHub repository.

Citation

If you find PosteriorBench helpful in your research, please consider citing our work:

@misc{yao2026posteriorbench,
  title={PosteriorBench: From Point Estimates to Posterior Matching in Evaluating Generative Inverse Solvers}, 
  author={Jiachen Yao and Zi-Siang Hsu and Xi Deng and Aditi Gupta and Xin Ju and Sally M Benson and Gege Wen and Anima Anandkumar},
  year={2026},
  eprint={2609.20794},
  archivePrefix={arXiv},
  primaryClass={cs.LG},
  url={https://arxiv.org/abs/2609.20794}, 
}

Changelog

See CHANGELOG.md for the release history.