High-resolution spectrographs are central to modern exoplanet research, particularly effective for detecting Earth-like planets with radial velocity (RV) signals of only a few tens of centimeters per second. To achieve this level of accuracy, high-precision wavelength calibration is required. A key factor in this process is the modeling of the instrumental profile (IP), which describes the response of the spectrograph to incident light. The true IP of a high-resolution instrument is often complex. It may display asymmetric or extended wings and undergo change on the detector because of optical aberrations, variations in fiber illumination, and environmental effects. These features lead to systematic errors in the measured line centers when traditional parametric models such as Gaussian functions are used, and they limit the achievable RV precision.

In this work, a non-parametric IP modeling method is adopted based on Gaussian process regression (GPR). The IP is treated as a smooth function with a flexible covariance structure, without being constrained by a predefined analytic form. GPR learns both the global structure and small-scale features of the line shape directly from the data. Since the IP varies slowly across the detector, the method divides each spectral order into several consecutive spatial segments. Each segment is fitted independently, and can capture local variations. The model includes measurement uncertainties and provides a probabilistic description of the IP. Adjacent segments are connected through smooth interpolation to ensure a continuous IP throughout the entire order. Model performance is evaluated using reduced chi-squared and root mean square error (RMSE), enabling quantitative assessment and comparison with traditional approaches.

The method is tested using laser frequency comb (LFC) exposure from the fiber-fed high resolution spectrograph (HRS) on a 2.16 m telescope at Xinglong Observatory. The LFC generates a dense and highly stable set of emission lines, which is well suitable for validating IP reconstruction. Three experiments show clear and consistent improvements. Using odd-numbered lines to predict even-numbered ones within a single exposure reduces the RMSE by 35.6% compared with a Gaussian model, showing better determination of line centers. Applying an IP model trained on one exposure to a later exposure reduces the RMSE by 42.5%, demonstrating improved stability when the model is transferred between exposures. A comparison between two channels under the same exposure conditions shows a 37.1% improvement in calibration consistency, indicating reduced channel-to-channel systematics.

The results from this study show that GPR provides a more accurate description of the instrumental profile and its spatial variation than traditional parametric models. The improved reconstruction of the IP leads to more accurate line center measurements and a more stable and precise wavelength solution. This capability is important for advancing the RV precision of high-resolution spectrographs toward the centimeter-per-second level. The GPR provides a promising method for modeling instrumental profiles and supports the precision required for detecting Earth-like exoplanets.