## 2 Methodology
### Theory of Interlayer Pressure Reconstruction  
In a large liquid hydrogen container, the interlayer pressure varies in the heat leakage direction. If the pressure of the vacuum chamber is regarded as the uniform interlayer pressure, the predicted thermal insulation performance of the MLI by the classical LBL model would remarkably deviate from the practical characteristics. Therefore, it is necessary to reconstruct the distribution of interlayer pressure according to the reflector's temperature characteristics using the following method. These assumptions are made before calculation: (1) The emissivity and the thermal conductivity of the MLI materials are accurate enough; (2) the samples of interlayer pressure distribution are physically reasonable.  
Firstly, groups of interlayer pressure distributions as sample data are manually designed with some features of results from the available literature. The polynomial coefficients of Equation (5), \(k_{i}\) can be obtained by data fitting. Secondly, considering the interlayer pressure distribution, the reflector temperature distribution across the MLI can be determined by the modified LBL model mentioned above. Here, the residual gas conduction can be revised by the given pressure distribution in Equation (3). As the iteration proceeds, one group of the temperature distributions corresponding to the pressure distribution will gradually reach the accurate solution. Thus, the sample set of the interlayer pressure distributions and the reflector temperature distributions have been built and used to train the ELM neuronal network. Then, based on the trained machine learning algorithm, the  
Figure 2: The solving process of the modified LBL model.  
interlayer pressure of the MLI can be reconstructed from a set of experimentally measured reflector temperatures.  
During the iteration of the interlayer pressure determination process, the deviation between the reconstructed interlayer pressure and the practical value should be minimized. Due to the strong couple interaction between the interlayer pressure and the reflector temperature, the ideal objective solution of the reconstructed interlayer pressure could be achieved if the following criterion could be satisfied,  
\[min\left|T_{\text{obj}}^{\text{-}}-T_{\text{obj}}\right| \tag{9}\]  
where \(T_{\text{obj}}^{\text{-}}\) represents the temperature distribution of the reflectors corresponding to the reconstructed pressure distribution obtained by the calculation of the modified LBL model, and \(T_{\text{obj}}\) is the measured reflector's temperature distribution of the MLI. In the present study, the practical interlayer pressure distribution is predicted by a machine learning algorithm.  
For an algorithm that can accurately reconstruct the interlayer pressure, the following requirements should be met. The reconstruction algorithm should have sufficient accuracy, reliability and extrapolation capability. Even if the sample data used to reconstruct the interlayer pressure are insufficient or not fully reasonable, the algorithm can still have an excellent generalized extrapolation capability to obtain the reasonable interlayer pressure distribution. Extrapolation refers to the ability of the algorithm to estimate values out of the input data range. In the case of interlayer pressure reconstruction, the algorithm should be able to accurately estimate the interlayer pressure not included in the sample set. In practical industrial applications, it is important for the reconstruction algorithm to yield results in a limited time, and to expand the sample set without significantly increasing the time required. An appropriate algorithm is needed to achieve the reconstruction mission with specific requirements and constraints, including limited predicting time and the desired accuracy of the calculation. Moreover, the reconstruction algorithm should be able to handle any inhomogeneity or variation in the material properties of the MLI.