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

2026-10-03

AI Summary

Solving the linear radiative transfer equation in high-dimensional phase space is computationally prohibitive, severely constraining outer-loop workflows such as design optimization. This study systematically evaluates two neural surrogate models—Transolver and BSMS-MGN—on Lattice and Hohlraum benchmarks, incorporating physics-informed attention, multiscale graph neural networks, Fourier features, and region-weighted losses. The analysis reveals architecture-specific inductive bias preferences, underscoring the necessity of re-examining design choices for physics-informed surrogates accordingly, while quantifying sensitivity disparities across architectures. To facilitate reproducibility and cross-scenario transferability, the training recipes and datasets have been made publicly available.

Abstract

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.

Problem

• Linear radiation transport equations
• Neural surrogates
• Inductive bias
• Benchmark evaluation
• Computational cost

Innovation

• Neural Surrogates
• Radiation Transport Equations
• Physics-Attention
• Multi-Scale Graph Network
• Inductive Bias