## 2 Materials and Methods
### Uncertainty Quantification Framework  
Detailed uncertainty estimations are necessary for accurately estimating the reactor's safety margins under various conditions and for identifying the most important contributors to these margins. Uncertainty propagation in multi-physics models, such as for the LFNMR, is typically carried out using a stochastic approach. The input sources of uncertainties are characterized statistically, and various samples are generated. For each sample, the multi-physics coupled system is executed to obtain the corresponding samples for the  
Figure 2: Initial core dimensions (**a**) and thermal-hydraulic boundary conditions (**b**) of the 2D LFMSR GeN-Foam model; top-down (**c**) and isometric (**d**) view of the 3D model that represents a 1/16 slice of the full core. outputs of interest. Different dimension reductions and designs of experiment techniques can be used to accelerate the statistical convergence and increase the efficacy of the physics solver. In the case of LFMSR modeling, strong coupling exists between the different physics, making the uncertainty analysis more challenging. Interactions between many inputs and the presence of non-linear input-output relations add to the complexity of an uncertainty study. In such cases, it is important to establish an uncertainty quantification framework that comprises different statistical tools that can propagate the input uncertainties through the codes and analyze the quantities of interest using appropriate statistical quantities [16]. Figure 3 presents a general framework for uncertainty quantification. Modeling and analysis comprise the first step in this process which is encircled in a dashed line in Figure 3. The user determines the appropriate methods to evaluate the physical phenomena under consideration. Uncertainty propagation and sensitivity analysis can be the next step, but it is often advantageous to include dimension reduction and surrogate model development. These two concepts estimate the cardinal relationships between inputs and outputs and reduce the computational burden associated with evaluating every output for a given input space. This input space is defined by the design of experiments, which is usually designed to explore all possible inputs as comprehensively as possible. The design of the experiment is always affected by input uncertainties, which include both aleatoric (natural variability) and epistemic (knowledge gap) components. These uncertainties can be informed by model calibration, which can be performed in various ways including experimental observations or high-fidelity numerical results. The 95% confidence level uncertainties for the selected sources of uncertainties, in this work, are shown in Table 4. Univariate normal distributions are used for each input with the mean value also being provided in Table 4. Each of the thermophysical properties and nuclear data properties are sampled using Latin Hypercube Sampling (LHS). Latin Hypercube Sampling was chosen because it provides more accuracy in mean prediction than random sampling and requires fewer samples than Monte Carlo sampling for the same statistical accuracy [17]. Each LHS bin contained 100 samples. The fuel salt's thermophysical properties uncertainties vary between 2% and 20% and are selected based on literature reviews [18; 19]. The heat transfer coefficient and pump momentum head are specific inputs for GeN-Foam. The former is applied to the heat exchanger region (Section 3.1.1), and the latter is applied to a smaller region near the heat exchanger (Section 3.1.2). These inputs are necessary to achieve a heat and mass transfer balance in the modeled domain. Figure 3: General framework for uncertainty quantification. Adopted from [16]. The nuclear data uncertainties considered in this study are for the total delayed neutron fraction (DNP) and delayed neutron precursor decay constant (\(\lambda\)). [PERSON] et al.