PosteriorBench: From Point Estimates to Posterior Matching in Evaluating Generative Inverse Solvers
Paper • 2609.20794 • Published
Dataset Viewer
The dataset viewer is not available for this split.
Cannot load the dataset split (in streaming mode) to extract the first rows.
Error code: StreamingRowsError
Exception: TypeError
Message: Couldn't cast array of type
float
to
List(Value('float32'))
Traceback: Traceback (most recent call last):
File "/src/services/worker/src/worker/utils.py", line 147, in get_rows_or_raise
return get_rows(
dataset=dataset,
...<4 lines>...
column_names=column_names,
)
File "/src/libs/libcommon/src/libcommon/utils.py", line 272, in decorator
return func(*args, **kwargs)
File "/src/services/worker/src/worker/utils.py", line 127, in get_rows
rows_plus_one = list(itertools.islice(safe_iter(ds, dataset=dataset), rows_max_number + 1))
File "/src/services/worker/src/worker/utils.py", line 483, in safe_iter
yield from ds.decode(False) if ds.features else ds
File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 2951, in __iter__
for key, example in ex_iterable:
^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 2461, in __iter__
for key, pa_table in self._iter_arrow():
~~~~~~~~~~~~~~~~^^
File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 2486, in _iter_arrow
for key, pa_table in self.ex_iterable._iter_arrow():
~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^
File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 547, in _iter_arrow
for key, pa_table in iterator:
^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 430, in _iter_arrow
for key, pa_table in self.generate_tables_fn(**gen_kwags):
~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/arrow/arrow.py", line 75, in _generate_tables
yield Key(file_idx, batch_idx), self._cast_table(pa_table)
~~~~~~~~~~~~~~~~^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/arrow/arrow.py", line 54, in _cast_table
pa_table = table_cast(pa_table, self.info.features.arrow_schema)
File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2378, in table_cast
return cast_table_to_schema(table, schema)
File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2312, in cast_table_to_schema
cast_array_to_feature(
~~~~~~~~~~~~~~~~~~~~~^
table[name] if name in table_column_names else pa.array([None] * len(table), type=schema.field(name).type),
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
feature,
^^^^^^^^
)
^
File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 1861, in wrapper
return pa.chunked_array([func(chunk, *args, **kwargs) for chunk in array.chunks])
~~~~^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2118, in cast_array_to_feature
casted_array_values = _c(array.values, feature.feature)
File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 1863, in wrapper
return func(array, *args, **kwargs)
File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2118, in cast_array_to_feature
casted_array_values = _c(array.values, feature.feature)
File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 1863, in wrapper
return func(array, *args, **kwargs)
File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2158, in cast_array_to_feature
raise TypeError(f"Couldn't cast array of type\n{_short_str(array.type)}\nto\n{_short_str(feature)}")
TypeError: Couldn't cast array of type
float
to
List(Value('float32'))Need help to make the dataset viewer work? Make sure to review how to configure the dataset viewer, and open a discussion for direct support.
PosteriorBench datasets
PosteriorBench provides paired physical fields and reference posterior ensembles for evaluating scientific inverse solvers. The four tasks are Poisson, Darcy flow, light transport (LTMI), and carbon capture and storage (CCS). 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_Multimode |
50,000 | 10 | 490 | 128 × 128 |
Darcy_Multimode |
50,000 | 10 | 490 | 128 × 128 |
LTMI_Multimode |
100,000 | 10 | 90 | 64 × 64 |
CCS_Multimode |
12,000 | 8 | 80 | 64 × 200 |
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.
For loading and development checks, pilot/ provides a smaller subset of the full data: 100 training examples and two validation cases per task.
Its posterior datasets contain only the validation split.
The training datasets and reference posteriors are stored separately:
PosteriorBench_hf/
├── PDEFieldDataset_hf/ # For training
│ ├── Poisson_Multimode/
│ ├── Darcy_Multimode/
│ ├── LTMI_Multimode/
│ └── CCS_Multimode/
└── PosteriorDataset_hf/ # For evaluation
│ ├── Poisson_Multimode/
│ ├── Darcy_Multimode/
│ ├── LTMI_Multimode/
│ └── CCS_Multimode/
└── 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 |
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 reference target field for a case, while the posterior sample arrays contain alternative reference realizations.
Channel dimensions and observation conventions differ between tasks.
Use the benchmark's task adapters to interpret sparse observations and sensor locations.
Usage
For loading, training, and evaluation, please follow the instructions in the PosteriorBench GitHub repository.
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