Gaussian Process Regression Research Articles

Cortical thickness deviations as biomarker for subtyping and prognosis in pediatric brainstem tumors

Brainstem tumors exert profound effects on cortical organization and functionality across the whole brain. However, the precise implications of changes in cortical thickness (CTh) for patient stratification and prognostic assessment remain unclear. Our study seeks to address these gaps and provide clearer insights into the distant impact of brainstem tumors. This study involved 124 pediatric patients with brainstem tumors and 849 healthy controls. Using CAT12 segmentation on 3D T1-weighted MRI scans and Gaussian process regression modeling, we established a normative CTh model from healthy data. CTh deviations of patients were quantified and clustered, revealing two distinct subtypes: Subtype 1 with extremely positive deviations and Subtype 2 with extremely negative deviations, correlating with better survival. Kaplan-Meier analysis confirmed significant survival differences between these subtypes. Additionally, a greater number of brain regions with positive CTh deviations was found to correlate with larger tumor volumes. These findings suggest that CTh deviation is a non-invasive imaging marker, facilitating patient subtyping and survival prediction. These insights equip clinicians to tailor treatment plans and establishes a valuable precision medical tool for clinical evaluation and monitoring.

Alignment Optimization of Elastically Supported Submarine Propulsion Shafting Based on Dynamic Bearing Load Influence Numbers

The design scheme of elastically supported submarine propulsion shafting can effectively realize the attenuation of the vibration energy and improve the stealth performance of the whole submarine. However, the elastic deformation generated by the system will affect the alignment state of shafting, thus affecting its safety and reliability. Aiming at this problem, taking a certain elastically supported submarine propulsion shafting as the study object of this paper, the alignment calculation model of the shafting was established and validated, and an equivalent line-surface method was proposed to measure the elastic bearing displacement. On this basis, the concept of the dynamic bearing load influence numbers (BLINs) was elicited, and a response surface method using Gaussian process regression (GPR) was designed to establish the mapping relationship between the elastic displacement and the dynamic BLINs. Taking the equivalent displacements of the bearings as variables, the alignment optimization of the shafting was achieved by combining the genetic algorithm and the response surfaces. After optimization, the load of the rear stern bearing was reduced by 16.67%, and the standard deviation of the bearing loads was reduced by 37.19%. Hence, the alignment state of the shafting was improved. The studied results can provide theoretical and technical support for the analysis and optimization of the alignment characteristics of elastically supported submarine propulsion shafting.

A machine-learning optimized vertical-axis wind turbine

Abstract Vertical-axis wind turbines (VAWTs) have garnered increasing attention in the field of renewable energy due to their unique advantages over traditional horizontal-axis wind turbines (HAWTs). However, traditional VAWTs including Darrieus and Savonius types suffer from significant drawbacks -- negative torque regions exist during rotation. In this work, we propose a new design of VAWT, which combines design principles from both Darrieus and Savonius but addresses their inherent defects. The performance of the proposed VAWT is evaluated through numerical simulations and validated by experimental testing. The results demonstrate that its power output is approximately three times greater than that of traditional Savonius VAWTs of comparable size. The performance of the proposed VAWT is further optimized using machine learning techniques, including Gaussian process regression and neural networks, based on extensive supercomputer simulations. This optimization leads to a 30% increase in power output.

Estimation and validation of solubility of recombinant protein in E. coli strains via various advanced machine learning models

This study presents a comprehensive approach to predicting solubility of recombinant protein in four E. coli samples by employing machine learning techniques and optimization algorithms. Various models, including AdaBoost, Decision Tree Regression (DT), Gaussian Process Regression (GPR), and K-Nearest Neighbors (KNN) are applied to capture the intricate relationships between experimental factors and protein solubility. The integration of these models within an AdaBoost framework, coupled with advanced hyperparameter tuning via the Firefly Algorithm (FA), demonstrates a novel strategy for improving predictive accuracy and model robustness. Key preprocessing techniques such as Histogram-Based Outlier Detection (HBOD) and Z-score normalization are employed to ensure data integrity and consistency. The Firefly Algorithm (FA), utilizing 5-fold cross-validation as the fitness function, adeptly navigates complex hyperparameter spaces, enhancing model performance across diverse data partitions. The AdaBoost with Gaussian Process Regression (ADA-GPR) model established to be superior to alternatives including ADA-DT and ADA-KNN, demonstrating great performance through high R2 test scores and low Mean Squared Error. With a standard deviation of 0.05188 across 5-fold cross-validation, ADA-GPR demonstrated exceptional consistency and robust generalization across diverse data partitions. Using hybrid optimization, this study sheds light on critical variables influencing protein solubility, providing a scalable and effective solution for modeling bioprocesses.

Efficient Adaptive Robust Aerodynamic Design Optimization Considering Uncertain Inflow Variations for a Diffusion Airfoil Across All Operating Incidences

The random fluctuations in inlet flow represent a common uncertainty in aero-engine compressors, necessitating the control of its effects through blade optimization design. To account for the impact of inlet flow fluctuations on performance in blade design optimization, an efficient multi-objective adaptive robust aerodynamic design optimization (ARADO) method is proposed. The optimization method employs a novel sparse polynomial chaos expansion (PCE) and the advanced noisy Gaussian process regression (NGPR) technique is used to establish an initial stochastic surrogate model (SSM) containing statistical moments of aerodynamic performance. By introducing advanced sparse signal processing concepts, the sparce PCE significantly enhances the efficiency of acquiring each training sample for SSM. During the optimization process, the initial SSM autonomously updates based on historical optimization data, without requiring high precision across the entire design space. Compared to traditional model-based aerodynamic robust optimizations, the proposed ARADO method exhibits a faster convergence speed and achieves a superior average level of the optimal solution set. It also better balances various optimization objectives, concentrating the space distribution of optimal solutions closer to the average level. Ultimately, the ARADO is applied to the aerodynamic robust design of a high-load compressor airfoil across all operating incidences. The optimization results enhance aerodynamic performance while reducing performance diversity, thus aligning more closely with practical engineering requirements. Through data analysis of the optimal solutions, robust design guidelines for blade aerodynamic shapes are obtained, along with insights into the flow mechanisms that enhance aerodynamic robustness.

Frequency Regulation Reserve Allocation for Integrated Hydropower Plant and Energy Storage Systems via the Marginal Substitution

With the increasing integration of large-scale renewable energy sources, the coordinated participation of hydropower and energy storage in frequency regulation has become a critical means of ensuring the safe and economical operation of power grids. This paper proposes an optimization method for the allocation of frequency regulation reserves between hydropower and energy storage based on marginal substitution rate (MRS) analysis. First, a frequency response model that captures the synergistic interaction between hydropower and energy storage is established, with the root mean square error (RMSE) of the area control error (ACE) serving as the performance metric for frequency regulation. To reduce simulation computational burdens, key simulation data are obtained via Gaussian process regression (GPR), and a piecewise polynomial fitting method is employed to generate the marginal substitution curve. Experimental results indicate that under the condition of achieving equivalent frequency regulation performance (ACERMSE), 51.60 MW of energy storage reserve can replace 68.38 MW of hydropower reserve, thereby reducing the total regulation capacity reduction of 13.42%. Furthermore, by incorporating the differing cost characteristics of hydropower and energy storage, the optimal configuration is determined, resulting in an overall cost reduction of 17.58%. This method not only ensures system frequency stability but also fully leverages the potential of the available frequency regulation resources.

Artificial intelligence approach for estimating energy density of liquid metal batteries

Achieving a high energy density in liquid metal batteries (LMBs) still remains a big challenge. Due to the multitude of affecting parameters within the system, traditional ways may not fully capture the complexity of LMBs. The artificial intelligence approach can be effectively applied to deal with low energy density issues. Herein, we represented the first implementation of the Gaussian Process Regression to predict the LMBs’ energy density to attain the highest accuracy compared to existing models. Four different kernels, namely Exponential, Matern5/2, Rational Quadratic, and Squared Exponential were utilized to achieve the most accurate GPR model. A huge dataset containing 2158 LMB datapoint was gathered from the literature. It contains 41 input parameters, including alloy-related, LMB-related, and creative features. The GPR-Exponential model showed the greatest battery energy density estimate accuracy among the proposed models. The training and testing R2 values were 0.9976 and 0.9975, respectively, indicating the near-perfect accuracy which makes it the most precise model that has been presented so far. According to sensitivity analysis outcomes, it can be claimed that Sb mole fraction, average ionization energy, and average melting temperature with the respective relevancy factors of 0.6672, 0.6550, and 0.6507 could noticeably affect the LMBs’ energy density. Furthermore, the results showed that the LMBs’ energy density is more sensitive to the electrode-dependent and operational parameters rather than the electrolyte situation.

Error Bounds for Gaussian Process Regression Under Bounded Support Noise with Applications to Safety Certification

Gaussian Process Regression (GPR) is a powerful and elegant method for learning complex functions from noisy data with a wide range of applications, including in safety-critical domains. Such applications have two key features: (i) they require rigorous error quantification, and (ii) the noise is often bounded and non-Gaussian due to, e.g., physical constraints. While error bounds for applying GPR in the presence of non-Gaussian noise exist, they tend to be overly restrictive and conservative in practice. In this paper, we provide novel error bounds for GPR under bounded support noise. Specifically, by relying on concentration inequalities and assuming that the latent function has low complexity in the reproducing kernel Hilbert space (RKHS) corresponding to the GP kernel, we derive both probabilistic and deterministic bounds on the error of the GPR. We show that these errors are substantially tighter than existing state-of-the-art bounds and are particularly well-suited for GPR with neural network kernels, i.e., Deep Kernel Learning (DKL). Furthermore, motivated by applications in safety-critical domains, we illustrate how these bounds can be combined with stochastic barrier functions to successfully quantify the safety probability of an unknown dynamical system from finite data. We validate the efficacy of our approach through several benchmarks and comparisons against existing bounds. The results show that our bounds are consistently smaller, and that DKLs can produce error bounds tighter than sample noise, significantly improving the safety probability of control systems.

Learning from Summarized Data: Gaussian Process Regression with Sample Quasi-Likelihood

Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit from this development. Difficulties still arise when we can only access summarized data consisting of representative features, summary statistics, and data point counts. Such situations frequently occur primarily due to concerns about confidentiality and management costs associated with spatial data. This study tackles learning and inference using only summarized data within the framework of Gaussian process regression. To address this challenge, we analyze the approximation errors in the marginal likelihood and posterior distribution that arise from utilizing representative features. We also introduce the concept of sample quasi-likelihood, which facilitates learning and inference using only summarized data. Non-Gaussian likelihoods satisfying certain assumptions can be captured by specifying a variance function that characterizes a sample quasi-likelihood function. Theoretical and experimental results demonstrate that the approximation performance is influenced by the granularity of summarized data relative to the length scale of covariance functions. Experiments on a real-world dataset highlight the practicality of our method for spatial modeling.

Multiple snapshot RFI localization fusion algorithm based on Gaussian process regression

ABSTRACT Radio frequency interferences (RFIs) in the L-band seriously contaminate remote sensing data from the synthetic aperture interferometric radiometer (SAIR). This may substantially degrade the quality of the data. Accurate localization of the RFI is the key to eliminating or mitigating the effects of the RFI. In previous studies, the localization accuracy was improved by averaging the localization results of the same RFI in multiple snapshots. However, the intensity of the same RFI can vary significantly in different snapshots, leading to varying degrees of localization accuracy across these snapshots. As a result, it poses a challenge for the simple averaging algorithm to attain optimal localization accuracy. In this paper, a multiple snapshot RFI localization fusion algorithm is proposed to further reduce the RFI localization bias. The algorithm obtains the corresponding localization error estimation model using the Gaussian process regression (GPR) model to perform regression learning on the localization error data of the RFI in different directions. The model is then used to estimate the localization error in different directions of the RFIs in each snapshot, and the weights are assigned based on this criterion. Finally, the accurate location of the RFI is obtained through weighted fusion. The results of numerical simulation verify the superiority of this method over the simple averaging algorithm. In addition, experiments based on SMOS data validate the reasonableness and practicality of the method presented in this paper.

State of Health Estimation for Lithium-Ion Batteries Using Electrochemical Impedance Spectroscopy and a Multi-Scale Kernel Extreme Learning Machine

An accurate state of health (SOH) estimation for lithium-ion batteries (LIBs) is crucial for reliable operations and extending service life. While electrochemical impedance spectroscopy (EIS) effectively characterizes LIBs degradation patterns, the high dimensionality of EIS data poses challenges for an efficient analysis. This study proposes a novel method that combines EIS with an equivalent circuit model (ECM) and distribution of relaxation time (DRT) analysis to extract low-dimensional health features from high-dimensional EIS data. A multi-scale kernel extreme learning machine (MS-KELM), optimized by the Sparrow Search Algorithm (SSA), estimates battery SOH with an average mean absolute error (MAE) of 1.37% and a root mean square error (RMSE) of 1.76%. In addition, compared with support vector regression (SVR) and Gaussian process regression (GPR), the proposed method reduces computational time by factors of 4 to 30 and lowers memory usage by approximately 18%.

SapFlower: an automated tool for sap flow data preprocessing, gap-filling, and analysis using deep learning.

Sap flow, a critical process in plant water use and ecosystem water cycles, is often measured using thermal dissipation probes (TDP) due to their ease of installation and continuous data collection. However, sap flow data frequently include noise, outliers, and gaps, creating challenges for analysis and requiring substantial manual processing. We developed SapFlower, a tool that automates data preprocessing, model training, gap-filling, sapwood area scaling and modeling, and water use analysis. It integrates autocleaning, machine learning and deep learning models (e.g. random forest, Gaussian process regression, long short-term memory (LSTM), bidirectional LSTM (BiLSTM)), and efficient workflows to process sap flow data. SapFlower can remove over 90% of noisy data while preserving legitimate variations and achieve high accuracy in gap-filling based on user-determined parameters. Random forest, LSTM, and BiLSTM models reduced root mean square error to 10% or less for long-term gaps. Model training and prediction can be performed efficiently within seconds. SapFlower significantly enhances the efficiency and accessibility of TDP data analysis by automating complex tasks, enabling researchers without programming expertise to employ advanced techniques. Future improvements will focus on species-specific corrections for TDP and support for additional measurement methods. SapFlower is openly available on GitHub (https://github.com/JiaxinWang123/SapFlower) and Zenodo (doi: 10.5281/zenodo.13665919).

Putting an End to the Handcuffs of the Periodic Table: Using Atomic Features for Predicting Detonation Velocity

ABSTRACTIn this study, a Gaussian process regressor is used to predict the detonation velocity. As features atomic values were used, which allows the application of the model to explosives of any elemental compositions. This approach does not require reparameterization for every element and can provide useful estimations for the detonation velocity of explosives. For initial validation purposes, this study will interpolate from materials containing elements from the first and second periods to explosives‐containing materials in the third period.

Early Prediction of Battery Lifetime Using Centered Isotonic Regression with Quantile-Transformed Features

The rapid development of lithium-ion (Li-ion) batteries has raised requirements for cycle life prediction to ensure safety and reliability. However, the intricate and nonlinear behavior of the battery degradation process poses significant challenges in accurately predicting its cycle life at an early stage. This work addresses the battery lifetime prediction problem by leveraging machine learning (ML) methods. First, we apply quantile transformation (QT) to both features and battery cycle lives to improve their correlation. Next, we adopt a centered isotonic regression (CIR) method in our work, a variant of isotonic regression (IR) that centers the feature values and then reduces overfitting to improve model performance. Finally, we perform convex regression (CR) to capture specific patterns in the battery dataset where monotonicity is absent and achieve an overall prediction for battery cycle lives. To validate our proposed method, we have done a comprehensive comparison among several different benchmarks, including elastic net, gradient boosting regression tree, decision tree, support vector machine, random forest, and Gaussian process regression. In contrast to existing methods, our CIR model has shown the best performance, with an average percentage error of 9.8% and a root mean square error of 149 cycles. These experiment results demonstrate the capability and potential of our proposed CIR model in the problem of battery lifetime prediction.

Decomposed Gaussian Processes for Efficient Regression Models with Low Complexity

In this paper, we address the challenges of inferring and learning from a substantial number of observations (N≫1) with a Gaussian process regression model. First, we propose a flexible construction of well-adapted covariances originally derived from specific differential operators. Second, we prove its convergence and show its low computational cost scaling as O(Nm2) for inference and O(m3) for learning instead of O(N3) for a canonical Gaussian process where N≫m. Moreover, we develop an implementation that requires less memory O(m2) instead of O(N2). Finally, we demonstrate the effectiveness of the proposed method with simulation studies and experiments on real data. In addition, we conduct a comparative study with the aim of situating it in relation to certain cutting-edge methods.

Forecasting Residential Real Estate Prices via Machine Learning for Taizhou City of Zhejiang Province in China

The Chinese real estate market has grown at such a fast rate over the last several decades, up to the present decline patterns that began at the end of 2021. As a result, projecting future property prices has become more challenging for investors and the government. This is a result of the state of the economy right now. In this work, we examine monthly residential property prices for Taizhou City, Zhejiang Province, China, using Gaussian process regressions with a variety of kernels and basis functions, spanning from April 2015 to the July 2024. Our forecasting activities employ estimated models, which we train using a combination of cross-validation and Bayesian optimisations for endowing the constructed model with good flexibility. The models that were created were successful in precisely predicting the prices from September 2022 to July 2024 outside the sample. These models had a relative root mean square error of 0.1120%, a root mean square error of 19.1482, a mean absolute error of 14.3875, and a correlation coefficient of 99.986%. It is plausible that our findings may be used alone or in combination with further projections to formulate conjectures about fluctuations in the residential real estate prices and conduct additional policy analysis, which will help investors and policymakers in better understanding the evolving market condition.

Integrative Assessment of Surface Water Contamination Using GIS, WQI, and Machine Learning in Urban–Industrial Confluence Zones Surrounding the National Capital Territory of the Republic of India

This study proposes an innovative framework integrating geographic information systems (GISs), water quality index (WQI) analysis, and advanced machine learning (ML) models to evaluate the prevalence and impact of organic and inorganic pollutants across the urban–industrial confluence zones (UICZ) surrounding the National Capital Territory (NCT) of India. Surface water samples (n = 118) were systematically collected from the Gautam Buddha Nagar, Ghaziabad, Faridabad, Sonipat, Gurugram, Jhajjar, and Baghpat districts to assess physical, chemical, and microbiological parameters. The application of spatial interpolation techniques, such as kriging and inverse distance weighting (IDW), enhances WQI estimation in unmonitored areas, improving regional water quality assessments and remediation planning. GIS mapping highlighted stark spatial disparities, with industrial hubs, like Faridabad and Gurugram, exhibiting WQI values exceeding 600 due to untreated industrial discharges and wastewater, while rural regions, such as Jhajjar and Baghpat, recorded values below 200, reflecting minimal anthropogenic pressures. The study employed four ML models—linear regression (LR), random forest (RF), Gaussian process regression (GPR), and support vector machines (SVM)—to predict WQI with high precision. SVM_Poly emerged as the most effective model, achieving testing CC, RMSE, and MAE values of 0.9997, 11.4158, and 5.6085, respectively, outperforming RF (0.9925, 29.8107, 21.7398) and GPR_PUK (0.9811, 68.4466, 54.0376). By leveraging machine learning models, this study enhances WQI prediction beyond conventional computation, enabling spatial extrapolation and early contamination detection in data-scarce regions. Sensitivity analysis identified total suspended solids as the most critical predictor influencing WQI, underscoring its relevance in monitoring programs. This research uniquely integrates ML algorithms with spatial analytics, providing a novel methodological contribution to water quality assessment. The findings emphasize the urgency of mitigating the fate and transport of organic and inorganic pollutants to protect Delhi’s hydrological ecosystems, presenting a robust decision-support system for policymakers and environmental managers.

Forecasts of wholesale soybean oil price indices via Gaussian process regressions

Forecasts of wholesale soybean oil price indices via Gaussian process regressions

Inverse Design of Compressor/fan Blade Profiles Based on Conditional Invertible Neural Networks

Abstract Compressors/fans are crucial in modern aircraft engines, providing power, thrust, and combustion efficiency. Blade profile design is a crucial aspect of their design, often involving multiple constraints. Current design methods heavily rely on the expertise of designers, and typically require many iterations. This paper proposes a blade profile inverse design approach based on a conditional Invertible Neural Networks (cINN) to address the limitations of the traditional methods. It can enable the direct generation of blade profiles that satisfy specified requirements, including aerodynamic performance and additional relevant constraints. This method encompasses two primary steps: forward process modeling and inverse process modeling. In the forward process, a surrogate model is established to map design parameters to blade profile performance metrics. Within a specified design space, a predetermined number of designs are sampled, and a dataset is produced through performing high-fidelity Computational Fluid Dynamics (CFD) analyses to obtain aerodynamic performance and other interested metrics. Subsequently, the dataset, after data preprocessing, is employed to train a Gaussian Process Regression (GPR) model to replace costly CFD analyses. In the inverse modeling step, based on the substantial data generated by the trained GPR model, a cINN is trained, mapping design parameters to a latent space under the specified target conditions. This renders the learning of the inverse process feasible. Upon the completion of model training, the design parameters and blade geometry that meet the desired target could be directly derived. The proposed method is demonstrated using a subsonic blade profile inverse design case study.

GAPF-DFT: A graph-based alchemical perturbation density functional theory for catalytic high-entropy alloys

High-entropy alloys (HEAs) exhibit exceptional catalytic performance due to their complex surface structures. However, the vast number of active binding sites in HEAs, as opposed to conventional alloys, presents a significant computational challenge in catalytic applications. To tackle this challenge, robust methods must be developed to efficiently explore the configurational space of HEA catalysts. Here, we introduce a novel approach that combines alchemical perturbation density functional theory (APDFT) with a graph-based correction scheme to explore the binding energy landscape of HEAs. Our results demonstrate that APDFT can accurately predict binding energies for isoelectronic permutations in HEAs at minimal computational cost, significantly accelerating configurational space sampling. However, APDFT errors increase substantially when permutations occur near binding sites. To address this issue, we developed a graph-based Gaussian process regression model to correct discrepancies between APDFT and conventional density functional theory values. Our approach enables the prediction of binding energies for hundreds of thousands of configurations with a mean average error of 30 meV, requiring a handful of ab initio simulations.