# Large Language Model-Informed X-ray Photoelectron Spectroscopy Data Analysis
## 4 Materials and Methodology  
This section presents the details of the materials and methodologies employed for this study. Our synthetic dataset consists of simulated XPS spectra from a hypothetical sample, created to represent typical complexities encountered in real XPS data, including peak overlaps and noise. The analysis is a two-step process, starting off with a curve fitting procedure, followed by interpreting the output using OpenAI's GPT-3.5 Turbo [30]. The synthetic XPS spectra generated for this study include the addition of simulated noise to closely mimic the characteristics of real-world experimental data. The noise in XPS spectra typically arises from various sources, including instrumental factors, environmental fluctuations, and inherent variations in the sample. To replicate these conditions, we have employed a noise simulation approach as follows:  
In our synthetic spectral data, noise was introduced to simulate the inherent fluctuations present in experimental measurements. The noise was generated as a normally  
\[f(x)=A\cdot e^{-(x-\mu)^{2}/(2\sigma^{2})}, \tag{2}\]  
where  
* \(A\) is the height of the curve's peak;
* \(\mu\) is the position of the center of the peak;
* \(\sigma\) is the standard deviation which determines the width of the peak. Our task is to fit a series of Gaussian distributions to the raw data to approximate the observed peaks, and, in the process, estimate the parameters (\(A\), \(\mu\), \(\sigma\)) for each distribution. We employ the algorithm Levenberg-Marquardt [31, 32] implemented in the library _Intfit_[33] for the curve-fitting procedure. This algorithm is widely used in curve-fitting problems, offering robustness in handling nonlinear least-square problems. The objective of this step is to minimize the sum of the squared residuals, defined as follows:  
\[S=\sum[y_{z}-f(x_{z},A,\mu,\sigma)]^{2}, \tag{3}\]  
where \(y_{z}\) are the observed values, \(x_{z}\) are the corresponding energy levels, and \(f(x_{z},A,\mu,\sigma)\) is the fitted Gaussian curve. Levenberg-Marquardt iteratively refines the parameters (\(A\), \(\mu\), \(\sigma\)) to reach a minimum for \(S\). Figure 1 provides a visual representation of a synthetic XPS data for Oxygen 1s, illustrating the contribution of multiple Gaussian peaks, and a linear baseline to the overall spectrum. In Figure 2, we showcase the results of the curve-fitting process applied to our synthetic oxygen XPS data. The initial guesses for peak centers, amplitudes, and sigma (widths) were carefully chosen within a reasonable range based on prior XPS data and domain expertise. These initial conditions were utilized to fit the Gaussian models to our synthetic data. The plot in the figure displays the original synthetic data in blue, and the best fit result obtained from the curve fitting process in red. The close overlap between these two lines indicates a successful curve fitting, providing meaningful peak information from the synthetic data. The robustness of this approach further emphasizes its potential applicability for real-world XPS data analysis. In our approach, the number of components (or peaks) for the fittings is determined using the continuous wavelet transform (CWT), and the optimization uses the python library _Intfit_. The fitting results for model Voigt [34] yielded specific parameters for each peak, such as center, amplitude, and sigma. The pseudocode is presented in Algorithm 1.