Combining stochastic density functional theory with deep potential molecular dynamics to study warm dense matter

In traditional finite-temperature Kohn–Sham density functional theory(KSDFT),the partial occupation of a large number of high-energy KS eigenstates restricts the use of first-principles molecular dynamics methods at extremely high temperatures.However,stochastic density functional theory(SDFT)can overcome this limitation.Recently,SDFT and the related mixed stochastic–deterministic density functional theory,based on a plane-wave basis set,have been implemented in the first-principles electronic structure software ABACUS[Q.Liu and M.Chen,Phys.Rev.B 106,125132(2022)].In this study,we combine SDFT with the Born–Oppenheimer molecular dynamics method to investigate systems with temperatures ranging from a few tens of eV to 1000 eV.Importantly,we train machine-learning-based interatomic models using the SDFT data and employ these deep potential models to simulate large-scale systems with long trajectories.Subsequently,we compute and analyze the structural properties,dynamic properties,and transport coefficients of warm dense matter.

A modified stochastic model for LS+AR hybrid method and its application in polar motion short-term prediction

Short-term(up to 30 days)predictions of Earth Rotation Parameters(ERPs)such as Polar Motion(PM:PMX and PMY)play an essential role in real-time applications related to high-precision reference frame conversion.Currently,least squares(LS)+auto-regressive(AR)hybrid method is one of the main techniques of PM prediction.Besides,the weighted LS+AR hybrid method performs well for PM short-term prediction.However,the corresponding covariance information of LS fitting residuals deserves further exploration in the AR model.In this study,we have derived a modified stochastic model for the LS+AR hybrid method,namely the weighted LS+weighted AR hybrid method.By using the PM data products of IERS EOP 14 C04,the numerical results indicate that for PM short-term forecasting,the proposed weighted LS+weighted AR hybrid method shows an advantage over both the LS+AR hybrid method and the weighted LS+AR hybrid method.Compared to the mean absolute errors(MAEs)of PMX/PMY sho rt-term prediction of the LS+AR hybrid method and the weighted LS+AR hybrid method,the weighted LS+weighted AR hybrid method shows average improvements of 6.61%/12.08%and 0.24%/11.65%,respectively.Besides,for the slopes of the linear regression lines fitted to the errors of each method,the growth of the prediction error of the proposed method is slower than that of the other two methods.

Prediction of subsurface settlement induced by shield tunnelling in sandy cobble stratum

This study focuses on the analytical prediction of subsurface settlement induced by shield tunnelling in sandy cobble stratum considering the volumetric deformation modes of the soil above the tunnel crown.A series of numerical analyses is performed to examine the effects of cover depth ratio(C/D),tunnel volume loss rate(h t)and volumetric block proportion(VBP)on the characteristics of subsurface settle-ment trough and soil volume loss.Considering the ground loss variation with depth,three modes are deduced from the volumetric deformation responses of the soil above the tunnel crown.Then,analytical solutions to predict subsurface settlement for each mode are presented using stochastic medium theory.The influences of C/D,h t and VBP on the key parameters(i.e.B and N)in the analytical expressions are discussed to determine the fitting formulae of B and N.Finally,the proposed analytical solutions are validated by the comparisons with the results of model test and numerical simulation.Results show that the fitting formulae provide a convenient and reliable way to evaluate the key parameters.Besides,the analytical solutions are reasonable and available in predicting the subsurface settlement induced by shield tunnelling in sandy cobble stratum.

Performance enhancement of a viscoelastic bistable energy harvester using time-delayed feedback control

This paper focuses on the stochastic analysis of a viscoelastic bistable energy harvesting system under colored noise and harmonic excitation, and adopts the time-delayed feedback control to improve its harvesting efficiency. Firstly, to obtain the dimensionless governing equation of the system, the original bistable system is approximated as a system without viscoelastic term by using the stochastic averaging method of energy envelope, and then is further decoupled to derive an equivalent system. The credibility of the proposed method is validated by contrasting the consistency between the numerical and the analytical results of the equivalent system under different noise conditions. The influence of system parameters on average output power is analyzed, and the control effect of the time-delayed feedback control on system performance is compared. The output performance of the system is improved with the occurrence of stochastic resonance(SR). Therefore, the signal-to-noise ratio expression for measuring SR is derived, and the dependence of its SR behavior on different parameters is explored.

Analytical and NumericalMethods to Study the MFPT and SR of a Stochastic Tumor-Immune Model

The Mean First-Passage Time (MFPT) and Stochastic Resonance (SR) of a stochastic tumor-immune model withnoise perturbation are discussed in this paper. Firstly, considering environmental perturbation, Gaussian whitenoise and Gaussian colored noise are introduced into a tumor growth model under immune surveillance. Asfollows, the long-time evolution of the tumor characterized by the Stationary Probability Density (SPD) and MFPTis obtained in theory on the basis of the Approximated Fokker-Planck Equation (AFPE). Herein the recurrenceof the tumor from the extinction state to the tumor-present state is more concerned in this paper. A moreefficient algorithmof Back-Propagation Neural Network (BPNN) is utilized in order to testify the correction of thetheoretical SPDandMFPT.With the existence of aweak signal, the functional relationship between Signal-to-NoiseRatio (SNR), noise intensities and correlation time is also studied. Numerical results show that both multiplicativeGaussian colored noise and additive Gaussian white noise can promote the extinction of the tumors, and themultiplicative Gaussian colored noise can lead to the resonance-like peak on MFPT curves, while the increasingintensity of the additiveGaussian white noise results in theminimum of MFPT. In addition, the correlation timesare negatively correlated with MFPT. As for the SNR, we find the intensities of both the Gaussian white noise andthe Gaussian colored noise, as well as their correlation intensity can induce SR. Especially, SNR is monotonouslyincreased in the case ofGaussian white noisewith the change of the correlation time.At last, the optimal parametersin BPNN structure are analyzed for MFPT from three aspects: the penalty factors, the number of neural networklayers and the number of nodes in each layer.

Far and Near Optimization:A New Simple and Effective Metaphor-LessOptimization Algorithm for Solving Engineering Applications

In this article,a novel metaheuristic technique named Far and Near Optimization(FNO)is introduced,offeringversatile applications across various scientific domains for optimization tasks.The core concept behind FNO lies inintegrating global and local search methodologies to update the algorithm population within the problem-solvingspace based on moving each member to the farthest and nearest member to itself.The paper delineates the theoryof FNO,presenting a mathematical model in two phases:(i)exploration based on the simulation of the movementof a population member towards the farthest member from itself and(ii)exploitation based on simulating themovement of a population member towards the nearest member from itself.FNO’s efficacy in tackling optimizationchallenges is assessed through its handling of the CEC 2017 test suite across problem dimensions of 10,30,50,and 100,as well as to address CEC 2020.The optimization results underscore FNO’s adeptness in exploration,exploitation,and maintaining a balance between them throughout the search process to yield viable solutions.Comparative analysis against twelve established metaheuristic algorithms reveals FNO’s superior performance.Simulation findings indicate FNO’s outperformance of competitor algorithms,securing the top rank as the mosteffective optimizer across a majority of benchmark functions.Moreover,the outcomes derived by employing FNOon twenty-two constrained optimization challenges from the CEC 2011 test suite,alongside four engineering designdilemmas,showcase the effectiveness of the suggested method in tackling real-world scenarios.

Effects of asymmetric coupling and boundary on the dynamic behaviors of a random nearest neighbor coupled system

This study investigates the dynamical behaviors of nearest neighbor asymmetric coupled systems in a confined space.First, the study derivative analytical stability and synchronization conditions for the asymmetrically coupled system in an unconfined space, which are then validated through numerical simulations. Simulation results show that asymmetric coupling has a significant impact on synchronization conditions. Moreover, it is observed that irrespective of whether the system is confined, an increase in coupling asymmetry leads to a hastened synchronization pace. Additionally, the study examines the effects of boundaries on the system's collective behaviors via numerical experiments. The presence of boundaries ensures the system's stability and synchronization, and reducing these boundaries can expedite the synchronization process and amplify its effects. Finally, the study reveals that the system's output amplitude exhibits stochastic resonance as the confined boundary size increases.

FLOCKING OF A THERMODYNAMIC CUCKER-SMALE MODEL WITH LOCAL VELOCITY INTERACTIONS

In this paper, we study the flocking behavior of a thermodynamic Cucker–Smale model with local velocity interactions. Using the spectral gap of a connected stochastic matrix, together with an elaborate estimate on perturbations of a linearized system, we provide a sufficient framework in terms of initial data and model parameters to guarantee flocking. Moreover, it is shown that the system achieves a consensus at an exponential rate.

A Probabilistic Approach for Predicting Vessel Motion

Dear Editor,This letter addresses the challenge of forecasting the motion of real-world vessels over an extended period with a limited amount of available data.By employing stochastic differential equation(SDE)modeling,we integrate both deterministic and stochastic components of the available information.Subsequently,we establish a recursive prediction methodology based on Bayes’rule to update the model state when new measurements are received.Furthermore,we develop a stochastic model tailored specifically to vessel dynamics and introduce an approximation method to tackle computational complexities.Finally,we present an application example and conduct a comparative experiment to validate the effectiveness and superiority of the proposed method.

Recursive Filtering for Stochastic Systems With Filter-and-Forward Successive Relays

In this paper,the recursive filtering problem is considered for stochastic systems over filter-and-forward successive relay(FFSR)networks.An FFSR is located between the sensor and the remote filter to forward the measurement.In the successive relay,two cooperative relay nodes are adopted to forward the signals alternatively,thereby existing switching characteristics and inter-relay interferences(IRI).Since the filter-and-forward scheme is employed,the signal received by the relay is retransmitted after it passes through a linear filter.The objective of the paper is to concurrently design optimal recursive filters for FFSR and stochastic systems against switching characteristics and IRI of relays.First,a uniform measurement model is proposed by analyzing the transmission mechanism of FFSR.Then,novel filter structures with switching parameters are constructed for both FFSR and stochastic systems.With the help of the inductive method,filtering error covariances are presented in the form of coupled difference equations.Next,the desired filter gain matrices are further obtained by minimizing the trace of filtering error covariances.Moreover,the stability performance of the filtering algorithm is analyzed where the uniform bound is guaranteed on the filtering error covariance.Finally,the effectiveness of the proposed filtering method over FFSR is verified by a three-order resistance-inductance-capacitance circuit system.

Stochastic seismic inversion and Bayesian facies classification applied to porosity modeling and igneous rock identification

We apply stochastic seismic inversion and Bayesian facies classification for porosity modeling and igneous rock identification in the presalt interval of the Santos Basin. This integration of seismic and well-derived information enhances reservoir characterization. Stochastic inversion and Bayesian classification are powerful tools because they permit addressing the uncertainties in the model. We used the ES-MDA algorithm to achieve the realizations equivalent to the percentiles P10, P50, and P90 of acoustic impedance, a novel method for acoustic inversion in presalt. The facies were divided into five: reservoir 1,reservoir 2, tight carbonates, clayey rocks, and igneous rocks. To deal with the overlaps in acoustic impedance values of facies, we included geological information using a priori probability, indicating that structural highs are reservoir-dominated. To illustrate our approach, we conducted porosity modeling using facies-related rock-physics models for rock-physics inversion in an area with a well drilled in a coquina bank and evaluated the thickness and extension of an igneous intrusion near the carbonate-salt interface. The modeled porosity and the classified seismic facies are in good agreement with the ones observed in the wells. Notably, the coquinas bank presents an improvement in the porosity towards the top. The a priori probability model was crucial for limiting the clayey rocks to the structural lows. In Well B, the hit rate of the igneous rock in the three scenarios is higher than 60%, showing an excellent thickness-prediction capability.

Exponential Synchronization of Delayed Stochastic Complex Dynamical Networks via Hybrid Impulsive Control

Dear Editor,This letter addresses the synchronization problem of a class of delayed stochastic complex dynamical networks consisting of multiple drive and response nodes.The aim is to achieve mean square exponential synchronization for the drive-response nodes despite the simultaneous presence of time delays and stochastic noises in node dynamics.

Partially-Observed Maximum Principle for Backward Stochastic Differential Delay Equations

Dear Editor,This letter investigates a partially-observed optimal control problem for backward stochastic differential delay equations(BSDDEs).By utilizing Girsanov’s theory and convex variational method,we obtain a maximum principle on the assumption that the state equation contains time delay and the control domain is convex.The adjoint processes can be represented as the solutions of certain time-advanced stochastic differential equations in finite-dimensional spaces.Linear backward stochastic differential equation(BSDE)was first introduced by Bismut in[1],while general BSDE was given by Pardoux and Peng[2].Since then,the theory of BSDEs developed rapidly.The corresponding optimal control problems,whose states are driven by BSDEs,have also been widely studied by some authors,see[3]-[5].

An underdamped and delayed tri-stable model-based stochastic resonance

Stochastic resonance(SR) is investigated in an underdamped tri-stable potential system driven by Gaussian colored noise and a periodic excitation, where both displacement and velocity time-delayed states feedback are considered. It is challenging to study SR in a second-order delayed multi-stable system analytically. In this paper, the improved energy envelope stochastic average method is developed to derive the analytical expressions of stationary probability density(SPD)and spectral amplification. The effects of noise intensity, damping coefficient, and time delay on SR are analyzed. The results show that the shapes of joint SPD can be adjusted to the desired structure by choosing the time delay and feedback gains. For fixed time delay, the SR peak is increased for negative displacement or velocity feedback gain. Meanwhile, the SR peak is decreased while the optimal noise intensity increases with increasing correlation time of noise. The Monte Carlo simulations(MCS) confirm the effectiveness of the theoretical results.

Technical efficiency of cocoa farms at varying elevation levels in Davao City, Philippines: implications to sustainable upland farming systems

Elevation is one of many components that influence agriculture, and this in turn affects the level of both inputs and outputs of farmers. This article focuses on the productivity and technical efficiency of 100 cocoa farms using cross-sectional data from areas ranging from 190 to 1021 m above sea level which were classified as low, medium, and high elevation in Davao City, considered as the chocolate capital of the Philippines. Using stochastic frontier analysis, the results showed that the cost of inputs per ha and the number of cocoa trees per ha significantly increase yield. Farms at high elevations were less technically efficient, as this entails lower temperatures and increased rainfall, and cocoa farming in those areas and conditions can be more challenging, especially with changes in farming practices, terrain, and distance to markets. Other significant variables were age of cocoa farms, married farmers, and age of the farmers. Older farms may be more developed, farmers who are married benefit from their spouses being able to readily contribute as farm labor, and lastly, older farmers' inefficiency may likely stem from nonadaptation of newer farming practices. With an average technical efficiency of 0.61, 0.63, and 0.26 in low, medium, and high elevation areas, respectively, farmers therefore have an incentive to improve farm practices and consider topographical variations found in high elevation areas. Recommendations for the improvement of technical efficiency of cocoa farms are better connectivity to markets, enhancing farm practices, and continuation and improvement of government programs on cocoa with an added emphasis on research. For farmers in high elevation areas, mitigating solutions such as sustainable agriculture practices and ecolabelling are key to improving efficiency and minimizing the potential negative impact on upland farming systems. Moreover, such adaptation measures may also contribute to sustainability of cocoa farming in high elevation areas.

Algorithms and statistical analysis for linear structured weighted total least squares problem

Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with random errors.However,in many geodetic applications,some elements are error-free and some random observations appear repeatedly in different positions in the augmented coefficient matrix.It is called the linear structured EIV(LSEIV)model.Two kinds of methods are proposed for the LSEIV model from functional and stochastic modifications.On the one hand,the functional part of the LSEIV model is modified into the errors-in-observations(EIO)model.On the other hand,the stochastic model is modified by applying the Moore-Penrose inverse of the cofactor matrix.The algorithms are derived through the Lagrange multipliers method and linear approximation.The estimation principles and iterative formula of the parameters are proven to be consistent.The first-order approximate variance-covariance matrix(VCM)of the parameters is also derived.A numerical example is given to compare the performances of our proposed three algorithms with the STLS approach.Afterwards,the least squares(LS),total least squares(TLS)and linear structured weighted total least squares(LSWTLS)solutions are compared and the accuracy evaluation formula is proven to be feasible and effective.Finally,the LSWTLS is applied to the field of deformation analysis,which yields a better result than the traditional LS and TLS estimations.

Decentralized Optimal Control and Stabilization of Interconnected Systems With Asymmetric Information

The paper addresses the decentralized optimal control and stabilization problems for interconnected systems subject to asymmetric information.Compared with previous work,a closed-loop optimal solution to the control problem and sufficient and necessary conditions for the stabilization problem of the interconnected systems are given for the first time.The main challenge lies in three aspects:Firstly,the asymmetric information results in coupling between control and estimation and failure of the separation principle.Secondly,two extra unknown variables are generated by asymmetric information(different information filtration)when solving forward-backward stochastic difference equations.Thirdly,the existence of additive noise makes the study of mean-square boundedness an obstacle.The adopted technique is proving and assuming the linear form of controllers and establishing the equivalence between the two systems with and without additive noise.A dual-motor parallel drive system is presented to demonstrate the validity of the proposed algorithm.

High Order IMEX Stochastic Galerkin Schemes for Linear Transport Equation with Random Inputs and Diffusive Scalings

In this paper,we consider the high order method for solving the linear transport equations under diffusive scaling and with random inputs.To tackle the randomness in the problem,the stochastic Galerkin method of the generalized polynomial chaos approach has been employed.Besides,the high order implicit-explicit scheme under the micro-macro decomposition framework and the discontinuous Galerkin method have been employed.We provide several numerical experiments to validate the accuracy and the stochastic asymptotic-preserving property.

An Interpolation Method for Karhunen-Loève Expansion of Random Field Discretization

In the context of global mean square error concerning the number of random variables in the representation,the Karhunen–Loève(KL)expansion is the optimal series expansion method for random field discretization.The computational efficiency and accuracy of the KL expansion are contingent upon the accurate resolution of the Fredholm integral eigenvalue problem(IEVP).The paper proposes an interpolation method based on different interpolation basis functions such as moving least squares(MLS),least squares(LS),and finite element method(FEM)to solve the IEVP.Compared with the Galerkin method based on finite element or Legendre polynomials,the main advantage of the interpolation method is that,in the calculation of eigenvalues and eigenfunctions in one-dimensional random fields,the integral matrix containing covariance function only requires a single integral,which is less than a two-folded integral by the Galerkin method.The effectiveness and computational efficiency of the proposed interpolation method are verified through various one-dimensional examples.Furthermore,based on theKL expansion and polynomial chaos expansion,the stochastic analysis of two-dimensional regular and irregular domains is conducted,and the basis function of the extended finite element method(XFEM)is introduced as the interpolation basis function in two-dimensional irregular domains to solve the IEVP.

A Stochastic Model to Assess the Epidemiological Impact of Vaccine Booster Doses on COVID-19 and Viral Hepatitis B Co-Dynamics with Real Data

A patient co-infected with COVID-19 and viral hepatitis B can be atmore risk of severe complications than the one infected with a single infection.This study develops a comprehensive stochastic model to assess the epidemiological impact of vaccine booster doses on the co-dynamics of viral hepatitis B and COVID-19.The model is fitted to real COVID-19 data from Pakistan.The proposed model incorporates logistic growth and saturated incidence functions.Rigorous analyses using the tools of stochastic calculus,are performed to study appropriate conditions for the existence of unique global solutions,stationary distribution in the sense of ergodicity and disease extinction.The stochastic threshold estimated from the data fitting is given by:R_(0)^(S)=3.0651.Numerical assessments are implemented to illustrate the impact of double-dose vaccination and saturated incidence functions on the dynamics of both diseases.The effects of stochastic white noise intensities are also highlighted.