Instrumental Profile Modelling of a HighResolution Spectrograph based on Gaussian Process Regression

Context. Knowledge of the spectrograph’s instrumental profile (IP) provides important information needed for wavelength calibration and for the use in scientific analyses. Aims. This work develops new methods for IP reconstruction in high-resolution spectrographs equipped with astronomical laser frequency comb (astrocomb) calibration systems and assesses the impact that assumptions on the IP shape have on achieving accurate spectroscopic measurements. Methods. Astrocombs produce ≈ 10 000 bright, unresolved emission lines with known wavelengths, making them excellent probes of the IP. New methods based on Gaussian process regression were developed to extract detailed information on the IP shape from these data. Applying them to HARPS, an extremely stable spectrograph installed on the ESO 3.6m telescope, we reconstructed its IP at 512 locations of the detector, covering 60% of the total detector area. Results. We found that the HARPS IP is asymmetric and that it varies smoothly across the detector. Empirical IP models provide a wavelength accuracy better than 10m s−1 (5m s−1) with a 92% (64%) probability. In comparison, reaching the same accuracy has a probability of only 29% (8%) when a Gaussian IP shape is assumed. Furthermore, the Gaussian assumption is associated with intra-order and inter-order distortions in the HARPS wavelength scale as large as 60 m s−1. The spatial distribution of these distortions suggests they may be related to spectrograph optics and therefore may generally appear in cross-dispersed echelle spectrographs when Gaussian IPs are used. Empirical IP models are provided as supplementary material in machine readable format. We also provide a method to correct the distortions in astrocomb calibrations made under the Gaussian IP assumption. Conclusions. Methods presented here can be applied to other instruments equipped with astrocombs, such as ESPRESSO, but also ANDES and G-CLEF in the future. The empirical IPs are crucial for obtaining objective and unbiased measurements of fundamental constants from high-resolution spectra, as well as measurements of the redshift drift, isotopic abundances, and other science cases.

A 25-GHz mode-spacing astro-comb with 470–720 nm wavelength coverage has been installed as the calibration source on the fiber-fed High Resolution Spectrograph (HRS) of the Chinese 2.16-m telescope at Xinglong Observatory. The calibration tests were carried out based on the single-channel system of HRS. The results have achieved a 2–8 times (for different orders) higher wavelength solution accuracy than the thorium argon (ThAr) lamp, and a short-term repeatability of 0.1 m s−1, which is around the photon noise limit. It proved that the coupling system linking the astro-comb to HRS successfully suppressed the negative effects of laser speckles. The comb-line overlapping exists in the acquired spectrum of the astro-comb on HRS. We demonstrated that when determining the comb-line center, the comb-line overlapping leads to a systematic bias, which is caused by asymmetrical sampling, and meanwhile a larger uncertainty. The correction for the systematic bias is feasible by simulating the overlapping comb lines according to actual comb-line spacing and pixel phase and then calculating the difference of the fitted line center with the true line center. A higher accuracy of wavelength solution has been achieved after correction.

The Southern African Large Telescope (SALT) is developing precision radial velocity capability for its high-resolution spectrograph (HRS). The instrument's high-stability (HS) mode includes a fibre double scrambler and makes provision for simultaneous thorium-argon (ThAr) injection into the calibration fibre. Given the limitations associated with ThAr lamps, as well as the cost and complexity of turn-key commercial laser frequency combs (LFCs), we are in the process of designing and building a bespoke LFC for the Red channel of the HRS (555-890 nm). At a later stage we plan to extend the wavelength range of the LFC to include parts of the blue channel (370-555 nm) as well. A data reduction pipeline capable of delivering precision radial velocity results for the HS mode is also currently under development. We aim to have the LFC and PRV pipeline available for science operations in early 2024.

Gaussian process regression (GPR) based non-invasive continuous blood pressure prediction method from cuff oscillometric signals

A stock price index measures the change in several share prices, which can describe the market and assist investors in deciding on a specific investment. Thus, foreseeing the stock price index benefits investors in creating a better investment strategy. However, forecasting the stock price index can be challenging due to its non-linearity, non-stationary and high uncertainty. Gaussian process regression (GPR) is an attractive and powerful approach for prediction, especially when the data fluctuates over time with fewer restrictions. Besides, the GPR gains advantages over other forecasting techniques as it can offer predictions with uncertainty to provide margin errors. In this study, we evaluate the use of GPR to predict the stock price of Thailand (SET). The SET data are divided into 2 datasets; the data in the year 2015 - 2020 and the data in the year 2020 due to the massive change during the COVID-19 pandemic. The prediction results from the GPR are then compared to the machine learning approaches, artificial neural network (ANN) and recurrent neural network (RNN) using evaluation scores; the root mean square error (RMSE), the mean absolute error (MAE), the mean absolute percentage error (MAPE) and the Nash-Sutcliffe efficiency (NSE). The results indicate that the GPR is superior to the ANN and RNN for both datasets as it provides a high prediction accuracy. Moreover, the results suggest that the GPR is less sensitive to the number of input lags in the model. Therefore, the GPR is more favorable for the prediction of SET than the ANN and RNN.
 HIGHLIGHTS
 
 The Gaussian process regression (GPR) was applied to predict the stock price index of Thailand (SET)
 The predictive performance of the GPR was compared to artificial neural networks (ANNs) and recurrent neural networks (RNNs)
 The results indicate that GPR outperformed the other methods as it provided a high prediction accuracy along with prediction intervals
 
 GRAPHICAL ABSTRACT

The aim of this article is to study the microwave‐assisted foam mat drying of papaya to form papaya powder. The process of foam mat drying of papaya using microwaves was modeled by machine learning approaches like artificial neural network (ANN), support vector regression (SVR), and Gaussian process regression (GPR). Effect of microwave power (480–640 W), inlet air temperature (40–50°C), and thickness of foam (2–4 mm) on the rate of drying were studied. The performance of the models was evaluated on the basis of different performance matrices including root mean square error (RMSE), coefficient of determination (R2), model predictive error, and Chi‐square (χ2). The microwave heating of the papaya foam reduced the drying time manifold. All three machine learning approaches were able to predict the drying process efficiently. SVR showed the best performance (R2 = 0.96; RMSE = 0.03) followed by GPR (R2 = 0.92; RMSE = 0.04) and ANN (R2 = 0.91; RMSE = 0.04). SVR‐based model was simulated to predict the effect of power, temperature, and thickness on drying rate. Machine learning approaches can be efficiently used for modeling and microwave‐assisted foam mat drying. SVR‐based model proves to be a good alternative of ANN.Practical ApplicationsFoam mat drying is the method of dehydrating for heat‐sensitive and viscous materials which cannot be dried by other conventional methods. It is cost‐effective, simple, and provides high product quality. The use of microwave‐assisted drying decreases the drying time manifold. Modeling of the drying process is significant for its scale‐up to industrial scale. Machine learning techniques have the capability of learning the hidden factors involved in the process and thus provide better predictions as compared with statistical regression methods. In this study, three machine learning methods (artificial neural network [ANN], support vector regression [SVR], and Gaussian process regression [GPR]) were compared for their efficiency in modeling the foam‐mat drying of papaya pulp using microwaves. SVR showed the best performance as compared with ANN and GPR.

This study presents a method to develop a series of unique deliverability smart models for underground natural gas storage (UNGS) in different types of target formations. The natural gas supply loop is defined by periodic mismatches between demand and supply. Efficient and faster approaches for forecasting UNGS deliverability may not only assist stakeholders but also the competitive natural gas industry. Due to this fact, this article suggests a series of robust deliverability estimation models for 387 UNGS sites in depleted fields, aquifers, and salt domes based on rigorous machine learning (ML) techniques. To this end, the potential of three ML algorithms, including Gaussian Process Regression (GPR), Least Squares Support Vector Machine (LSSVM), and Extra Tree (ET), is employed. To assess and compare the proposed models, statistical parameters including coefficient of determination (R2), root mean square error (RMSE), mean absolute error (MAE), and standard deviation (SD) were employed. Accordingly, in the case of depleted fields, the GPR, LSSVM, and ET paradigms show overall R2, RMSE, and MAE of 0.999999998, 4.75E−06, 0.00021, and 0.00021. For salt domes, the GPR, LSSVM, and ET models indicate overall R2, RMSE, and MAE of 0.987, 0.0046, and 0.11. Finally, for aquifers, the GPR, LSSVM, and ET algorithms represent overall R2, RMSE, and MAE of 0.999999997, 7.1094E−06, and 0.0002102. The prediction performance reveals that the GPR model is superior to the LSSVM and ET models. This study found that the proposed intelligent models could be utilized as a template for fast estimating the deliverability of UNGS in depleted fields, aquifers, and salt domes with high accuracy. In the end, the outcomes of this study contribute to a deeper understanding of the critical role of machine learning in resolving the difficulty of forecasting the UNSG on cleaner production and sustainable development strategies.

The prediction of Manning coefficients plays a prominent role in the estimation of head losses along culvert systems. Although the Manning coefficient is treated as a constant, previous studies showed the dependency of this coefficient on several parameters. This study aims to evaluate the effective parameters of the Manning roughness coefficient using intelligence approaches such as Gaussian process regression (GPR) and support vector machines (SVM), in which the input variables were considered as dimensionless and dimensional. In addition to the enhanced efficiency of the SVM approach compared to the GPR approach in model development with dimensionless input variables, the accuracy of model A(I) with input parameters of Fr (Froude) and y/D (the ratio of water depth to culvert diameter) and performance criteria of correlation coefficient (R) = 0.738, determination coefficient (DC) = 0.0962, root mean square errors (RMSE) = 0.0015 and R = 0.818, DC = 0.993 and RMSE = 0.0006 for GPR and SVM approaches were the highest. Thus, for the second category, a model with an input parameter of discharge (Q), hydraulic radius (RH), and culvert's slope (S0) showed good efficiency in predicting the Manning coefficient, in which the performance criteria of GPR and SVM approaches were (R = 0.719, DC = 0.949, RMSE = 0.0013) and (R = 0.742, DC = 0.991, RMSE = 0.007), respectively. Furthermore, developed OAT (one-at-a-time) sensitivity analysis revealed that relative depth y/D and Q are the most important parameters in the prediction of the Manning coefficient for models with dimensionless and dimensional input variables, respectively.

Chapter 20 - Wavelet decomposition based on Gaussian process regression and multiple linear regression: Monthly reservoir evaporation prediction

The leaf chlorophyll content (LCC) is a critical index to characterize crop growth conditions, photosynthetic capacity, and physiological status. Its dynamic change characteristics are of great significance for monitoring crop growth conditions and understanding the process of material and energy exchange between crops and the environment. Extensive research has focused on LCC retrieval with hyperspectral data onboard various sensor platforms. Nevertheless, limited attention has been paid to LCC inversion from multispectral data, such as the data from Landsat-8, and the potentials and capabilities of the data for crop LCC estimation have not been fully explored. The present study made use of Landsat-8 Operational Land Imager (OLI) imagery and the corresponding field experimental data to evaluate their capabilities and potentials for LCC modeling using four different retrieval methods: vegetation indices (VIs), machine learning regression algorithms (MLRAs), lookup-table (LUT)-based inversion, and hybrid regression approaches. The results showed that the modified triangular vegetation index (MTVI2) exhibited the best estimate accuracy for LCC retrieval with a root mean square error (RMSE) of 5.99 μg/cm2 and a relative RMSE (RRMSE) of 10.49%. Several other vegetation indices that were established from red and near-infrared (NIR) bands also exhibited good accuracy. Models established from Gaussian process regression (GPR) achieved the highest accuracy for LCC retrieval (RMSE = 5.50 μg/cm2, RRMSE = 9.62%) compared with other MLRAs. Moreover, red and NIR bands outweighed other bands in terms of GPR modelling. LUT-based inversion methods with the “K(x) = −log (x) + x” cost function that belongs to the “minimum contrast estimates” family showed the best estimation results (RMSE = 8.08 μg/cm2, RRMSE = 14.14%), and the addition of multiple solution regularization strategies effectively improved the inversion accuracy. For hybrid regression methods, the use of active learning (AL) techniques together with GPR for LCC modelling significantly increased the estimation accuracy, and the combination of entropy query by bagging (EQB) AL and GPR had the best accuracy for LCC estimation (RMSE = 12.43 μg/cm2, RRMSE = 21.77%). Overall, our study suggest that Landsat-8 OLI data are suitable for crop LCC retrieval and could provide a basis for LCC estimation with similar multispectral datasets.

Gaussian Process Regression (GPR) emerged as a powerful algorithm since last decade in many applications. However, it is not fully explored in remote sensing applications, especially for predicting plant biophysical variables in the heterogeneous environment of India. This kernel-based machine learning technique has effectively replaced conventional approaches for estimating vegetation characteristics from remotely sensed data. In this work, an attempt has been made to test the ability of GPR to estimate the leaf area index (LAI) of wheat crops using the Sentinel-1 (S1) derived Dual-Polarized Radar Vegetation Index (DpRVI) and Sentinel-2 (S2) Top of Atmosphere (TOA) products. Further, the ability of the atmospheric correction procedure was tested by S2 Bottom of Atmosphere (BOA) images. To accomplish this, the field measurements of LAI were carried out from January to March 2020. Further comparisons of the GPR’s performance were made with the Artificial Neural Network (ANN) coupled with the PROSAIL (PROSPECT+SAIL) radiative transfer model, available through the Sentinel Application Platform (SNAP) Biophysical processor. The accuracy of the estimated LAI was evaluated using the statistical indicators, for example, coefficient of determination (R 2 ), Root Mean Square Error (RMSE), and Nash Sutcliffe Efficiency (NSE). The results showed that the synergy of the GPR and DpRVI provided the most accurate result (R 2 = 0.822, RMSE = 0.503 m2 m−2, NSE = 0.831) as compared to the GPR and TOA (R 2 = 0.816, RMSE = 0.596 m2 m−2, NSE = 0.803) and SNAP biophysical processor (based on ANN) (R 2 = 0.696, RMSE = 0.760 m2 m−2, NSE = 0.578). Therefore, the study demonstrated the importance of S1 SAR images and GPR as an alternative tool among the other well-established machine learning algorithms to estimate the crop biophysical parameters.

Radial velocity (RV) searches for Earth-mass exoplanets in the habitable zone around Sun-like stars are limited by the effects of stellar variability on the host star. In particular, suppression of convective blueshift and brightness inhomogeneities due to photospheric faculae/plage and starspots are the dominant contribution to the variability of such stellar RVs. Gaussian process (GP) regression is a powerful tool for statistically modeling these quasi-periodic variations. We investigate the limits of this technique using 800 days of RVs from the solar telescope on the High Accuracy Radial velocity Planet Searcher for the Northern hemisphere (HARPS-N) spectrograph. These data provide a well-sampled time series of stellar RV variations. Into this data set, we inject Keplerian signals with periods between 100 and 500 days and amplitudes between 0.6 and 2.4 m s−1. We use GP regression to fit the resulting RVs and determine the statistical significance of recovered periods and amplitudes. We then generate synthetic RVs with the same covariance properties as the solar data to determine a lower bound on the observational baseline necessary to detect low-mass planets in Venus-like orbits around a Sun-like star. Our simulations show that discovering planets with a larger mass (∼0.5 m s−1) using current-generation spectrographs and GP regression will require more than 12 yr of densely sampled RV observations. Furthermore, even with a perfect model of stellar variability, discovering a true exo-Venus (∼0.1 m s−1) with current instruments would take over 15 yr. Therefore, next-generation spectrographs and better models of stellar variability are required for detection of such planets.

The MINiature Exoplanet Radial Velocity Array (MINERVA) is a dedicated observatory of four 0.7 m robotic telescopes fiber-fed to a KiwiSpec spectrograph. The MINERVA mission is to discover super-Earths in the habitable zones of nearby stars. This can be accomplished with MINERVA’s unique combination of high precision and high cadence over long time periods. In this work, we detail changes to the MINERVA facility that have occurred since our previous paper. We then describe MINERVA’s robotic control software, the process by which we perform 1D spectral extraction, and our forward modeling Doppler pipeline. In the process of improving our forward modeling procedure, we found that our spectrograph’s intrinsic instrumental profile is stable for at least nine months. Because of that, we characterized our instrumental profile with a time-independent, cubic spline function based on the profile in the cross dispersion direction, with which we achieved a radial velocity precision similar to using a conventional “sum-of-Gaussians” instrumental profile: 1.8 m s−1 over 1.5 months on the RV standard star HD 122064. Therefore, we conclude that the instrumental profile need not be perfectly accurate as long as it is stable. In addition, we observed 51 Peg and our results are consistent with the literature, confirming our spectrograph and Doppler pipeline are producing accurate and precise radial velocities.

Context. High-precision radial velocity (RV) measurements with slit spectrographs require the instrument profile (IP) and Earth’s atmospheric spectrum to be known and to be incorporated into the RV calculation. Aims. We developed an RV pipeline, called Velocity and IP EstimatoR (viper), to achieve high-precision RVs in the near-infrared (NIR). The code is able to process observations taken with a gas cell and includes modelling of the IP and telluric lines. Methods. We utilised least-square fitting and telluric forward modelling to account for instrument instabilities and atmospheric absorption lines. As part of this process, we demonstrate the creation of telluric-free stellar spectra. Results. By applying viper to observations obtained with the upgraded CRyogenic high-resolution InfraRed Echelle Spectrograph (CRIRES+) and a gas absorption cell in the K band, we are able to reach an RV precision of around 3 m/s over a time span of 2.5 years. For observations using telluric lines for the wavelength reference, an RV precision of 10 m/s is achieved. Conclusions. We demonstrate that despite telluric contamination, a high RV precision is possible at NIR wavelengths, even for a slit spectrograph with varying IP. Furthermore, we show that CRIRES+ performs well and is an excellent choice for science studies requiring precise stellar RV measurements in the infrared.

A novel combined multi-task learning and Gaussian process regression model for the prediction of multi-timescale and multi-component of solar radiation