Gespeichert in:
| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2505.23190 |
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Inhaltsangabe:
- In this paper, we propose a novel neural network approach, termed DeepRTE, to address the steady-state Radiative Transfer Equation (RTE). The RTE is a differential-integral equation that governs the propagation of radiation through a participating medium, with applications spanning diverse domains such as neutron transport, atmospheric radiative transfer, heat transfer, and optical imaging. Our DeepRTE framework demonstrates superior computational efficiency for solving the steady-state RTE, surpassing traditional methods and existing neural network approaches. This efficiency is achieved by embedding physical information through derivation of the RTE and mathematically-informed network architecture. Concurrently, DeepRTE achieves high accuracy with significantly fewer parameters, largely due to its incorporation of mechanisms such as multi-head attention. Furthermore, DeepRTE is a mesh-free neural operator framework with inherent zero-shot capability. This is achieved by incorporating Green's function theory and pre-training with delta-function inflow boundary conditions into both its architecture design and training data construction. The efficacy of the proposed approach is substantiated through comprehensive numerical experiments.