Radiation heat transfer in a graded-index medium often suffers accuracy problems due to the gradual changes in the refractive index. The finite element method, meshfree, and other numerical methods often struggle to maintain accuracy when applied to this medium. To address this issue, we apply physics-informed neural networks (PINNs)-based machine learning algorithms to simulate forward and inverse problems for this medium. We also provide the theoretical upper bounds. This theoretical framework is validated through numerical experiments of predefined and newly developed models that demonstrate the accuracy and robustness of the algorithms in solving radiation transport problems in the medium. The simulations show that the novel algorithm goes on with numerical stability and effectively mitigates oscillatory errors, even in cases with more pronounced variations in the refractive index.

翻译：梯度折射率介质中的辐射传热常因折射率的渐变特性而面临精度问题。有限元法、无网格法及其他数值方法应用于此类介质时往往难以保持计算精度。为解决此问题，我们应用基于物理信息神经网络（PINNs）的机器学习算法来模拟该介质的正问题与反问题，并提供了理论误差上界。该理论框架通过预设模型与新开发模型的数值实验得到验证，实验结果表明算法在求解该介质辐射传输问题时具有精度与鲁棒性。模拟显示，即使折射率变化更为显著的情况，该新型算法仍能保持数值稳定性，并有效抑制振荡误差。