## 2 Multi-Fidelity Machine Learning  
### Framework  
As shown in Figure 1, the implementation of the proposed data-driven approach involves four steps: (1) establishing the input-output dataset, (2) training and evaluating machine learning models using the dataset, (3) comparing different algorithms and optimising the hyperparameters, and (4) applying the trained model to real-world LNG storage tanks. Based on the workflow, to address the data scarcity, enhance the generalisability, and fully leverage the domain knowledge, this study proposes a multi-fidelity machine learning framework for perlite settlement identification, enabling knowledge transfer between multi-fidelity data. The monitored temperature field of the outer tanks is used as the input for machine learning for identifying perlite settlement. Note that the monitored environmental temperature and LNG level are also part of the input, both of which influence the temperature field of the outer tanks together with perlite settlement. As a result, the input of the proposed approach includes the monitored temperature field, environmental temperature, and LNG level. The output is the identified perlite settlement.  
Figure 1: Overall workflow.  
The dataset used to train the machine learning models includes multi-fidelity data from different data sources. For example, the data generated using a numerical simulation effectively captures the universal mapping relationship between perlite settlement and the temperature field. However, the numerical simulation is theoretical, and the parameters selected in the numerical model will inevitably deviate from real-world conditions, leading to systematic errors in the data. These data are referred to as low-fidelity data in this study. The machine learning models that were trained on low-fidelity data will then be systematically biased. On the other hand, accurate data acquired from an engineering field is often scarce. Such data are referred to as high-fidelity data. Machine learning models trained solely on high-fidelity data struggle to adequately capture the underlying mapping relationships due to the limited quantity of available data. In summary, both low- and high-fidelity data have their advantages: (1) low-fidelity data have good accessibility but contain systematic errors and (2) high-fidelity data is accurate but costly to acquire. Note that data fidelity is a relative concept, as shown in Figure 2.  
Hence, a multi-fidelity machine learning framework is proposed for perlite settlement identification, utilising both low- and high-fidelity data for model training to maximise the value of all data available. As shown in Figure 3, the multi-fidelity machine learning framework consists of two sub-models, namely the low- and high-fidelity models, corresponding to low- and high-fidelity data, respectively. The low-fidelity data was used solely to train the low-fidelity model, while the high-fidelity data were employed only for training the high-fidelity model. When training, evaluating, or applying the high-fidelity model, the high-fidelity data were first input into the trained low-fidelity model to generate preliminary low-fidelity predictions. These low-fidelity predictions were then used as part of the input for the high-fidelity model, which performed further computations to produce the final high-fidelity predictions as the output of multi-fidelity machine learning. In the multi-fidelity machine learning framework, the primary role of the high-fidelity model is to correct the systematic bias learned from the low-fidelity data. By incorporating a relatively small amount of high-fidelity data, the generalisability of the data-driven approach is enhanced, allowing it to achieve higher accuracy.  
Figure 2: The concept of data fidelity.