Gaussian Process Research Articles

Gaussian processes modeling for the prediction of polymeric nanoparticle formulation design to enhance encapsulation efficiency and therapeutic efficacy.

Conventional drugs have been facing various drug delivery obstacles, including first-pass metabolism for oral medications, drug degradation by cellular enzymes, off-target effects, and cytotoxicity of healthy cells. Nanoparticles (NP) application in drug delivery can compensate for these drawbacks to a great extent. NPs can be fabricated using different materials and structures to achieve desired therapeutic effects. For each type of NP material, its physicochemical properties determine compatibility with specific drugs and other supplemental compositions. The optimized material selection becomes prominent in NP development to improve NP performances. Due to the nature of NP fabrication, the process is long and expensive. To accelerate NP composition optimization, machine learning (ML) techniques are among the most promising methods for efficient data predictions and optimizations.As a proof-of concept, we created Gaussian Process (GP) models to make predictions for drug encapsulation efficiency (EE%) and therapeutic efficacy of 32 poly (lactic-co-glycolic acid) (PLGA) NPs that are formed with materials with different physicochemical properties. Two model drugs, doxorubicin (DOX) and docetaxel (DTX) were loaded separately. The IC50 values for the various NPs formulations were evaluated using the OVCAR3 epithelial ovarian cancer cell line. EE% GP model has the highest prediction accuracy with the lowest normalized root-mean-squared-error (RMSE) of 0.187. The DOX and DTX IC50 GP models have normalized RMSEs of 0.296 and 0.206, respectively, which are higher than that of the EE% GP model.

Bayesian Optimization for Efficient Prediction of Gas Uptake in Nanoporous Materials.

The discovery and optimization of novel nanoporous materials (NPMs) such as Metal-Organic Frameworks (MOFs) are crucial for addressing global challenges. Traditional experimental approaches for optimizing these materials are time-consuming and resource-intensive. This research paper presents a strategy using Bayesian optimization (BO) to efficiently navigate the NPMs for gas storage. For a MOF dataset drawn from 19 different sources, we present a quantitative evaluation of BO. In our study, we employed machine learning (ML) techniques to conduct regression analysis on many models. Following this, we identified the three ML models that exhibited the highest accuracy, which were subsequently chosen as surrogates in our investigation, includingthe conventional Gaussian Process (GP) model. We found that GP with expected improvement (EI) as the acquisition function but without a gamma prior which is standard in Bayesian Optimization python library outperforms other surrogate models. Additionally, it should be noted that while the machine learning model that exhibits superior performance in predicting the target variable may be considered the best choice, it may not necessarily serve as the most suitable surrogate model for BO. This observation has significant importance and warrants further investigation. This comprehensive framework accelerates the pace of materials discovery.

Gasification process modelling and optimization using Gaussian process regression and hybrid population-based algorithms

Gasification process modelling and optimization using Gaussian process regression and hybrid population-based algorithms

Fast calculation of Gaussian process multiple-fold cross-validation residuals and their covariances

Fast calculation of Gaussian process multiple-fold cross-validation residuals and their covariances

Crowdsourcing with the drift diffusion model of decision making.

Crowdsourcing involves the use of annotated labels with unknown reliability to estimate ground truth labels in datasets. A common task in crowdsourcing involves estimating reliabilities of annotators (such as through the sensitivities and specificities of annotators in the binary label setting). In the literature, beta or dirichlet distributions are typically imposed as priors on annotator reliability. In this study, we investigated the use of a neuroscientifically validated model of decision making, known as the drift-diffusion model, as a prior on the annotator labeling process. Two experiments were conducted on synthetically generated data with non-linear (sinusoidal) decision boundaries. Variational inference was used to predict ground truth labels and annotator related parameters. Our method performed similarly to a state-of-the-art technique (SVGPCR) in prediction of crowdsourced data labels and prediction through a crowdsourced-generated Gaussian process classifier. By relying on a neuroscientifically validated model of decision making to model annotator behavior, our technique opens the avenue of predicting neuroscientific biomarkers of annotators, expanding the scope of what may be learnt about annotators in crowdsourcing tasks.

A unifying representation of path integrals for fractional Brownian motions

Fractional Brownian motion (fBm) is an experimentally-relevant, non-Markovian Gaussian stochastic process with long-ranged correlations between the increments, parametrised by the so-called Hurst exponent H; depending on its value the process can be sub-diffusive (0<H<1/2) , diffusive (H=1/2) or super-diffusive (1/2<H<1) . There exist three alternative equally often used definitions of fBm—due to Lévy and due to Mandelbrot and van Ness (MvN), which differ by the interval on which the time variable is formally defined. Respectively, the covariance functions of these fBms have different functional forms. Moreover, the MvN fBms have stationary increments, while for the Lévy fBm this is not the case. One may therefore be tempted to conclude that these are, in fact, different processes which only accidentally bear the same name. Recently determined explicit path integral representations also appear to have very different functional forms, which only reinforces the latter conclusion. Here we develop a unifying equivalent path integral representation of all three fBms in terms of Riemann–Liouville fractional integrals, which links the fBms and proves that they indeed belong to the same family. We show that the action in such a representation involves the fractional integral of the same form and order (dependent on whether H<1/2 or H>1/2 ) for all three cases, and differs only by the integration limits.

Task-oriented machine learning surrogates for tipping points of agent-based models

We present a machine learning framework bridging manifold learning, neural networks, Gaussian processes, and Equation-Free multiscale approach, for the construction of different types of effective reduced order models from detailed agent-based simulators and the systematic multiscale numerical analysis of their emergent dynamics. The specific tasks of interest here include the detection of tipping points, and the uncertainty quantification of rare events near them. Our illustrative examples are an event-driven, stochastic financial market model describing the mimetic behavior of traders, and a compartmental stochastic epidemic model on an Erdös-Rényi network. We contrast the pros and cons of the different types of surrogate models and the effort involved in learning them. Importantly, the proposed framework reveals that, around the tipping points, the emergent dynamics of both benchmark examples can be effectively described by a one-dimensional stochastic differential equation, thus revealing the intrinsic dimensionality of the normal form of the specific type of the tipping point. This allows a significant reduction in the computational cost of the tasks of interest.

Improving Wheat Leaf Nitrogen Concentration (LNC) Estimation across Multiple Growth Stages Using Feature Combination Indices (FCIs) from UAV Multispectral Imagery

Leaf nitrogen concentration (LNC) is a primary indicator of crop nitrogen status, closely related to the growth and development dynamics of crops. Accurate and efficient monitoring of LNC is significant for precision field crop management and enhancing crop productivity. However, the biochemical properties and canopy structure of wheat change across different growth stages, leading to variations in spectral responses that significantly impact the estimation of wheat LNC. This study aims to investigate the construction of feature combination indices (FCIs) sensitive to LNC across multiple wheat growth stages, using remote sensing data to develop an LNC estimation model that is suitable for multiple growth stages. The research employs UAV multispectral remote sensing technology to acquire canopy imagery of wheat during the early (Jointing stage and Booting stage) and late (Early filling and Late filling stages) in 2021 and 2022, extracting spectral band reflectance and texture metrics. Initially, twelve sensitive spectral feature combination indices (SFCIs) were constructed using spectral band information. Subsequently, sensitive texture feature combination indices (TFCIs) were created using texture metrics as an alternative to spectral bands. Machine learning algorithms, including partial least squares regression (PLSR), random forest regression (RFR), support vector regression (SVR), and Gaussian process regression (GPR), were used to integrate spectral and texture information, enhancing the estimation performance of wheat LNC across growth stages. Results show that the combination of Red, Red edge, and Near-infrared bands, along with texture metrics such as Mean, Correlation, Contrast, and Dissimilarity, has significant potential for LNC estimation. The constructed SFCIs and TFCIs both enhanced the responsiveness to LNC across multiple growth stages. Additionally, a sensitive index, the Modified Vegetation Index (MVI), demonstrated significant improvement over NDVI, correcting the over-saturation concerns of NDVI in time-series analysis and displaying outstanding potential for LNC estimation. Spectral information outperforms texture information in estimation capability, and their integration, particularly with SVR, achieves the highest precision (coefficient of determination (R2) = 0.786, root mean square error (RMSE) = 0.589%, and relative prediction deviation (RPD) = 2.162). In conclusion, the sensitive FCIs developed in this study improve LNC estimation performance across multiple growth stages, enabling precise monitoring of wheat LNC. This research provides insights and technical support for the construction of sensitive indices and the precise management of nitrogen nutrition status in field crops.

CO2 emission from the electricity sector in Iran; calculation, prediction and reduction policies

Fossil fuel power plants produce a significant amount of CO2 emissions, and this pollutant causes global warming, respiratory and heart diseases, and other significant issues. Electricity interprets as a primary and rising demand in each energy system; thus, in this paper, carbon dioxide (CO2) emission reduction was selected as the objective value for 2025. Power plant fuel consumption was surveyed to calculate the CO2 emission caused by each fuel. Also, Esfahan province (an industrial province in Iran) was investigated as the study case. Forecasting the fuel consumption for 2025 was run by two parameters: population and Gross Domestic Production (GDP), which were forecasted by the report of the Iran Statics Center and the Gaussian Process Regression (GPR) method, respectively. The CO2 emission of power plants was obtained using the coefficients of each fuel. Based on Iran's commitment to the Paris Agreement, a 4% reduction of CO2 emissions is the main objective. Thus, this study aims to reach this goal by implementing four scenarios: a) adding renewable energies, b) adding renewable energies and improving the generation efficiency, c) adding renewable energies and decreasing the grid losses, and d) combining the three scenarios mentioned above. According to these scenarios, reformation strategies compensated 10.5% of the required power, which was satisfied by renewable energies, and finally, this province can gradually satisfy a 4% reduction until 2025.

Prediction of mechanical properties of LPBF built part based on process monitoring and Gaussian process regression

As a highly promising technology in additive manufacturing, the laser powder bed fusion has only limited application due to its low reproducibility. In this study, the image information of the 316L specimen after laser scanning and powder paving of each layer was acquired by a complementary metal–oxide–semiconductor industrial camera. The important features were selected, extracted and quantificated by analyzing the tensile test results. Finally, combined with the laser power, the quantified features were as input of a Gaussian process regression model based on optimization algorithm of grid search to predict the tensile strength of 316L specimen. The results show that the quantized image features have a significant improvement on the regression effect, and the coefficient of determination (R 2) is improved from 63% to 90.57% compared to using only the laser power as input.

Short-term traffic flow prediction in heterogeneous traffic conditions using Gaussian process regression

Short-term traffic flow prediction in heterogeneous traffic conditions using Gaussian process regression

Gaussian process regression for three-dimensional soil mapping over multiple spatial supports

This study investigates the complexity of spatial soil modelling, particularly focusing on the challenge of variable vertical support in traditional soil data collection. Traditional soil sampling, described in terms of horizons, often fails to accurately pinpoint the specific depths for specific soil properties. This gap is significant, as depth-specific data is crucial for a thorough understanding of soil formation processes and for assessing potential environmental impacts. In digital soil mapping (DSM), the prevalent reliance on standardised depth intervals and mass-preserving spline functions for data resampling results in a modelling approach that tends to disregard depth-related details, thereby introducing potential uncertainties.To address these limitations, this work explores how effectively Gaussian process regression (GPR) can model soil in 3D. This technique comprises two key components: a mean function and a semivariogram-like kernel. Unlike conventional methods that make a single prediction, GPR provides detailed probability distributions. This capability allows for the quantification of prediction uncertainty at various points, offering insights for decision-making and risk assessment purposes. Moreover, GPR has the capability to make volume or block estimates and assess associated uncertainties. Enabling volume-based predictions enriches the range of strategies available for land management.In this research, we employ GPR as a novel 3D soil modelling technique and compare its performance with traditional spline-based methods. The comparison is conducted through a case study on a farm in northern New South Wales, Australia, focusing on the 3D mapping of soil pH and electrical conductivity (EC). Our results demonstrate the ability of GPR to estimate soil properties across various volumes, utilising data from multiple vertical supports, thereby offering a more versatile approach for soil modelling in diverse spatial contexts.

Robust Gaussian Process Regression Method for Efficient Tunneling Pathway Optimization: Application to Surface Processes.

Simulation of surface processes is a key part of computational chemistry that offers atomic-scale insights into mechanisms of heterogeneous catalysis, diffusion dynamics, and quantum tunneling phenomena. The most common theoretical approaches involve optimization of reaction pathways, including semiclassical tunneling pathways (called instantons). The computational effort can be demanding, especially for instanton optimizations with an ab initio electronic structure. Recently, machine learning has been applied to accelerate reaction-pathway optimization, showing great potential for a wide range of applications. However, previous methods still suffer from numerical and efficiency issues and were not designed for condensed-phase reactions. We propose an improved framework based on Gaussian process regression for general transformed coordinates, which has improved efficiency and numerical stability, and we propose a descriptor that combines internal and Cartesian coordinates suitable for modeling surface processes. We demonstrate with 11 instanton optimizations in three representative systems that the improved approach makes ab initio instanton optimization significantly cheaper, such that it becomes not much more expensive than a classical transition-state theory rate calculation.

An improved correction of radial velocity systematics for the SOPHIE spectrograph

High-precision spectrographs can on occasion exhibit temporal variations in their reference velocity or nightly zero point (NZP). One way to monitor the NZP is to measure bright stars, whose intrinsic radial velocity variation is assumed to be much smaller than the instrument precision. The variations of these bright stars, which is primarily assumed to be instrumental, are then smoothed into a reference radial velocity time series (master constant) that is subtracted from the observed targets. While this method is effective in most cases, it does not fully propagate the uncertainty arising from NZP variations. We present a new method for correcting for NZP variations in radial velocity time series. This method uses Gaussian processes based on ancillary information to model these systematic effects. Moreover, it enables us to propagate the uncertainties of this correction into the overall error budget. Another advantage of this approach is that it relies on ancillary data that are collected simultaneously with the spectra and does not solely depend on dedicated observations of constant stars. We applied this method to the SOPHIE spectrograph at the Haute-Provence Observatory using a few instrument housekeeping data, such as the internal pressure and temperature variations. Our results demonstrate that this method effectively models the red noise of constant stars, even with a limited number of housekeeping data, while preserving the signals of exoplanets. Using simulations with mock planets and real data, we found that this method significantly improves the false-alarm probability of detections. It improves the probability by several orders of magnitude. Additionally, by simulating numerous planetary signals, we were able to detect up to 10 $&lt;!PCT!&gt;$ more planets with small-amplitude radial velocity signals. We used this new correction to reanalyse the planetary system around HD158259 and to improve the detection of the outermost planets. We propose this technique as a complementary approach to the classical master-constant correction of the instrumental red noise. We also suggest to decrease the observing cadence of the constant stars to optimise the telescope time for scientific targets.

Cox processes driven by transformed Gaussian processes on linear networks—A review and new contributions

Cox processes driven by transformed Gaussian processes on linear networks—A review and new contributions

Effect of Human Head Shape on the Risk of Traumatic Brain Injury: A Gaussian Process Regression-based Machine Learning Approach.

Computational head injury models are promising tools for understanding and predicting traumatic brain injuries. However, most available head injury models are "average" models that employ a single set of head geometry (e.g., 50th-percentile U.S. male) without considering variability in these parameters across the human population. A significant variability of head shapes exists in U.S. Army soldiers, evident from the Anthropometric Survey of U.S. Army Personnel (ANSUR II). The objective of this study is to elucidate the effects of head shape on the predicted risk of traumatic brain injury from computational head injury models. Magnetic resonance imaging scans of 25 human subjects are collected. These images are registered to the standard MNI152 brain atlas, and the resulting transformation matrix components (called head shape parameters) are used to quantify head shapes of the subjects. A generative machine learning model is used to generate 25 additional head shape parameter datasets to augment our database. Head injury models are developed for these head shapes, and a rapid injurious head rotation event is simulated to obtain several brain injury predictor variables (BIPVs): Peak cumulative maximum principal strain (CMPS), average CMPS, and the volume fraction of brain exceeding an injurious CMPS threshold. A Gaussian process regression model is trained between head shape parameters and BIPVs, which is then used to study the relative sensitivity of the various BIPVs on individual head shape parameters. We distinguish head shape parameters into 2 types: Scaling components ${T_{xx}}$, ${T_{yy}}$, and ${T_{zz}}$ that capture the breadth, length, and height of the head, respectively, and shearing components (${T_{xy}},{T_{xz}},{T_{yx}},{T_{yz}},{T_{zx}}$, and ${T_{zy}}$) that capture the relative skewness of the head shape. An overall positive correlation is evident between scaling components and BIPVs. Notably, a very high, positive correlation is seen between the BIPVs and the head volume. As an example, a 57% increase in peak CMPS was noted between the smallest and the largest investigated head volume parameters. The variation in shearing components ${T_{xy}},{T_{xz}},{T_{yx}},{T_{yz}},{T_{zx}}$, and ${T_{zy}}$ on average does not cause notable changes in the BIPVs. From the Gaussian process regression model, all 3 BIPVs showed an increasing trend with each of the 3 scaling components, but the BIPVs are found to be most sensitive to the height dimension of the head. From the Sobol sensitivity analysis, the ${T_{zz}}$ scaling parameter contributes nearly 60% to the total variance in peak and average CMPS; ${T_{yy}}$ contributes approximately 20%, whereas ${T_{xx}}$ contributes less than 5%. The remaining contribution is from the 6 shearing components. Unlike peak and average CMPS, the VF-CMPS BIPV is associated with relatively evenly distributed Sobol indices across the 3 scaling parameters. Furthermore, the contribution of shearing components on the total variance in this case is negligible. Head shape has a considerable influence on the injury predictions of computational head injury models. Available "average" head injury models based on a 50th-percentile U.S. male are likely associated with considerable uncertainty. In general, larger head sizes correspond to greater BIPV magnitudes, which point to potentially a greater injury risk under rapid neck rotation for people with larger heads.

Prediction and optimisation of gasoline quality in petroleum refining: The use of machine learning model as a surrogate in optimisation framework

Prediction and optimisation of gasoline quality in petroleum refining: The use of machine learning model as a surrogate in optimisation framework

Transfer-Learning-Enhanced Regression Generative Adversarial Networks for Optimal eVTOL Takeoff Trajectory Prediction

Electric vertical takeoff and landing (eVTOL) aircraft represent a crucial aviation technology to transform future transportation systems. The unique characteristics of eVTOL aircraft include reduced noise, low pollutant emission, efficient operating cost, and flexible maneuverability, which in the meantime pose critical challenges to advanced power retention techniques. Thus, optimal takeoff trajectory design is essential due to immense power demands during eVTOL takeoffs. Conventional design optimizations, however, adopt high-fidelity simulation models in an iterative manner resulting in a computationally intensive mechanism. In this work, we implement a surrogate-enabled inverse mapping optimization architecture, i.e., directly predicting optimal designs from design requirements (including flight conditions and design constraints). A trained inverse mapping surrogate performs real-time optimal eVTOL takeoff trajectory predictions with no need for running optimizations; however, one training sample requires one design optimization in this inverse mapping setup. The excessive training cost of inverse mapping and the characteristics of optimal eVTOL takeoff trajectories necessitate the development of the regression generative adversarial network (regGAN) surrogate. We propose to further enhance regGAN predictive performance through the transfer learning (TL) technique, creating a scheme termed regGAN-TL. In particular, the proposed regGAN-TL scheme leverages the generative adversarial network (GAN) architecture consisting of a generator network and a discriminator network, with a combined loss of the mean squared error (MSE) and binary cross-entropy (BC) losses, for regression tasks. In this work, the generator employs design requirements as input and produces optimal takeoff trajectory profiles, while the discriminator differentiates the generated profiles and real optimal profiles in the training set. The combined loss facilitates the generator training in the dual aspects: the MSE loss targets minimum differences between generated profiles and training counterparts, while the BC loss drives the generated profiles to share analogous patterns with the training set. We demonstrated the utility of regGAN-TL on optimal takeoff trajectory designs for the Airbus A3 Vahana and compared its performance against representative surrogates, including the multi-output Gaussian process, the conditional GAN, and the vanilla regGAN. Results showed that regGAN-TL reached the 99.5% generalization accuracy threshold with only 200 training samples while the best reference surrogate required 400 samples. The 50% reduction in training expense and reduced standard deviations of generalization accuracy achieved by regGAN-TL confirmed its outstanding predictive performance and broad engineering application potential.

A solution to the ill‐conditioning of gradient‐enhanced covariance matrices for Gaussian processes

A solution to the ill‐conditioning of gradient‐enhanced covariance matrices for Gaussian processes

Combining spectrum, thermal, and texture features using machine learning algorithms for wheat nitrogen nutrient index estimation and model transferability analysis

The nitrogen nutrition index (NNI) has been extensively applied for the diagnosis of crop nitrogen status, providing insights into efficient nitrogen utilization and plant growth. In this study, we utilized a low-altitude unmanned aerial vehicle (UAV) platform, equipped with multispectral (MS), red–green–blue (RGB), and thermal infrared (TIR) cameras, to comprehensively capture wheat spectral information. The analysis of the relationship between NNI and relative yield revealed an initially linear relationship, which saturated for high NNI values. To enhance accuracy and minimize complexity, we employed a random forest (RF) – recursive feature elimination (RFE) method to select features as inputs for four machine learning (ML) models: back propagation neural network (BPNN), extreme learning machine (ELM), support vector regression (SVR), and Gaussian process regression (GPR). After feature selection, the prediction accuracies of single-sensor models were ranked as: MS > RGB > TIR. The R2 values for the four ML models were in the range of 0.54–0.75. Among multi-sensor combinations, the GPR with MS + RGB + TIR input features achieved the best results with R2 = 0.89 and RPD = 2.52. Further, the dataset was partitioned into six subsets based on location and cultivar variety to evaluate model transferability. The results showed that the transferability largely suffered during the bivariate conditions of different varieties at different locations; the transferability of the model was average improved by 11 % when GPR was combined with transfer component analysis (TCA). The accuracy and transferability of the NNI estimation models significantly improved, offering valuable guidance and methodological support for diagnosing the nitrogen nutrient status of wheat.