Gaussian Process Technique Research Articles

Scalable interpolation of satellite altimetry data with probabilistic machine learning

We present GPSat; an open-source Python programming library for performing efficient interpolation of non-stationary satellite altimetry data, using scalable Gaussian process techniques. We use GPSat to generate complete maps of daily 50 km-gridded Arctic sea ice radar freeboard, and find that, relative to a previous interpolation scheme, GPSat offers a 504 × computational speedup, with less than 4 mm difference on the derived freeboards on average. We then demonstrate the scalability of GPSat through freeboard interpolation at 5 km resolution, and Sea-Level Anomalies (SLA) at the resolution of the altimeter footprint. Interpolated 5 km radar freeboards show strong agreement with airborne data (linear correlation of 0.66). Footprint-level SLA interpolation also shows improvements in predictive skill over linear regression. In this work, we suggest that GPSat could overcome the computational bottlenecks faced in many altimetry-based interpolation routines, and hence advance critical understanding of ocean and sea ice variability over short spatio-temporal scales.

Building spectral templates and reconstructing parameters for core-collapse supernovae with CASTOR

ABSTRACT The future of time-domain optical astronomy relies on the development of techniques and software capable of handling a rising amount of data and gradually complementing, or replacing if necessary, real observations. Next-generation surveys, like the Large Synoptic Survey Telescope, will open the door to the new era of optical astrophysics, creating, at the same time, a deficiency in spectroscopic data necessary to confirm the nature of each event and to fully recover the parametric space. In this framework, we developed Core collApse Supernovae parameTers estimatOR (CASTOR), a novel software for data analysis. CASTOR combines Gaussian process and other machine-learning techniques to build time-series templates of synthetic spectra and to estimate parameters of core-collapse supernovae (CCSNe) for which only multiband photometry is available. Techniques to build templates are fully data driven and non-parametric through empirical and robust models, and rely on the direct comparison with a training set of 111 CCSNe from the literature. Furthermore, CASTOR employees the real photometric data and the reconstructed synthetic spectra of an event to estimate parameters that belong to the supernova ejecta, to the stellar progenitor and to the event itself, in a rapid and user-friendly framework. In this work, we provide a demonstration of how CASTOR works, studying available data from SN 2015ap and comparing our results with those available in literature.

Reconstruction of Cenozoic δ11Bsw Using a Gaussian Process

AbstractThe boron isotope ratio of seawater (δ11Bsw) is a parameter which must be known to reconstruct palaeo pH and CO2 from boron isotope measurements of marine carbonates. Beyond a few million years ago, δ11Bsw is likely to have been different to modern. Palaeo δ11Bsw can be estimated by simultaneously constraining the vertical gradients in foraminiferal δ11B (Δδ11B) and pH (ΔpH). A number of subtly different techniques have been used to estimate ΔpH in the past, all broadly based on assumptions about vertical gradients in oxygen, and/or carbon, or other carbonate system constraints. In this work we pull together existing data from previous studies, alongside a constraint on the rate of change of δ11Bsw from modeling. We combine this information in an overarching statistical framework called a Gaussian Process. The Gaussian Process technique allows us to bring together data and constraints on the rate of change in δ11Bsw to generate random plausible evolutions of δ11Bsw. We reconstruct δ11Bsw, and by extension palaeo pH, across the last 65Myr using this novel methodology. Reconstructed δ11Bsw is compared to other seawater isotope ratios, namely , , and δ7Li, which we also reconstruct with Gaussian Processes. Our method provides a template for incorporation of future δ11Bsw constraints, and a mechanism for propagation of uncertainty in δ11Bsw into future studies.

A ML strategy for the identification of optimal LPT design region and related blade shape

This work presents a machine-learning (ML) strategy for the identification of the design region that guarantees minimum losses for Low Pressure Turbine (LPT) blades, allowing the definition of the optimal blade shape. The data-driven procedure is twofold. Firstly, an advanced loss-correlation model (M1) that describes the LPT efficiency as a function of the main flow and geometrical parameters, also accounting for unsteady effects, has been trained from a numerical database. Then, a second model (M2) has been tuned to interpret the corresponding blade geometries. Proper Orthogonal Decomposition (POD) has been applied to formally decompose the blade shape into modes and coefficients. The modes provide basis functions, while the coefficients give the weights that, depending on the combination of the design parameters, define the blade shape. Gaussian Process (GP) and Cross-Validation techniques have been used for tuning both M1 and M2. Once properly tuned, the overall procedure provides the loss-correlation model (M1) for the identification of the design region that is expected to minimize losses, and the geometrical model (M2) for a quick definition of the corresponding optimal blade shape. The procedure can be extended to other engineering applications where own efficiency and geometrical data are available.

Image Matting With Deep Gaussian Process.

We observe a common characteristic between the classical propagation-based image matting and the Gaussian process (GP)-based regression. The former produces closer alpha matte values for pixels associated with a higher affinity, while the outputs regressed by the latter are more correlated for more similar inputs. Based on this observation, we reformulate image matting as GP and find that this novel matting-GP formulation results in a set of attractive properties. First, it offers an alternative view on and approach to propagation-based image matting. Second, an application of kernel learning in GP brings in a novel deep matting-GP technique, which is pretty powerful for encapsulating the expressive power of deep architecture on the image relative to its matting. Third, an existing scalable GP technique can be incorporated to further reduce the computational complexity to O(n) from O(n3) of many conventional matting propagation techniques. Our deep matting-GP provides an attractive strategy toward addressing the limit of widespread adoption of deep learning techniques to image matting for which a sufficiently large labeled dataset is lacking. A set of experiments on both synthetically composited images and real-world images show the superiority of the deep matting-GP to not only the classical propagation-based matting techniques but also modern deep learning-based approaches.

Assessing the soil salinity vulnerability and groundwater quality variations due to drying up of the lake.

Shrinkage of lakes is considered a serious ecological challenge. The impact of this phenomenon on the environment can be devastating. Monitoring the spatiotemporal variations of lake's water surface and its salinization is essential for planning and adopting mitigation measures. In this study, a new multiscale-kernel-based method was used to assess the spatiotemporal variations of the shrinkage of the Urmia Lake and develop soil salinity vulnerability map for its basin. For this aim, remote sensing, empirical wavelet transform (EWT), differential symbolic entropy (DSE), and Gaussian regression process (GPR) techniques were used. Vulnerable areas were identified using geo-environmental parameters extracted from the in situ observations and satellite datasets. In the next step, considering three time periods including the lake normal period, lake drying period, and lake restoration period, the variations in the quality of groundwater were investigated. Results showed that the east and south sections of the lake were more prone to severe salinization. Saline lands caused negative impacts on air quality and agricultural activities in these areas. It was found that both climate change and human activities had contributed to the shrinking of the lake. Results showed that the quality of groundwater in the area around the lake has been affected by the excessive salinity of the lake water and the encroachment process of saline water. The water quality index has increased during the drying period of the lake and caused negative effects on the quality of water used for drinking and agricultural activities. In the lake restoration period, a slight increase in water quality was observed.

A Stochastic Approach to Reconstruct Gamma-Ray-burst Light Curves

Gamma-ray bursts (GRBs), as they are observed at high redshift (z = 9.4), are vital to cosmological studies and investigating Population III stars. To tackle these studies, we need correlations among relevant GRB variables with the requirement of small uncertainties on their variables. Thus, we must have good coverage of GRB light curves (LCs). However, gaps in the LC hinder the precise determination of GRB properties and are often unavoidable. Therefore, extensive categorization of GRB LCs remains a hurdle. We address LC gaps using a stochastic reconstruction, wherein we fit two preexisting models (the Willingale model; W07; and a broken power law; BPL) to the observed LC, then use the distribution of flux residuals from the original data to generate data to fill in the temporal gaps. We also demonstrate a model-independent LC reconstruction via Gaussian processes. At 10% noise, the uncertainty of the end time of the plateau, its correspondent flux, and the temporal decay index after the plateau decreases by 33.3%, 35.03%, and 43.32% on average for the W07, and by 33.3%, 30.78%, 43.9% for the BPL, respectively. The uncertainty of the slope of the plateau decreases by 14.76% in the BPL. After using the Gaussian process technique, we see similar trends of a decrease in uncertainty for all model parameters for both the W07 and BPL models. These improvements are essential for the application of GRBs as standard candles in cosmology, for the investigation of theoretical models, and for inferring the redshift of GRBs with future machine-learning analyses.

Inelastic N_2+H_2 collisions and quantum-classical rate coefficients: large datasets and machine learning predictions

Rate coefficients for vibrational energy transfer are calculated for collisions between molecular nitrogen and hydrogen in a wide range of temperature and of initial vibrational states (vle 40 for N_2 and wle 10 for H_2). These data are needed for the modelling of discharges in N_2/H_2 plasma or of atmospheric and interstellar medium chemistry in different temperature ranges. The calculations were performed by a mixed quantum-classical method, to recover quantum effects associated with the vibrational motion, on a refined potential energy surface. The obtained rates present striking discrepancies with those evaluated by first-order perturbation theories, like the SSH (Schwartz, Slavsky, Herzfeld) theory, which are often adopted in kinetic modelling. In addition, we present a detailed, though preliminary, analysis on the performance of different Machine Learning models based on the Gaussian Process or Neural Network techniques to produce complete datasets of inelastic scattering rate coefficients. Eventually, by using the selected models, we give the complete dataset (i.e., covering the whole vibrational ladder) of rate coefficients for the textrm{N}_2(v)+textrm{H}_2(0) longrightarrow textrm{N}_2(v-Delta v)+textrm{H}_2(0), Delta v=1,2,3 processes.Graphical abstract

Assessing Waste Marble Powder Impact on Concrete Flexural Strength Using Gaussian Process, SVM, and ANFIS

The study’s goal is to assess the flexural strength of concrete that includes waste marble powder using machine learning methods, i.e., ANFIS, Support vector machines, and Gaussian processes approaches. Flexural strength has also been studied by using the most reliable approach of sensitivity analysis in order to determine the influential independent variable to predict the dependent variable. The entire dataset consists of 202 observations, of which 120 were experimental and 82 were readings from previous research projects. The dataset was then arbitrarily split into two subsets, referred to as the training dataset and the testing dataset, each of which contained a weighted percentage of the total observations (70–30). Output was concrete mix flexural strength, whereas inputs comprised cement, fine and coarse aggregates, water, waste marble powder, and curing days. Using statistical criteria, an evaluation of the efficacy of the approaches was carried out. In comparison to other algorithms, the results demonstrate that the Gaussian process technique has a lower error bandwidth, which contributes to its superior performance. The Gaussian process is capable of producing more accurate predictions of the results of an experiment due to the fact that it has a higher coefficient of correlation (0.7476), a lower mean absolute error value (1.0884), and a smaller root mean square error value (1.5621). The number of curing days was identified as a significant predictor, in addition to a number of other factors, by sensitivity analysis.

Efficient Full-Wave Modeling of Microwave Components With Interval-Valued Electromagnetic Parameters by Polynomial Chaos Expansion-Based DGTD Method

An efficient polynomial chaos expansion (PCE)-based discontinuous Galerkin time-domain (DGTD) method is proposed to analyze microwave components with interval-valued electromagnetic (EM) parameters. The proposed method retains the flexibility of the conventional DGTD method in the element-level domain decomposition and parallel computing. Numerical examples with the interval-valued electron density of plasma and permittivity of a dielectric block are presented to demonstrate the accuracy and capability of the proposed method. The scattering from a dielectric sphere with an interval-valued permittivity is evaluated to verify the applicability of the proposed method in unbounded scattering analysis. Numerical results illustrate that the proposed PCE-based DGTD method has great superiority in computational accuracy and efficiency over the Gaussian process (GP) technique and the Monte Carlo (MC) method in both deterministic and stochastic analyses with the interval-valued parameters, and it requires only a single simulation to obtain all results in the high-dimensional interval domains.

A Laplacian‐regularized dual‐phase Gaussian process technique for semi‐supervised response surface modeling of black‐box functions

AbstractNumerous semi‐supervised learning strategies are designed to reduce the number of experiments to model expensive black‐box functions. However, most of the existing methods do not utilize the information of the estimated responses and the associated gradients in an effective manner. In this paper, we proposed a semi‐supervised learning configuration for the Gaussian process which utilizes the estimated responses and their gradients in a dual‐phase framework to improve the accuracy of estimation and reduce the number of expensive experiments required to represent a latent function. We also explore the incorporation of Laplacian regularization for information transfer using a combination of design vector and response surface elements between measured and unmeasured data points. Through several simulation studies and a case study on the evaluation of concrete strength prediction accuracy, we assess the effectiveness of the proposed framework and compare its performance against some of the existing Laplacian‐regularized methods in the Literature.

HADES RV Programme with HARPS-N at TNG

Aims. We present the complete Bayesian statistical analysis of the HArps-n red Dwarf Exoplanet Survey (HADES), which monitored the radial velocities of a large sample of M dwarfs with HARPS-N at TNG over the last 6 yr. Methods. The targets were selected in a narrow range of spectral types from M0 to M3, 0.3 M⊙ < M★ < 0.71 M⊙, in order to study the planetary population around a well-defined class of host stars. We take advantage of Bayesian statistics to derive an accurate estimate of the detectability function of the survey. Our analysis also includes the application of a Gaussian Process approach to take into account stellar-activity-induced radial velocity variations and improve the detection limits around the most-observed and most-active targets. The Markov chain Monte Carlo and Gaussian process technique we apply in this analysis has proven very effective in the study of M-dwarf planetary systems, helping the detection of most of the HADES planets. Results. From the detectability function we can calculate the occurrence rate of small-mass planets around early-M dwarfs, either taking into account only the 11 already published HADES planets or adding the five new planetary candidates discovered in this analysis, and compare them with the previous estimates of planet occurrence around M-dwarf or solar-type stars: considering only the confirmed planets, we find the highest frequency for low-mass planets (1 M⊕ < mp sin i < 10 M⊕) with periods 10 d < P < 100 d, ${f_{{\rm{occ}}}} = 0.85_{ - 0.21}^{ + 0.46}$, while for short-period planets (1 d < P < 10 d) we find a frequency of ${f_{{\rm{occ}}}} = 0.10_{ - 0.03}^{ + 0.10}$, significantly lower than for later-M dwarfs; if instead we also take into account the new candidates, we observe the same general behaviours, but with consistently higher frequencies of low-mass planets. We also present new estimates of the occurrence rates of long-period giant planets and temperate planets inside the habitable zone of early-M dwarfs: in particular we find that the frequency of habitable planets could be as low as η⊕ < 0.23. These results, and their comparison with other surveys focused on different stellar types, confirm the central role that stellar mass plays in the formation and evolution of planetary systems.

Data-driven photocatalytic degradation activity prediction with Gaussian process

Photocatalysis has emerged as a powerful technology with beneficial impacts on the fields of science and engineering. To date, most photocatalysis research are experimentally-based that strongly rely on various experimental conditions. As the coronavirus pandemic hit the world in 2020, research and experiments were disrupted in various scientific disciplines. During these unprecedented times, machine learning plays a vital role in the continuity of photocatalysis research, notably for researchers under physical access restrictions. More specifically, machine learning is capable of predicting the photocatalytic efficiency and analysing the photocatalytic activity. In recent work, it was demonstrated that a Support Vector Regression (SVR) model succeeded in predicting the efficiency of methyl tert-butyl ether (MTBE) photodegradation using titanium dioxide (TiO2) as a photocatalyst, achieving a Root Mean Square Error (RMSE) of 5%. In this work, we investigate the applicability of the Gaussian Process (GP) technique to predict the photodegradation efficiency of contaminants catalyzed by pure and doped-titanium dioxide (TiO2); and we compare their performance with the current state-of-the-art SVR. Within this context, we discuss the foundations of both the machine learning models, as well as demonstrate how photocatalysis researchers can apply them to solving relevant problems in the field of photocatalysis.

Directed Energy Deposition via Artificial Intelligence‐Enabled Approaches

Additive manufacturing (AM) has been gaining pace, replacing traditional manufacturing methods. Moreover, artificial intelligence and machine learning implementation has increased for further applications and advancements. This review extensively follows all the research work and the contemporary signs of progress in the directed energy deposition (DED) process. All types of DED systems, feed materials, energy sources, and shielding gases used in this process are also analyzed in detail. Implementing artificial intelligence (AI) in the DED process to make the process less human‐dependent and control the complicated aspects has been rigorously reviewed. Various AI techniques like neural networks, gradient boosted decision trees, support vector machines, and Gaussian process techniques can achieve the desired aim. These models implemented in the DED process have been trained for high‐precision products and superior quality monitoring.

Constraints on interacting dark energy models through cosmic chronometers and Gaussian process

In this paper, after reconstructing the redshift evolution of the Hubble function by adopting Gaussian process techniques, we estimate the best-fit parameters for some flat Friedmann cosmological models based on a modified Chaplygin gas interacting with dark matter. In fact, the expansion history of the Universe will be investigated because passively evolving galaxies constitute cosmic chronometers. An estimate for the present-day values of the deceleration parameter, adiabatic speed of sound within the dark energy fluid, effective dark energy, and dark matter equation of state parameters is provided. By this, we mean that the interaction term between the two dark fluids, which breaks the Bianchi symmetries, will be interpreted as an effective contribution to the dark matter pressure similarly to the framework of the “Generalized Dark Matter”. We investigate whether the estimates of the Hubble constant and of the present-day abundance of dark matter are sensitive to the dark matter–dark energy coupling. We will also show that the cosmic chronometers data favor a cold dark matter, and that our findings are in agreement with the Le Châtelier–Braun principle according to which dark energy should decay into dark matter.

An inverse model‐based multiobjective estimation of distribution algorithm using Random‐Forest variable importance methods

AbstractMost existing methods of multiobjective estimation of distributed algorithms apply the estimation of distribution of the Pareto‐solution on the decision space during the search and little work has proposed on making a regression‐model for representing the final solution set. Some inverse‐model‐based approaches were reported, such as inversed‐model of multiobjective evolutionary algorithm (IM‐MOEA), where an inverse functional mapping from Pareto‐Front to Pareto‐solution is constructed on nondominated solutions based on Gaussian process and random grouping technique. But some of the effective inverse models, during this process, may be removed. This paper proposes an inversed‐model based on random forest framework. The main idea is to apply the process of random forest variable importance that determines some of the best assignment of decision variables (xn) to objective functions (fm) for constructing Gaussian process in inversed‐models that map all nondominated solutions from the objective space to the decision space. In this work, three approaches have been used: classical permutation, Naïve testing approach, and novel permutation variable importance. The proposed algorithm has been tested on the benchmark test suite for evolutionary algorithms [modified Deb K, Thiele L, Laumanns M, Zitzler E (DTLZ) and Walking Fish Group (WFG)] and indicates that the proposed method is a competitive and promising approach.

Gaussian process model predictive control of unknown non‐linear systems

Model Predictive Control (MPC) of an unknown system that is modelled by Gaussian Process (GP) techniques is studied in this paper. Using GP, the variances computed during the modelling and inference processes allow us to take model uncertainty into account. The main issue in using MPC to control systems modelled by GP is the propagation of such uncertainties within the control horizon. In this paper, two approaches to solve this problem, called GPMPC1 and GPMPC2, are proposed. With GPMPC1, the original Stochastic Model Predictive Control (SMPC) problem is relaxed to a deterministic nonlinear MPC based on a basic linearized GP local model. The resulting optimization problem, though non-convex, can be solved by the Sequential Quadratic Programming (SQP). By incorporating the model variance into the state vector, an extended local model is derived. This model allows us to relax the non-convex MPC problem to a convex one which can be solved by an active-set method efficiently. The performance of both approaches is demonstrated by applying them to two trajectory tracking problems. Results show that both GPMPC1 and GPMPC2 produce effective controls but GPMPC2 is much more efficient computationally.

Polycrystal plasticity modeling of nickel-based superalloy IN 617 subjected to cyclic loading at high temperature

A crystal plasticity finite element (CPFE) model considering isothermal, large deformation and cyclic loading conditions has been formulated and employed to investigate the mechanical response of a nickel-based alloy at high temperature. The investigations focus on fatigue and creep-fatigue hysteresis response of IN 617 subjected to fatigue and creep-fatigue cycles. A new slip resistance evolution equation is proposed to account for cyclic transient features induced by solute drag creep that occur in IN 617 at 950 °C. The crystal plasticity model parameters are calibrated against the experimental fatigue and creep-fatigue data based on an optimization procedure that relies on a surrogate modeling (i.e. Gaussian process) technique to accelerate multi-parameter optimizations. The model predictions are validated against experimental data, which demonstrates the capability of the proposed model in capturing the hysteresis behavior for various hold times and strain ranges in the context of fatigue and creep-fatigue loading.

A Practical Design and Implementation of a Low Cost Platform for Remote Monitoring of Lower Limb Health of Amputees in the Developing World

In many areas of the world accessing professional physicians “when needed/as needed” might not be always possible for a variety of reasons. Therefore, in such cases, a targeted e-Health solution to safeguard patient long-term health could be a meaningful approach. Today’s modern healthcare technologies, often built around electronic and computer-based equipment, require an access to a reliable electricity supply. Many healthcare technologies and products also presume access to the high speed internet is available, making them unsuitable for use in areas where there is no fixed-line internet connectivity, access is slow, unreliable, and expensive, yet where the most benefit to patients may be gained. In this paper, a full mobile sensor platform is presented, based around readily-purchased consumer components, to facilitate a low cost and efficient means of monitoring the health of patients with prosthetic lower limbs. This platform is designed such that it can also be operated in a standalone mode, i.e., in the absence of internet connectivity, thereby making it suitable to the developing world. Also, to counter the challenge of power supply issues in e-Health monitoring, a self-contained rechargeable solution to the platform is proposed and demonstrated. The platform works with an Android mobile device, in order to allow for the capture of data from a wireless sensor unit, and to give the clinician access to results from the sensors. The results from the analysis, carried out within the platform’s Raspberry Pi Zero, are demonstrated to be of use for remote monitoring. This is specifically targeted for monitoring the tissue health of lower limb amputees. The monitoring of residual limb temperature and gait can be a useful indicator of tissue viability in lower limb amputees especially those suffering from diabetes. We describe a route wherein non-invasive monitoring of tissue health is achievable using the Gaussian process technique. This knowledge will be useful in establishing biomarkers related to a possible deterioration in a patient’s health or for assessing the impact of clinical interventions.

Skin Temperature Prediction in Lower Limb Prostheses.

Increased temperature and perspiration within a prosthetic socket is a common complaint of many amputees. The heat dissipation in prosthetic sockets is greatly influenced by the thermal conductive properties of the socket and interface liner materials. These materials influence the body's temperature regulation mechanism and might be the reason for thermal discomfort in prosthetic sockets. Monitoring interface temperature at skin level is notoriously complicated. The problem might be considered notorious because embedding wires and sensors in an elastomer eventually results in elastomer failures because of the high strain induced when donning a liner (amputees roll the liners onto their limbs). Another reason is because placing sensors and wires directly against the skin could cause irritation and chaffing over just a short period of time. We describe a route wherein if the thermal properties of the socket and liner materials are known, the in-socket residual limb temperature could be accurately predicted by monitoring the temperature between socket and liner rather than skin and liner using the Gaussian process technique.