# Efficient Neural Surrogates for Linear Radiation Transport on the Lattice and Hohlraum benchmarks

arXiv: https://arxiv.org/abs/2610.04665 · HTML: https://mlsanity.com/paper/2610.04665/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 57 references that are in the map.
- First posted on arXiv 3 Oct 2026.

## Builds on (most cited first, 14 of 14)

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- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Transolver: A Fast Transformer Solver for PDEs on General Geometries](https://mlsanity.com/paper/2402.02366/) (2024)
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- [A Mathematical Guide to Operator Learning](https://mlsanity.com/paper/2312.14688/) (2023)
- [Operator Learning: A Statistical Perspective](https://mlsanity.com/paper/2504.03503/) (2025)

## Abstract (arXiv)

Linear radiation transport equations (RTEs) form the simulation foundations underpinning design and analysis tasks in nuclear engineering, inertial confinement fusion, medical imaging, and astrophysics, but resolving the high-dimensional phase space at engineering fidelity remains expensive enough that outer-loop workflows, such as design optimization, uncertainty quantification, and parameter sweeps, are routinely budget-bound on traditional solvers. Neural surrogates promise to relax this bottleneck by amortizing simulation cost across thousands of downstream queries, but the architectural choices and engineered inductive biases that make a surrogate accurate on one transport problem do not transfer straightforwardly across model families. We benchmark two parameter-matched neural surrogate architectures, the physics-attention Transolver and the multi-scale graph network Bi-Stride Multi-Scale MeshGraphNet (BSMS-MGN), as end-to-end approximations of the final-time particle concentration for the two-dimensional linear RTE on the canonical Lattice and Hohlraum benchmarks. An ablation across Fourier features and region-weighted training loss exposes strongly architecture-dependent inductive-bias preferences, indicating that design choices common to physics-informed surrogate workflows must be revisited per architecture rather than imported across model families, and that downstream utility depends on per-QoI sensitivity rather than a single field-level score. The model training recipe, training data, and evaluation pipeline are released alongside this paper to support reproduction, transfer to related transport problems, and evaluation as amortized forward-model components in larger outer-loop simulation workflows.