Gaussian Process Research Articles

Accelerated, physics-inspired inference of skeletal muscle microstructure from diffusion-weighted MRI.

Muscle health is a critical component of overall health and quality of life. However, current measures of skeletal muscle health take limited account of microstructural variations within muscle, which play a crucial role in mediating muscle function. To address this, we present a physics-inspired, machine learning-based framework for the non-invasive estimation of microstructural organization in skeletal muscle from diffusion-weighted MRI (dMRI) in an uncertainty-aware manner. To reduce the computational expense associated with direct numerical simulations of dMRI physics, a polynomial meta-model is developed that accurately represents the input/output relationships of a high-fidelity numerical model. This meta-model is used to develop a Gaussian process (GP) model that provides voxel-wise estimates and confidence intervals of microstructure organization in skeletal muscle. Given noise-free data, the GP model accurately estimates microstructural parameters. In the presence of noise, the diameter, intracellular diffusion coefficient, and membrane permeability are accurately estimated with narrow confidence intervals, while volume fraction and extracellular diffusion coefficient are poorly estimated and exhibit wide confidence intervals. A reduced-acquisition GP model, consisting of one-third the diffusion-encoding measurements, is shown to predict parameters with similar accuracy to the original model. The fiber diameter and volume fraction estimated by the reduced GP model is validated via histology, with both parameters accurately estimated, demonstrating the capability of the proposed framework as a promising non-invasive tool for assessing skeletal muscle health and function.

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.

Two Bayesian approaches of monitoring mean of Gaussian process using Bayes factor

AbstractThis paper develops two novel process monitoring schemes for the mean of a Gaussian process: the Bayes factor (BF) and the improved Bayes factor (IBF) schemes. Conjugate priors are used to construct the plotting statistics. The performance of the proposed schemes is evaluated in terms of average run length (ARL), standard deviation of run length (SDRL), and several percentiles, and these performance metrics across different hyper‐parameters and various sample sizes are evaluated via Monte Carlo simulations. Both zero‐state and steady‐state out‐of‐control (OOC) performances are investigated comprehensively. The simulation results show that the IBF scheme outperforms the existing Bayesian exponentially weighted moving average (EWMA) schemes under different loss functions in zero‐state. In steady‐state conditions, the IBF scheme outperforms for small shifts. Finally, we present two examples to illustrate the practical application of the proposed schemes.

Global ranking of the sensitivity of interaction potential contributions within classical molecular dynamics force fields

Uncertainty quantification (UQ) is rapidly becoming a sine qua non for all forms of computational science out of which actionable outcomes are anticipated. Much of the microscopic world of atoms and molecules has remained immune to these developments but due to the fundamental problems of reproducibility and reliability, it is essential that practitioners pay attention to the issues concerned. Here a UQ study is undertaken of classical molecular dynamics with a particular focus on uncertainties in the high-dimensional force-field parameters, which affect key quantities of interest, including material properties and binding free energy predictions in drug discovery and personalized medicine. Using scalable UQ methods based on active subspaces that invoke machine learning and Gaussian processes, the sensitivity of the input parameters is ranked. Our analyses reveal that the prediction uncertainty is dominated by a small number of the hundreds of interaction potential parameters within the force fields employed. This ranking highlights what forms of interaction control the prediction uncertainty and enables systematic improvements to be made in future optimizations of such parameters.

A unifying representation of path integrals for fractional Brownian motions

Abstract 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 develope 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.

Design of high-performance entangling logic in silicon quantum dot systems with Bayesian optimization

Device engineering based on computer-aided simulations is essential to make silicon (Si) quantum bits (qubits) be competitive to commercial platforms based on superconductors and trapped ions. Combining device simulations with the Bayesian optimization (BO), here we propose a systematic design approach that is quite useful to procure fast and precise entangling operations of qubits encoded to electron spins in electrode-driven Si quantum dot (QD) systems. For a target problem of the controlled-X (CNOT) logic operation, we employ BO with the Gaussian process regression to evolve design factors of a Si double QD system to the ones that are optimal in terms of speed and fidelity of a CNOT logic driven by a single microwave pulse. The design framework not only clearly contributes to cost-efficient securing of solutions that enhance performance of the target quantum operation, but can be extended to implement more complicated logics with Si QD structures in experimentally unprecedented ways.

Serial monitoring of the audiogram in hearing conservation using Gaussian processes

Most hearing conservation programs repeatedly monitor a subject's pure tone thresholds before, during, and after exposure to audiopathic agents. Changes to the audiogram that meet significant shift criteria such as ASHA, CTCAE, and so forth are considered evidence of audiopathic injury. Despite a wide variety of definitions for significant change, all current serial monitoring methods are biased due to regression to the mean and are prone to inconclusive results. These problems diminish the diagnostic accuracy and utility of serial monitoring. Here we propose adopting Gaussian processes to address these issues in a manner that maximizes time efficiency and can be administered using portable equipment at the point of care.

Multiobjective optimization of carbon fiber–reinforced epoxy composite properties using nonparametric modeling

Carbon fiber–reinforced epoxy composites are widely used in the marine and aviation sectors due to their superior mechanical properties. As research into these materials progresses, the demand for materials with even more complex and superior properties has increased. Traditional trial-and-error methods are limited to optimizing single factors and are plagued by heavy workloads and prohibitive costs when applied to multifactor composite designs. Addressing these problems, this study introduces a nonparametric multiobjective optimization process for composite materials. This approach employs a Gaussian process (GP) to establish a multiobjective regression model and uses nondominated sorting genetic algorithm II (NSGA II) to determine the Pareto front. Pareto solutions were ranked in accordance with their similarity to ideal solutions and on the basis of predetermined preference weights. The results demonstrate variations in optimal outcomes contingent on the weight values assigned. The differences between the optimized results and experimental validations reached 12.9%, with the minimum deviation being 0.6%. The effectiveness of the proposed method was demonstrated. The strategy combines GP and NSGA II to extend design methods for small samples and materials with multiple attributes. This method enables the simultaneous optimization of multiple conflicting objectives, offering greater efficiency than addressing them individually.

Probabilistic models applied to concrete corrosion depth prediction under sulfuric acid environment

Accurate prediction of corrosion depth degradation law can provide a basis for the determination of the sacrificial layer thickness and the cover thickness of the concrete structural members in a corrosive environment. This study aims to explore a more accurate and safe method to predict corrosion depth. Six sets of concrete cylinder concrete specimens were adopted to perform an accelerated corrosion test in sulfuric acid solution with pH ≈ 0.95 for six different scheduled durations. 3D coordinates of a large number of points on the corroded cylindrical surface were obtained with the help of the 3D laser scanning technology. Then, a comparative study was carried out for the corrosion depth measured with the laser scanning method and vernier caliper method. The results prove that concrete corrosion depth predicted by the Gaussian random process model established by the laser scanning method was considered to possess higher credibility and better security.

SAN: Mitigating spatial covariance heterogeneity in cortical thickness data collected from multiple scanners or sites.

In neuroimaging studies, combining data collected from multiple study sites or scanners is becoming common to increase the reproducibility of scientific discoveries. At the same time, unwanted variations arise by using different scanners (inter-scanner biases), which need to be corrected before downstream analyses to facilitate replicable research and prevent spurious findings. While statistical harmonization methods such as ComBat have become popular in mitigating inter-scanner biases in neuroimaging, recent methodological advances have shown that harmonizing heterogeneous covariances results in higher data quality. In vertex-level cortical thickness data, heterogeneity in spatial autocorrelation is a critical factor that affects covariance heterogeneity. Our work proposes a new statistical harmonization method called spatial autocorrelation normalization (SAN) that preserves homogeneous covariance vertex-level cortical thickness data across different scanners. We use an explicit Gaussian process to characterize scanner-invariant and scanner-specific variations to reconstruct spatially homogeneous data across scanners. SAN is computationally feasible, and it easily allows the integration of existing harmonization methods. We demonstrate the utility of the proposed method using cortical thickness data from the Social Processes Initiative in the Neurobiology of the Schizophrenia(s) (SPINS) study. SAN is publicly available as an R package.

Rough paths and symmetric-Stratonovich integrals driven by singular covariance Gaussian processes

Rough paths and symmetric-Stratonovich integrals driven by singular covariance Gaussian processes

Regression based stochastic energy management strategy for a grid connected microgrid using Artificial Electric Field Algorithm

Recent decade has witnessed steep technological advancement in the renewable energy sector due to growing concern of climate change and emission cut target. The lack of availability of fossil fuels and the high price of the same have made the use of Renewable Energy Sources (RES) as a promising approach for generating clean and sustainable energy at local level. This persuades the implementation of Microgrid (MG) supported with RES, to cater various types of load demand. However, planning and optimizing a MG operation have become challenging due to the intermittent nature of RES and uncertain loads. To address this issue, this paper introduces a Stochastic Energy Management Strategy (SEMS) for a grid connected MG comprising Photovoltaic, Wind Turbine, Fuel Cell, Micro Turbine, Battery Energy Storage and electrical as well as heat energy demand. The volatilities of RES power output and energy demand are modeled via Gaussian Process Regression (GPR) and Monte Carlo Simulation (MCS) respectively. The problem is framed as non-linear (NL) dynamic stochastic optimization problem and solved using ‘Artificial Electric Field Algorithm (AEFA)’. Here, minimization of expected value of operational and emission cost are taken as objective functions; while various practicality aspects are modeled as constraints in the problem. Further, the efficacy of the proposed approach is validated around the first central moment of the load. Various case studies are performed to estimate the day ahead optimum operating schedule of the Distributed Energy Resources (DER) and to assess the impact of load uncertainties on DER operation and total MG operation cost. Further, the efficacy of the GPR is verified through comparison with MCS based result.

Experimental-based groundwater salinization from the carbonate aquifer of eastern Saudi Arabia: Insight into machine learning coupled with meta-heuristic algorithms

Groundwater (GW) salinization of coastal aquifers has become a serious problem for attaining sustainable water resource management in Saudi Arabia and other parts of the world. Therefore, it is crucial to assess the extent of this salinization to protect and manage our water resources effectively. This research proposed real fieldwork GW samples at several locations supported with experimental based on chromatography (IC) and inductively coupled plasma mass spectrometry (ICP-MS) to analyze several GW physical, chemical, and hydro-geochemical elements. In this study, we model GW salinization with machine learning algorithms such as support vector regression, gaussian process regression, artificial neural networks, and least squares ensemble boosting regression tree. The performance of the standalone models was optimized with metaheuristic optimization-based algorithms such as fuzzy hybridized genetic algorithm (ANFIS-GA) and particle swarm optimization (ANFIS-PSO). The outcomes based on three variable input combinations were validated using several performance indicators and graphical methods. The quantitative analysis indicated that GPR-Combo1(MAE=0.006 mg/L), Ensm- Combo2 (MAE=0.025 mg/L), and GPR- Combo3 (MAE=0.078 mg/L) proved merit among the standalone combinations. Where combo 1, 2, and 3 stand for model combinations derived from feature selection. The cumulative probability function (CPF) demonstrated that heuristic optimization ANFIS-GA (MAE=0.0025 mg/L, MAPE=0.19183) and ANFIS-PSO (MAE=0.0018 mg/L, MAPE=0.0723) outperformed the standalone error accuracy and served reliable approach. Both the standalone models and heuristic algorithms used for GW salinization modeling have demonstrated promising results in accurately predicting salinity. This approach could aid in effectively managing the GW resources for sustainable development.

Artificial intelligence-based prediction models of bio-treated sand strength for sustainable and green infrastructure applications

As a sustainable, environmentally friendly, and green solution, biomineralization/bio-treatment process has recently emerged for enhancing the strength characteristics of loose sands by inducing cementation material commonly referred to as microbially induced calcite/cementation precipitation (MICP). To date, existing research on the unconfined compression strength of MICP-treated sands (UCSmicp) relies heavily on experimental data, with predictions primarily based on linear or curvilinear models that consider calcite (CaCO3) as the main influencing factor. However, there is limited exploration into the application of artificial intelligence (AI) and machine learning (ML) methods for UCSmicp prediction involving multiple influencing factors and their validation on unseen laboratory data. Therefore, this study intends to propose new prediction models of UCSmicp using four advanced ML techniques: Gaussian Process Regression (GPR), Adaptive Neuro Fuzzy Inference System (ANFIS), Artificial Neural Network (ANN), and Gene Expression Programming (GEP). The models incorporate various factors affecting UCSmicp, including sand uniformity coefficient (Cu), initial void ratio (e), mean grain size (D50), optical density at 600 mm wavelength (OD600), urea concentration (U), calcium concentration (Ca), and calcite content (C). Performance evaluation of models involved statistical assessments, error analysis, cross validation on laboratory data, and sensitivity and monotonicity studies. Results indicate that the proposed models exhibit exceptional precision across training, testing, and validation data in predicting UCSmicp, with ANN demonstrating the highest accuracy, followed by GPR, ANFIS, and GEP. Sensitivity analysis identifies CaCO3 as the main influencing factor on UCSmicp, while monotonicity analysis confirms alignment with physical processes. This work advocates for MICP as an eco-friendly solution and highlights the efficacy of advanced ML techniques in fostering sustainable infrastructure.

Efficient Analysis of Composites Manufacturing Using Multi-fidelity Simulation and Probabilistic Machine Learning

This paper introduces an innovative approach for the efficient analysis of composites manufacturing processes and phenomena. The method combines low- and high-fidelity simulation schemes with limited amounts of experimental data to train surrogate machine learning (ML) models. Guided by a novel approach, Spatially Weighted Gaussian Process Regression (SWGPR), a predictive model is efficiently constructed and calibrated by assigning datapoint-dependent noise levels to simulation points, establishing a multi-scale data-driven uncertainty structure. This study demonstrates the effectiveness of the method in accurately predicting process-induced deformations (PIDs) for L-shaped cross-ply laminates using minimal experimental efforts. The presented method aims to provide a cost-effective and broadly applicable framework for understanding and improving the design, development, and manufacturing of composites.

GausSN: Bayesian time-delay estimation for strongly lensed supernovae

Abstract We present GausSN, a Bayesian semi-parametric Gaussian Process (GP) model for time-delay estimation with resolved systems of gravitationally lensed supernovae (glSNe). GausSN models the underlying light curve non-parametrically using a GP. Without assuming a template light curve for each SN type, GausSN fits for the time delays of all images using data in any number of wavelength filters simultaneously. We also introduce a novel time-varying magnification model to capture the effects of microlensing alongside time-delay estimation. In this analysis, we model the time-varying relative magnification as a sigmoid function, as well as a constant for comparison to existing time-delay estimation approaches. We demonstrate that GausSN provides robust time-delay estimates for simulations of glSNe from the Nancy Grace Roman Space Telescope and the Vera C. Rubin Observatory’s Legacy Survey of Space and Time (Rubin-LSST). We find that up to 43.6 % of time-delay estimates from Roman and 52.9 % from Rubin-LSST have fractional errors of less than 5 %. We then apply GausSN to SN Refsdal and find the time delay for the fifth image is consistent with the original analysis, regardless of microlensing treatment. Therefore, GausSN maintains the level of precision and accuracy achieved by existing time-delay extraction methods with fewer assumptions about the underlying shape of the light curve than template-based approaches, while incorporating microlensing into the statistical error budget. GausSN is scalable for time-delay cosmography analyses given current projections of glSNe discovery rates from Rubin-LSST and Roman.

Learning-based model predictive secondary frequency control of PV-ESS-EV microgrid

Microgrids comprising photovoltaic (PV), energy-storage systems and electric vehicles have received increasing attention. However, the increase in renewable energy sources, such as PVs, will introduce uncertainty factors to the frequency response, resulting in frequency fluctuations that can reduce power quality. Hence, we propose an outstanding learning-based control approach that combines a model of physical principles with a Gaussian Process (GP) learning approach. The learning model corrects the physical principles model and estimates its uncertainty. Simulations are performed by comparing the proposed controller with conventional model-predictive controllers. The results indicate that the learning-based controller proposed can adjust the frequency with less overshooting and a lower root mean square error compared to the conventional MPC control method.

Determining Cosmological-model-independent H 0 with Gravitationally Lensed Supernova Refsdal

The reappearance of supernova Refsdal with detailed modeling of the lens cluster allows us to measure the time-delay distance, which serves as a powerful tool to determine the Hubble constant (H 0). We give a cosmological-model-independent method to estimate H 0 through Gaussian process regression, using time-delay measurements from this lensed supernova in combination with supernova data from the Pantheon+ sample. Using eight mass models for the lens cluster, we infer H0=64.2−4.3+4.4kms−1Mpc−1 , and using two cluster models most consistent with the observations, we infer H0=66.3−3.6+3.8kms−1Mpc−1 . Our estimates of the value of H 0 are in 1σ agreement with the results assuming a flat ΛCDM model and the uncertainties are comparable. Our constraint results on H 0 from the eight lens models and the two lens models indicate 2σ and 1.8σ tensions with that estimated by Supernova H0 for the Equation of State, respectively. However, our median values of H 0 from the two sets of lens models show good consistency with H 0 inferred from Planck cosmic microwave background observations assuming a ΛCDM model within 1σ. We also find that our results for H 0 indicate 2σ deviations and 1.7σ deviations from the constraint results of H 0 using six time-delay quasars by H0LiCOW with the same analysis method.

Prediction of key quality attributes in Salvia miltiorrhiza standard decoction using a Gaussian process regression model.

Nonstationary, nonlinear mass transfer in traditional Chinese medicine (TCM) extraction poses challenges to correlating process characteristics with quality parameters, particularly in defining clear parameter ranges for the process. The aim of the study was to provide a solution for quality consistency analysis in TCM preparation processes. Salvia miltiorrhiza was taken as an example for 15 batches of standard decoction. Using aqueous extract, alcoholic extract, and the content of salvianolic acid B as herb material key quality attributes, multiple nonlinear regression, Gaussian process regression, and artificial neural network models were employed to predict the key quality attributes including the paste yield, the content of salvianolic acid B, and the transfer rate. The evaluation criteria were root mean square error, mean absolute percentage error, and R2. The Gaussian process regression model had the best prediction effect on the paste yield, the content of salvianolic acid B, and the transfer rate, with R2 being 0.918, 0.934, and 0.919, respectively. Utilizing Gaussian process regression model confidence intervals, along with Shewhart control and intervals optimized through process capability index analysis, the quality control range of the standard decoction was determined as follows: paste yield, 25.14%-33.19%; salvianolic acid B content, 2.62%-4.78%; and transfer rate, 56.88%-64.80%. This study combined the preparation process of standard decoction with the Gaussian process regression model, accurately predicted the key quality attributes, and determined the quality parameter range by using process analysis tools, providing a new idea for the quality consistency standard of TCMprocesses.

First upper limits on the 21 cm signal power spectrum from cosmic dawn from one night of observations with NenuFAR

The redshifted 21 cm signal from neutral hydrogen is a direct probe of the physics of the early universe and has been an important science driver of many present and upcoming radio interferometers. In this study we use a single night of observations with the New Extension in Nan cay Upgrading LOFAR (NenuFAR) to place upper limits on the 21 cm power spectrum from cosmic dawn at a redshift of $z$ = 20.3. NenuFAR is a new low-frequency radio interferometer, operating in the 10--85 MHz frequency range, currently under construction at the Nan cay Radio Observatory in France. It is a phased array instrument with a very dense $u coverage at short baselines, making it one of the most sensitive instruments for 21 cm cosmology analyses at these frequencies. Our analysis adopts the foreground subtraction approach, in which sky sources are modeled and subtracted through calibration and residual foregrounds are subsequently removed using Gaussian process regression. The final power spectra are constructed from the gridded residual data cubes in the $u plane. Signal injection tests are performed at each step of the analysis pipeline, the relevant pipeline settings are optimized to ensure minimal signal loss, and any signal suppression is accounted for through a bias correction on our final upper limits. We obtain a best 2sigma upper limit of $2.4 mK $ at $z$ = 20.3 and $k$ = 0.041 $h\ cMpc $. We see a strong excess power in the data, making our upper limits two orders of magnitude higher than the thermal noise limit. We investigate the origin and nature of this excess power and discuss further improvements to the analysis pipeline that can potentially mitigate it and consequently allow us to reach thermal noise sensitivity when multiple nights of observations are processed in the future.