A NOTE ON SAMPLE PATH PROPERTIES OF l^p-VALUED GAUSSIAN PROCESSES

The a.s. sample path properties for l p valued Gaussian processes with stationary increments under some more general conditions are established.

Recent Advances in Data-Driven Wireless Communication Using Gaussian Processes: A Comprehensive Survey

Data-driven paradigms are well-known and salient demands of future wireless communication. Empowered by big data and machine learning techniques,next-generation data-driven communication systems will be intelligent with unique characteristics of expressiveness, scalability, interpretability, and uncertainty awareness, which can confidently involve diversified latent demands and personalized services in the foreseeable future. In this paper, we review a promising family of nonparametric Bayesian machine learning models,i.e., Gaussian processes(GPs), and their applications in wireless communication. Since GP models demonstrate outstanding expressive and interpretable learning ability with uncertainty, they are particularly suitable for wireless communication. Moreover, they provide a natural framework for collaborating data and empirical models(DEM). Specifically, we first envision three-level motivations of data-driven wireless communication using GP models. Then, we present the background of the GPs in terms of covariance structure and model inference. The expressiveness of the GP model using various interpretable kernels, including stationary, non-stationary, deep and multi-task kernels,is showcased. Furthermore, we review the distributed GP models with promising scalability, which is suitable for applications in wireless networks with a large number of distributed edge devices. Finally, we list representative solutions and promising techniques that adopt GP models in various wireless communication applications.

Limit theorems for supremum of Gaussian processes over a random interval

Let {X(t), t ≥ 0} be a centered stationary Gaussian process with correlation r(t)such that 1-r(t) is asymptotic to a regularly varying function. With T being a nonnegative random variable and independent of X(t), the exact asymptotics of P(sup_(t∈[0,T])X(t) > x) is considered, as x → ∞.

THE LOCAL CONTINUITY MODULI FOR TWO CLASSES OF GAUSSIAN PROCESSES

In this article,local continuity moduli for the fractional Wiener process and l ∞\|valued Gaussian processes is discussed.

Multi-output Gaussian Process Regression Model with Combined Kernel Function for Polyester Esterification Processes

In polyester fiber industrial processes,the prediction of key performance indicators is vital for product quality.The esterification process is an indispensable step in the polyester polymerization process.It has the characteristics of strong coupling,nonlinearity and complex mechanism.To solve these problems,we put forward a multi-output Gaussian process regression(MGPR)model based on the combined kernel function for the polyester esterification process.Since the seasonal and trend decomposition using loess(STL)can extract the periodic and trend characteristics of time series,a combined kernel function based on the STL and the kernel function analysis is constructed for the MGPR.The effectiveness of the proposed model is verified by the actual polyester esterification process data collected from fiber production.

Reliable calculations of nuclear binding energies by the Gaussian process of machine learning

Reliable calculations of nuclear binding energies are crucial for advancing the research of nuclear physics. Machine learning provides an innovative approach to exploring complex physical problems. In this study, the nuclear binding energies are modeled directly using a machine-learning method called the Gaussian process. First, the binding energies for 2238 nuclei with Z > 20 and N > 20 are calculated using the Gaussian process in a physically motivated feature space, yielding an average deviation of 0.046 MeV and a standard deviation of 0.066 MeV. The results show the good learning ability of the Gaussian process in the studies of binding energies. Then, the predictive power of the Gaussian process is studied by calculating the binding energies for 108 nuclei newly included in AME2020. The theoretical results are in good agreement with the experimental data, reflecting the good predictive power of the Gaussian process. Moreover, the α-decay energies for 1169 nuclei with 50 ≤ Z ≤ 110 are derived from the theoretical binding energies calculated using the Gaussian process. The average deviation and the standard deviation are, respectively, 0.047 MeV and 0.070 MeV. Noticeably, the calculated α-decay energies for the two new isotopes ^ (204 )Ac(Huang et al. Phys Lett B 834, 137484(2022)) and ^ (207) Th(Yang et al. Phys Rev C 105, L051302(2022)) agree well with the latest experimental data. These results demonstrate that the Gaussian process is reliable for the calculations of nuclear binding energies. Finally, the α-decay properties of some unknown actinide nuclei are predicted using the Gaussian process. The predicted results can be useful guides for future research on binding energies and α-decay properties.

Operational optimization of copper flotation process based on the weighted Gaussian process regression and index-oriented adaptive differential evolution algorithm

Concentrate copper grade(CCG)is one of the important production indicators of copper flotation processes,and keeping the CCG at the set value is of great significance to the economic benefit of copper flotation industrial processes.This paper addresses the fluctuation problem of CCG through an operational optimization method.Firstly,a density-based affinity propagationalgorithm is proposed so that more ideal working condition categories can be obtained for the complex raw ore properties.Next,a Bayesian network(BN)is applied to explore the relationship between the operational variables and the CCG.Based on the analysis results of BN,a weighted Gaussian process regression model is constructed to predict the CCG that a higher prediction accuracy can be obtained.To ensure the predicted CCG is close to the set value with a smaller magnitude of the operation adjustments and a smaller uncertainty of the prediction results,an index-oriented adaptive differential evolution(IOADE)algorithm is proposed,and the convergence performance of IOADE is superior to the traditional differential evolution and adaptive differential evolution methods.Finally,the effectiveness and feasibility of the proposed methods are verified by the experiments on a copper flotation industrial process.

Optimization of Generator Based on Gaussian Process Regression Model with Conditional Likelihood Lower Bound Search

The noise that comes from finite element simulation often causes the model to fall into the local optimal solution and over fitting during optimization of generator.Thus,this paper proposes a Gaussian Process Regression(GPR)model based on Conditional Likelihood Lower Bound Search(CLLBS)to optimize the design of the generator,which can filter the noise in the data and search for global optimization by combining the Conditional Likelihood Lower Bound Search method.Taking the efficiency optimization of 15 kW Permanent Magnet Synchronous Motor as an example.Firstly,this method uses the elementary effect analysis to choose the sensitive variables,combining the evolutionary algorithm to design the super Latin cube sampling plan;Then the generator-converter system is simulated by establishing a co-simulation platform to obtain data.A Gaussian process regression model combing the method of the conditional likelihood lower bound search is established,which combined the chi-square test to optimize the accuracy of the model globally.Secondly,after the model reaches the accuracy,the Pareto frontier is obtained through the NSGA-II algorithm by considering the maximum output torque as a constraint.Last,the constrained optimization is transformed into an unconstrained optimizing problem by introducing maximum constrained improvement expectation(CEI)optimization method based on the re-interpolation model,which cross-validated the optimization results of the Gaussian process regression model.The above method increase the efficiency of generator by 0.76%and 0.5%respectively;And this method can be used for rapid modeling and multi-objective optimization of generator systems.

Dynamic System Identification of Underwater Vehicles Using Multi-output Gaussian Processes

Non-parametric system identification with Gaussian processes for underwater vehicles is explored in this research with the purpose of modelling autonomous underwater vehicle(AUV) dynamics with a low amount of data. Multi-output Gaussian processes and their aptitude for modelling the dynamic system of an underactuated AUV without losing the relationships between tied outputs are used. The simulation of a first-principle model of a Remus 100 AUV is employed to capture data for the training and validation of the multi-output Gaussian processes. The metric and required procedure to carry out multi-output Gaussian processes for AUV with 6 degrees of freedom(DoF) is also shown in this paper. Multi-output Gaussian processes compared with the popular technique of recurrent neural network show that multi-output Gaussian processes manage to surpass RNN for non-parametric dynamic system identification in underwater vehicles with highly coupled DoF with the added benefit of providing the measurement of confidence.

Some Limit Theorems on the Increments of l^p-valued Multi-Parameter Gaussian Processes

In this paper,we establish some limit theorems on the increments of an l^p-valued multi- parameter Gaussian process under weaker conditions than those of Cs(?)rg(?)-Shao theorems published in Ann.Probab.(1993).

The Limit Theorems for Maxima of Stationary Gaussian Processes with Random Index

Let {X（t）, t ≥ 0} be a standard（zero-mean, unit-variance） stationary Gaussian process with correlation function r（·） and continuous sample paths. In this paper, we consider the maxima M（T） = max{X（t）, t∈ [0, T ]} with random index TT, where TT /T converges to a non-degenerate distribution or to a positive random variable in probability, and show that the limit distribution of M（TT） exists under some additional conditions related to the correlation function r（·）.

Fast Remaining Capacity Estimation for Lithium-ion Batteries Based on Short-time Pulse Test and Gaussian Process Regression

It remains challenging to effectively estimate the remaining capacity of the secondary lithium-ion batteries that have been widely adopted for consumer electronics,energy storage,and electric vehicles.Herein,by integrating regular real-time current short pulse tests with data-driven Gaussian process regression algorithm,an efficient battery estimation has been successfully developed and validated for batteries with capacity ranging from 100%of the state of health(SOH)to below 50%,reaching an average accuracy as high as 95%.Interestingly,the proposed pulse test strategy for battery capacity measurement could reduce test time by more than 80%compared with regular long charge/discharge tests.The short-term features of the current pulse test were selected for an optimal training process.Data at different voltage stages and state of charge(SOC)are collected and explored to find the most suitable estimation model.In particular,we explore the validity of five different machine-learning methods for estimating capacity driven by pulse features,whereas Gaussian process regression with Matern kernel performs the best,providing guidance for future exploration.The new strategy of combining short pulse tests with machine-learning algorithms could further open window for efficiently forecasting lithium-ion battery remaining capacity.

Moduli of Continuity of a Class of N-parameter Gaussian Processes and Their Fast Points

We study the moduli of continuity of a class of N-parameter Gaussian processes and get some results on＇the packing dimension of the set of their fast points.

Maxima and sum for discrete and continuous time Gaussian processes

We study the asymptotic relation among the maximum of continuous weakly and strongly dependent stationary Gaussian process, the maximum of this process sampled at discrete time points, and the partial sum of this process. It is shown that these two extreme values and the sum are asymptotically independent if the grid of the discrete time points is sufficiently sparse and the Gaussian process is weakly dependent, and asymptotically dependent if the grid points are Pickands grids or dense grids.

Chung-type Law of the Iterated Logarithm on l^p-valued Gaussian Processes

By estimating small ball probabilities for l^P-valued Gaussian processes, a Chung-type law of the iterated logarithm of l^P-valued Gaussian processes is given.

ON LARGE INCREMENTS OF l^p-VALUED GAUSSIAN PROCESSES

Let{X k(t),t≥0},k=1,2,…,be a sequence of independent Gaussian processes withσk 2(h)=E(X k(t+h)-X k(t))2.Putσ(p,h)=(∑∞k=1σk p(h))1/p,p≥1.The author establishes the large increment results for boundedσ(p,h).

ON LOCAL CONTINUITY MODULI FOR GAUSSIAN PROCESSES

In this paper, we get three local continuity moduli theorems for the almost surely continuous, stationary increments Gaussian process {Y(t), t0}, the partial sum processes X(t,N)= (t) of infinite dimensional Ornstein-Uhlenbeck processes {Xk(t), t0}, and lp-valued Gaussian processes {Y(t), t0}={Xk(t), t0}, separately. The first theorem implies the local continuity modulus theorem for the series X(t)=, Xk(t) of infinite dimensional OrnsteinUhlenbeck processes which has been obtained in [3].

QUANTUM GAUSSIAN PROCESSES

In this paper,we will define the quantum Gaussian processes based on ordinary Gaussian processes by means of reproducing kernel Hilbert spaces,and investigate the relation between their stochastic properties. Particularly,we are interested in Brownian bridges and quantum Ornstein Uhlenbeck processes.We are even able to construct each of them in two different ways:to construct quantum processes based on ordinary Brownian bridges(Ornstein-Uhlenbeck processes resp.)or to solve the quantum S.D.E. driven by quantum Brownian motions. But essentially they are the same.

Peri-Net-Pro: the neural processes with quantified uncertainty for crack patterns

This paper develops a deep learning tool based on neural processes(NPs)called the Peri-Net-Pro,to predict the crack patterns in a moving disk and classifies them according to the classification modes with quantified uncertainties.In particular,image classification and regression studies are conducted by means of convolutional neural networks(CNNs)and NPs.First,the amount and quality of the data are enhanced by using peridynamics to theoretically compensate for the problems of the finite element method(FEM)in generating crack pattern images.Second,case studies are conducted with the prototype microelastic brittle(PMB),linear peridynamic solid(LPS),and viscoelastic solid(VES)models obtained by using the peridynamic theory.The case studies are performed to classify the images by using CNNs and determine the suitability of the PMB,LBS,and VES models.Finally,a regression analysis is performed on the crack pattern images with NPs to predict the crack patterns.The regression analysis results confirm that the variance decreases when the number of epochs increases by using the NPs.The training results gradually improve,and the variance ranges decrease to less than 0.035.The main finding of this study is that the NPs enable accurate predictions,even with missing or insufficient training data.The results demonstrate that if the context points are set to the 10th,100th,300th,and 784th,the training information is deliberately omitted for the context points of the 10th,100th,and 300th,and the predictions are different when the context points are significantly lower.However,the comparison of the results of the 100th and 784th context points shows that the predicted results are similar because of the Gaussian processes in the NPs.Therefore,if the NPs are employed for training,the missing information of the training data can be supplemented to predict the results.

ASYMPTOTICS OF THE CROSS-VARIATION OF YOUNG INTEGRALS WITH RESPECT TO A GENERAL SELF-SIMILAR GAUSSIAN PROCESS

We show in this work that the limit in law of the cross-variation of processes having the form of Young integral with respect to a general self-similar centered Gaussian process of orderβ∈(1/2,3/4]is normal according to the values ofβ.We apply our results to two self-similar Gaussian processes:the subfractional Brownian motion and the bifractional Brownian motion.