---
license: cc-by-4.0
pretty_name: Linear Radiation Transport (Lattice + Hohlraum)
tags:
  - physics
  - radiation-transport
  - scientific-machine-learning
  - surrogate-modeling
  - point-cloud
  - cfd
  - physicsnemo
  - kit-rt
size_categories:
  - 1K<n<10K
---

## Dataset Description:
A point-cloud surrogate-modeling dataset for the final-time 2-D linear
**Radiation Transport Equation (RTE)**, covering two canonical benchmarks
that vary along complementary axes:

- **Lattice** (707 samples, 494 train / 106 val / 107 test) — fixed
  `7 × 7` block geometry; per-sample variation in the white-background
  scattering coefficient (σ_s ∈ [0.1, 10.1]) and the blue-absorber
  cross-section (σ_a ∈ [5, 105]). QoI: final-time absorption integral
  \\(\int_B \sigma_a\, \phi\, dx\\) over the absorbing blocks.

  ![Lattice layout](docs/images/lattice_layout.png)

- **Hohlraum** (846 samples, 592 train / 126 val / 128 test) — fixed
  per-region cross-sections; per-sample variation in 8 geometry parameters
  (`ulr, llr, urr, lrr, hlr, hrr, cx, cy`) controlling the inner edges
  and y-extents of two wall-anchored red strips and the (x, y) offset of
  a center insert. QoI: final-time absorption integral
  \\(\int_S \sigma_a\, \phi\, dx\\) evaluated over three material regions
  \\(S \in \{\text{center insert},\ \text{vertical strip},\ \text{horizontal strip}\}\\).

  ![Hohlraum layout](docs/images/hohlraum_layout.png)

Simulations were produced with [KiT-RT](https://github.com/KiT-RT) using
a discrete-ordinate (S_N) angular discretization, a finite-volume scheme
on an unstructured mesh, and an explicit SSP Runge-Kutta time integrator,
then curated into the PhysicsNeMo `Mesh` memmap format.

## How to download

The dataset is **not** a `datasets`-loadable Parquet dataset; it ships
PhysicsNeMo `tensordict` memmap stores packed as per-sample
`.pmsh.tar.gz` archives. Download the full repo and extract the
archives in place:

```python
import tarfile
from pathlib import Path
from huggingface_hub import snapshot_download

local_dir = Path(snapshot_download(
    repo_id="nvidia/Linear-Radiation-Transport",
    repo_type="dataset",
))

for arc in (local_dir / "mesh").rglob("*.pmsh.tar.gz"):
    with tarfile.open(arc) as tf:
        tf.extractall(arc.parent)
```

After extraction each `<name>.pmsh/` directory is loadable with
PhysicsNeMo's `Mesh` API.

## Dataset Owner(s):
NVIDIA Corporation

## Dataset Creation Date:
May 2026

## License/Terms of Use:
[CC BY 4.0](https://creativecommons.org/licenses/by/4.0/)

## Intended Usage:
Training, evaluation, and benchmarking of point-cloud / mesh-based neural
surrogates for final-time linear radiation transport. The two
benchmarks are complementary stress tests: Lattice probes the surrogate's
ability to generalise across **material parameters** at fixed geometry,
while Hohlraum probes generalisation across **geometry** at fixed
material parameters. Suitable for graph neural networks, neural operators,
point-cloud regressors, and mixed-fidelity / uncertainty-quantification
studies that build on KiT-RT reference solutions.

## Dataset Characterization
** Data Collection Method<br>
* [Synthetic] - High-resolution KiT-RT (S_N + finite-volume) simulations
  on unstructured triangular meshes, post-processed into PhysicsNeMo
  `Mesh` memmap stores. <br>


** Labeling Method<br>
* [Synthetic] - Per-cell scalar flux and derived per-region absorption
  QoIs are computed directly by the numerical solver; no human labeling
  is involved. <br>

## Dataset Format
- **Modality**: 2-D point cloud / unstructured-mesh, per-cell tensors
  plus per-simulation scalar metadata.
- **Per-sample container**: PhysicsNeMo `Mesh` (a tensordict memmap
  store) shipped on disk as a `<name>.pmsh/` directory plus a
  `<name>.attrs.json` sidecar; on the Hub each simulation is bundled
  as a single `<name>.pmsh.tar.gz` archive for transport.
- **Per-cell fields**: `cell_areas` (float32), `sigma_a`, `sigma_s`,
  `sigma_t` (float32), `Q` (float32), `material_properties` (int64),
  `scalar_flux` (float32, shape `(N, 2)` for initial + final snapshots).
- **Cell-center coordinates**: `Mesh.points` (float32, `(N, 2)` — the
  simulations are 2-D so points are stored without a z column).
- **Per-simulation fields** (`Mesh.global_data`): `sim_times` / `timesteps`
  / `wall_times`, `flux_statistics`, `global_metrics`, plus flattened
  `attr__*` parameter draws.
- **Splits**: JSON files at `splits/{lattice,hohlraum}_splits.json`
  storing per-split lists of sample basenames.
- **Auxiliary**: PNG schematics under `docs/images/`, conversion
  manifests at `mesh/{lattice,hohlraum}/conversion_manifest.json`.

## Dataset Quantification
- **Record count**: 1,553 simulations covered by the train/val/test splits
  (707 Lattice + 846 Hohlraum).
- **Cells per sample**: lattice ≈79.9k (constant); hohlraum ≈70k–81k.
- **Per-cell features per sample**: 7 fields (cell_areas, sigma_a,
  sigma_s, sigma_t, Q, material_properties, scalar_flux) plus 2-D
  cell-center coordinates and per-simulation metadata.
- **Total storage**: ~6.0 GB for the extracted `.pmsh/` directories;
  ~2.4 GB as the per-sample `.pmsh.tar.gz` archives shipped to the
  Hugging Face Hub (gzip-compressed).

## Reference(s):
- Schotthöfer, S., & Hauck, C. (2025). "Reference solutions for linear
  radiation transport: the Hohlraum and Lattice benchmarks."
  *arXiv preprint* [arXiv:2505.17284](https://arxiv.org/abs/2505.17284).
- Kusch, J., Schotthöfer, S., Stammer, P., Wolters, J., & Xiao, T.
  (2023). "KiT-RT: An extendable framework for radiative transfer and
  therapy." *ACM Transactions on Mathematical Software*, **49**(4), 1–24.
- KiT-RT solver: <https://github.com/KiT-RT>.

## Ethical Considerations:
NVIDIA believes Trustworthy AI is a shared responsibility and we have established policies and practices to enable development for a wide array of AI applications.  When downloaded or used in accordance with our terms of service, developers should work with their internal developer teams to ensure this dataset meets requirements for the relevant industry and use case and addresses unforeseen product misuse.   
Please report quality, risk, security vulnerabilities or NVIDIA AI Concerns here.