## 1 Introduction  
Liquefied natural gas (LNG) storage tanks play a critical role in the global ocean energy supply chain, enabling the safe storage and transportation of LNG [1, 2, 3]. LNG is natural gas that has been cooled to approximately \(-162\)\({}^{\circ}\)C, reducing its volume by \(\sim\)600 times and making it more efficient to store and transport. However, the extreme cryogenic temperatures required to maintain LNG in its liquid state pose significant engineering challenges. Due to the cryogenics of LNG, LNG storage tanks are influenced by their storage conditions and thus their thermal behaviours become significant [4]. The storage tanks must not only retain the LNG safely but must also minimise heat transfer to ensure structural health [5]. LNG storage tanks are typically designed with a double-tank structure, consisting of an inner tank (usually steel) to hold the LNG and an outer tank (typically reinforced concrete) that provides mechanical support [6]. Investigations have shown that repeated freeze-thawcycles, which is a common process for LNG storage, result in strength reductions and structural damage to the reinforced concrete [7]. The damage triggered by repeated freeze-thaw cycles is more severe when the reinforced concrete is in moist conditions, and LNG storage tanks are usually constructed in marine areas. On the other hand, heat transfer between the cryogenic inner tank and the external structure/environment also causes the generation of boil-off gas [8; 9], harming the sustainability of LNG storage. Therefore, the space between the inner and outer tanks is filled with insulation materials, with perlite being one of the most widely used [10]. Perlite is a kind of lightweight particle with excellent thermal insulation properties. In LNG storage tanks, perlite serves to minimise heat transfer between the cryogenic inner tank and external structure/environment. The perlite insulation layer plays a critical role in maintaining the thermal integrity of LNG storage tanks. However, perlite settlement can occur due to thermal cycles, compaction, vibration, or fabric properties [11], reducing insulation efficacy and resulting in thermal leaks [9]. Numerical simulations have demonstrated that the integrity of perlite insulation layers has significant influences on thermal behaviours [12]. In severe cases, this may result in structural failures [13] or environmental hazards [14; 15; 16]. The perlite insulation layers also contribute to structural damping, improving the storage tank's dynamic resistance to earthquakes [17]. Therefore, monitoring the settlement and condition of the perlite insulation layer is critical for preventing risks and ensuring the sustainability of LNG storage infrastructures. Despite the importance of perlite settlement, direct measurement is challenging due to the enclosed nature of the LNG storage tanks. As a result, indirect approaches, such as analysing anomalies in the temperature field of the outer tanks using optical fibres [18] or infrared images [19] to infer insulation conditions, are increasingly being focused on. Additionally, the temperature field of LNG storage tanks is also influenced by multiple factors including the LNG level and environmental temperature. This motivates the need for advanced data-driven approaches that are capable of accurately identifying perlite settlement based on monitoring data [20], which is an inverse problem [21; 22]. Machine learning is an emerging technique used for solving inverse problems [23; 24]. Using machine learning, the mapping relationship embedded in the data can be learnt and utilised for inference [25; 26; 27]. For inverse problems in LNG storage tanks, machine learning has been applied to relevant tasks such as leakage detection [20; 28] and stress prediction [29; 30]. These research articles follow the paradigm of utilising individual data sources; however, for complex engineering systems, data are usually available at different levels of fidelity [31; 32].