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Slow kinetic processes in molecular systems can be analyzed by computing the dominant eigenpairs of the Koopman operator or its generator. In this context, the Variational Approach to Markov Processes (VAMP) provides a rigorous way of discerning the quality of different approximate models. Kernel methods have been shown to provide accurate and robust estimates for slow kinetic processes, but they are sensitive to hyper-parameter selection and require the solution of large-scale generalized eigenvalue problems, which can easily become computationally demanding for large data sizes. In this contribution, we employ a stochastic approximation of the kernel based on random Fourier features (RFFs) to derive a small-scale dual eigenvalue problem that can be easily solved. We provide an interpretation of this procedure in terms of a finite, randomly generated basis set. By combining the RFF approach and model selection by means of the VAMP score, we show that kernel parameters can be efficiently tuned and accurate estimates of slow molecular kinetics can be obtained for several benchmarking systems, such as deca alanine and the NTL9 protein. [ABSTRACT FROM AUTHOR]

Classical optimizers play a crucial role in determining the accuracy and convergence of variational quantum algorithms; leading algorithms use a near-term quantum computer to solve the ground state properties of molecules, simulate dynamics of different quantum systems, and so on. In the literature, many optimizers, each having its own architecture, have been employed expediently for different applications. In this work, we consider a few popular and efficacious optimizers and assess their performance in variational quantum algorithms for applications in quantum chemistry in a realistic noisy setting. We benchmark the optimizers with critical analysis based on quantum simulations of simple molecules, such as hydrogen, lithium hydride, beryllium hydride, water, and hydrogen fluoride. The errors in the ground state energy, dissociation energy, and dipole moment are the parameters used as yardsticks. All the simulations were carried out with an ideal quantum circuit simulator, a noisy quantum circuit simulator, and finally a noisy simulator with noise embedded from the IBM Cairo quantum device to understand the performance of the classical optimizers in ideal and realistic quantum environments. We used the standard unitary coupled cluster ansatz for simulations, and the number of qubits varied from two starting from the hydrogen molecule to ten qubits in hydrogen fluoride. Based on the performance of these optimizers in the ideal quantum circuits, the conjugate gradient, limited-memory Broyden—Fletcher—Goldfarb—Shanno bound, and sequential least squares programming optimizers are found to be the best-performing gradient-based optimizers. While constrained optimization by linear approximation (COBYLA) and Powell's conjugate direction algorithm for unconstrained optimization (POWELL) perform most efficiently among the gradient-free methods, in noisy quantum circuit conditions, simultaneous perturbation stochastic approximation, POWELL, and COBYLA are among the best-performing optimizers. [ABSTRACT FROM AUTHOR]

In this paper, we devise a stochastic extragradient-like algorithm incorporated with inertial terms, which requires a single projection onto our feasible set and employs a stochastic approximation version of an Armijo-type line search scheme along a feasible direction, for solving pseudomonotone stochastic variational inequalities. In the algorithm, two different stepsize strategies are employed to update steplength sequences without using the prior knowledge of the Lipschitz constant of involved operators. In the process of the stochastic approximation, we iteratively reduce the variance of stochastic errors. The almost sure convergence, the complexity analysis, and rates are provided in a dimensional space under reasonable conditions. Finally, some numerical experiments with graphical illustrations are reported to demonstrate the applicability and the efficiency of our algorithm in comparison with some projection type methods in the literature. [ABSTRACT FROM AUTHOR]

Stochastic optimization has experienced significant growth in recent decades, with the increasing prevalence of variance reduction techniques in stochastic optimization algorithms to enhance computational efficiency. In this paper, we introduce two projection-free stochastic approximation algorithms for maximizing diminishing return (DR) submodular functions over convex constraints, building upon the Stochastic Path Integrated Differential EstimatoR (SPIDER) and its variants. Firstly, we present a SPIDER Continuous Greedy (SPIDER-CG) algorithm for the monotone case that guarantees a (1 - e - 1) OPT - ε approximation after O (ε - 1) iterations and O (ε - 2) stochastic gradient computations under the mean-squared smoothness assumption. For the non-monotone case, we develop a SPIDER Frank–Wolfe (SPIDER-FW) algorithm that guarantees a 1 4 (1 - min x ∈ C ‖ x ‖ ∞) OPT - ε approximation with O (ε - 1) iterations and O (ε - 2) stochastic gradient estimates. To address the practical challenge associated with a large number of samples per iteration, we introduce a modified gradient estimator based on SPIDER, leading to a Hybrid SPIDER-FW (Hybrid SPIDER-CG) algorithm, which achieves the same approximation guarantee as SPIDER-FW (SPIDER-CG) algorithm with only O (1) samples per iteration. Numerical experiments on both simulated and real data demonstrate the efficiency of the proposed methods. [ABSTRACT FROM AUTHOR]

Inspired from quantum Monte Carlo, by sampling discrete and continuous variables at the same time using the Metropolis–Hastings algorithm, we present a novel, fast, and accurate high performance Monte Carlo Parametric Expectation Maximization (MCPEM) algorithm. We named it Randomized Parametric Expectation Maximization (RPEM). We compared RPEM with NONMEM's Importance Sampling Method (IMP), Monolix's Stochastic Approximation Expectation Maximization (SAEM), and Certara's Quasi‐Random Parametric Expectation Maximization (QRPEM) for a realistic two‐compartment voriconazole model with ordinary differential equations using simulated data. We show that RPEM is as fast and as accurate as the algorithms IMP, QRPEM, and SAEM for the voriconazole model in reconstructing the population parameters, for the normal and log‐normal cases. [ABSTRACT FROM AUTHOR]

In 1976–1977, Polyak published in the journal Avtomatica i Telemekhanika (Automation and Remote Control) two remarkable papers on how to study the properties of estimates of iterative pseudogradient algorithms. The first paper published in 1976 considered the general case based on the stochastic Lyapunov function, and the second one considered the linear case. The assumptions formulated in these papers and the estimates obtained in them can still be considered the state-of-the art. In the current paper, Polyak's approach is applied to the study of the properties of estimates of a (randomized) stochastic approximation search algorithm for the case of unknown-but-bounded noise in observations. The obtained asymptotic estimates were already known earlier, and exact estimates for a finite number of observations are published for the first time. [ABSTRACT FROM AUTHOR]

This article deals with the active redundancy allocation to coherent systems. We extend the optimal allocation policy uniformly maximizing the redundant system reliability function to that maximizing the mean lower semi-deviation of the redundant system lifetime, and then we propose a stochastic algorithm to approximate the optimal redundancy allocation policy through maximizing the mean lower semi-deviation of the system lifetime. Some numerical examples are presented to illustrate the algorithm as well. [ABSTRACT FROM AUTHOR]

We propose a new class of weak approximation schemes for stochastic differential equations with coefficients of suplinearly growth. Both the modified weak Euler schemes and the drift-implicit weak Euler scheme are studied. Under certain non-globally Lipschitz conditions, the proposed schemes are proved to have first-order convergence in the weak sense. Numerical experiments are included to confirm the theoretical results. [ABSTRACT FROM AUTHOR]

It is shown that higher-order influence functions for M-estimators are mathematically equivalent to higher-order stochastic approximations to these estimators. The stochastic expansions are also shown to have corresponding higher-order U-statistic representations, providing an alternative approach for deriving and analyzing the approximate properties of M-estimators. [ABSTRACT FROM AUTHOR]

Recently, Kovács et al. considered a Mittag‐Leffler Euler integrator for a stochastic semilinear Volterra integral‐differential equation with additive noise and proved the strong convergence error estimates [see SIAM J. Numer. Anal. 58(1) 2020, pp. 66‐85]. In this article, we shall consider the Mittag‐Leffler integrators for more general models: stochastic semilinear subdiffusion and superdiffusion driven by fractionally integrated additive noise. The mild solutions of our models involve four different Mittag‐Leffler functions. We first consider the existence, uniqueness and the regularities of the solutions. We then introduce the full discretization schemes for solving the problems. The temporal discretization is based on the Mittag‐Leffler integrators and the spatial discretization is based on the spectral method. The optimal strong convergence error estimates are proved under the reasonable assumptions for the semilinear term and for the regularity of the noise. Numerical examples are given to show that the numerical results are consistent with the theoretical results. [ABSTRACT FROM AUTHOR]

In this work, we conduct the first systematic study of stochastic variational inequality (SVI) and stochastic saddle point (SSP) problems under the constraint of differential privacy (DP). We propose two algorithms: Noisy Stochastic Extragradient (NSEG) and Noisy Inexact Stochastic Proximal Point (NISPP). We show that a stochastic approximation variant of these algorithms attains risk bounds vanishing as a function of the dataset size, with respect to the strong gap function; and a sampling with replacement variant achieves optimal risk bounds with respect to a weak gap function. We also show lower bounds of the same order on weak gap function. Hence, our algorithms are optimal. Key to our analysis is the investigation of algorithmic stability bounds, both of which are new even in the nonprivate case. The dependence of the running time of the sampling with replacement algorithms, with respect to the dataset size n, is n 2 for NSEG and O ~ (n 3 / 2) for NISPP. [ABSTRACT FROM AUTHOR]

The aim of this article is to obtain convergence in mean in the uniform topology of piecewise linear approximations of stochastic differential equations (SDEs) with C1 drift and C2 diffusion coefficients with uniformly bounded derivatives. Convergence analyses for such Wong-Zakai approximations most often assume that the coefficients of the SDE are uniformly bounded. Almost sure convergence in the unbounded case can be obtained using now standard rough path techniques, although Lq convergence appears yet to be established and is of importance for several applications involving Monte-Carlo approximations. We consider L2 convergence in the unbounded case using a combination of traditional stochastic analysis and rough path techniques. We expect our proof technique extend to more general piecewise smooth approximations. [ABSTRACT FROM AUTHOR]

In this paper, we develop a mixed stochastic approximation expectation‐maximization (MSAEM) algorithm coupled with a Gibbs sampler to compute the marginalized maximum a posteriori estimate (MMAPE) of a confirmatory multidimensional four‐parameter normal ogive (M4PNO) model. The proposed MSAEM algorithm not only has the computational advantages of the stochastic approximation expectation‐maximization (SAEM) algorithm for multidimensional data, but it also alleviates the potential instability caused by label‐switching, and then improved the estimation accuracy. Simulation studies are conducted to illustrate the good performance of the proposed MSAEM method, where MSAEM consistently performs better than SAEM and some other existing methods in multidimensional item response theory. Moreover, the proposed method is applied to a real data set from the 2018 Programme for International Student Assessment (PISA) to demonstrate the usefulness of the 4PNO model as well as MSAEM in practice. [ABSTRACT FROM AUTHOR]

We establish an almost sure convergence theorem of the stochastic approximation process of Oja for estimating eigenvectors of the Q-symmetric expectation of a random matrix, under a correlation model between the incoming random matrices. This theorem generalizes previous theorems and extends them to the case where the metric Q is unknown and estimated online in parallel. We apply it to streaming principal component analysis of a random vector Z, when a mini-batch of observations of Z is used at each step or all the observations up to the current step. We deal with the case of streaming generalized canonical correlation analysis, with a metric estimated online in parallel. [ABSTRACT FROM AUTHOR]

Beyond solar and wind energy, wave energy is gaining great interest due to its very high theoretical potential, although its stochastic nature causes intermittent and fluctuating power production. Energy storage system (ESS) integration to wave energy converter (WEC) plants represents a promising solution to mitigate this issue. To overcome the technological limits of the single storage devices, the hybridization of complementary ESSs represents an effective solution, extending the operating range over different timeframes. This paper analyzes the benefits of Li-ion battery–supercapacitor hybrid ESS integration into a grid-connected WEC, aiming at smoothing the produced power oscillations. The hybridization concept involves coupling a power-intensive technology, such as a supercapacitor devoted to managing fluctuations at higher frequency, with a battery technology exploited to manage power variations over longer timeframes to mitigate degradation issues. In this study, a multi-objective data-driven power management strategy, based on the simultaneous perturbation stochastic approximation (SPSA) algorithm, is implemented to minimize power fluctuations in terms of power ramp (representing the power variation between two consecutive values with a 1 s time step), both at the Point of Common Coupling (PCC) and the Li-ion battery terminals, thanks to the supercapacitor peak-shaving function. The SPSA management strategy, together with a suitable sizing procedure, allows a reduction of more than 70% in the power oscillations at the PCC with respect to those at the WEC terminals, while decreasing battery stress by more than 25% if compared to a non-hybrid ESS consisting of a Li-ion battery. This shows how supercapacitor features can extend battery lifespan when integrated in a hybrid ESS. [ABSTRACT FROM AUTHOR]

A popular approach to the simulation of multivariate, non-normal data in the social sciences is to define a multivariate normal distribution first, and then alter its lower-dimensional marginals to achieve the shape of the distribution intended by the researchers. A consequence of this process is that the correlation structure is altered, so further methods are needed to specify an intermediate correlation matrix in the multivariate normal distribution step. Most of the techniques available in the literature estimate this intermediate correlation matrix bivariately (i.e., correlation by correlation), risking the possibility of generating a non-positive definite matrix. The present article addresses this issue by offering an algorithm that estimates all elements of the intermediate correlation matrix simultaneously, through stochastic approximation. A small simulation study demonstrates the feasibility of the present method to induce the correlation structure both in simulated and empirical data. [ABSTRACT FROM AUTHOR]

We present new stellarator equilibria that have been optimized for reduced turbulent transport using nonlinear gyrokinetic simulations within the optimization loop. The optimization routine involves coupling the pseudo-spectral GPU-native gyrokinetic code GX with the stellarator equilibrium and optimization code DESC. Since using GX allows for fast nonlinear simulations, we directly optimize for reduced nonlinear heat fluxes. To handle the noisy heat flux traces returned by these simulations, we employ the simultaneous perturbation stochastic approximation (SPSA) method that only uses two objective function evaluations for a simple estimate of the gradient. We show several examples that optimize for both reduced heat fluxes and good quasi-symmetry as a proxy for low neoclassical transport. Finally, we run full transport simulations using the T3D stellarator transport code to evaluate the changes in the macroscopic profiles. [ABSTRACT FROM AUTHOR]

We establish theoretical properties of the solution to a two-variance-driven interest rate model with super-linear coefficient terms. Since this model is not tractable analytically, we construct an implementable numerical method to approximate it and prove the finite-time strong convergence theory under the local Lipschitz condition. Finally, we provide simulation examples to demonstrate the theoretical results. [ABSTRACT FROM AUTHOR]

In this work, we develop a multifactor approximation for d-dimensional Stochastic Volterra Equations (SVE) with Lipschitz coefficients and kernels of completely monotone type that may be singular. First, we prove an L^2-estimation between two SVEs with different kernels, which provides a quantification of the error between the SVE and any multifactor Stochastic Differential Equation (SDE) approximation. For the particular rough kernel case with Hurst parameter lying in (0,1/2), we propose various approximating multifactor kernels, state their rates of convergence and illustrate their efficiency for the rough Bergomi model. Second, we study a Euler discretization of the multifactor SDE and establish a convergence result towards the SVE that is uniform with respect to the approximating multifactor kernels. These obtained results lead us to build a new multifactor Euler scheme that reduces significantly the computational cost in an asymptotic way compared to the Euler scheme for SVEs. Finally, we show that our multifactor Euler scheme outperforms the Euler scheme for SVEs for option pricing in the rough Heston model. [ABSTRACT FROM AUTHOR]

We investigate existence, uniqueness and approximation of solutions to stochastic delay differential equations (SDDEs) under Carathéodory-type drift coefficients. Moreover, we also assume that both drift f = f (t , x , z) and diffusion g = g (t , x , z) coefficient are Lipschitz continuous with respect to the space variable x , but only Hölder continuous with respect to the delay variable z. We provide a construction of randomized Euler scheme for approximation of solutions of Carathéodory SDDEs, and investigate its upper error bound. Finally, we report results of numerical experiments that confirm our theoretical findings. [ABSTRACT FROM AUTHOR]

This paper studies the convergence of mean field games (MFGs) with finite state space to MFGs with a continuous state space. We examine a space discretization of a diffusive dynamics, which is reminiscent of the Markov chain approximation method in stochastic control, but also of finite difference numerical schemes; time remains continuous in the discretization, and the time horizon is arbitrarily long. We are mainly interested in the convergence of the solution of the associated master equations as the number of states tends to infinity. We present two approaches, to treat the case without or with common noise, both under monotonicity assumptions. The first one uses the system of characteristics of the master equation, which is the MFG system, to establish a convergence rate for the master equations without common noise and the associated optimal trajectories, both when there is a smooth solution to the limit master equation and when there is not. The second approach relies on the notion of monotone solutions introduced by [8, 9]. In the presence of common noise, we show convergence of the master equations, with a convergence rate if the limit master equation is smooth, and by compactness arguments otherwise. [ABSTRACT FROM AUTHOR]

This article proposes an identification method of continuous-time fractional-order Hammerstein model using smoothed functional algorithm with a norm-limited update vector (NL-SFA). In particular, the standard smoothed functional algorithm (SFA) based method is modified by implementing a limit function in the update vector of the standard SFA based method to solve the issue of high tendency of divergence during the identification process. As a result of this, the proposed NL-SFA based method is applied to identify the variables of the linear and non-linear subsystems in the Hammerstein model. While most of the actual linear subsystems can be naturally expressed in a continuous-time domain, the implementation of the fractional-order could also reduce the computational complexity in finding a more accurate reduced-order model. Moreover, three experiments of the Hammerstein model identification based on a numerical example, an actual twin-rotor system, and an actual flexible manipulator system were carried out in this study to verify the effectiveness of the proposed NL-SFA-based method. The numerical and experimental results were analyzed to correspond to the measurement of the objective function and variable identification error and time-domain and frequency-domain responses. Conclusively, the proposed NL-SFA-based method can provide stable convergence and significantly better accuracy of the Hammerstein model in the numerical example, the actual twin-rotor system, and the flexible manipulator system compared to the standard SFA. Moreover, the proposed NL-SFA also provides slightly competitive identification accuracy with the existing norm-limited simultaneous perturbation stochastic approximation (NL-SPSA) and the average multi-verse optimizer sine cosine algorithm (AMVO-SCA) based methods. [ABSTRACT FROM AUTHOR]

We consider a numerical approximation for stochastic fractional differential equations driven by integrated multiplicative noise. The fractional derivative is in the Caputo sense with the fractional order  α ∈ (0 , 1) , and the non-linear terms satisfy the global Lipschitz conditions. We first approximate the noise with the piecewise constant function to obtain the regularized stochastic fractional differential equation. By applying Minkowski's inequality for double integrals, we establish that the error between the exact solution and the solution of the regularized problem has an order of  O (Δ t α)  in the mean square norm, where  Δ t  denotes the step size. To validate our theoretical conclusions, numerical examples are presented, demonstrating the consistency of the numerical results with the established theory. [ABSTRACT FROM AUTHOR]

The paper provides a precise error estimate for an asymptotic expansion of a certain stochastic control problem related to relative entropy minimization. In particular, it is shown that the expansion error depends on the regularity of functionals on path space. An efficient numerical scheme based on a weak approximation with Monte Carlo simulation is employed to implement the asymptotic expansion in multidimensional settings. Throughout numerical experiments, it is confirmed that the approximation error of the proposed scheme is consistent with the theoretical rate of convergence. [ABSTRACT FROM AUTHOR]

AbstractEstimating free energy differences, an important problem in computational drug discovery and in a wide range of other application areas, commonly involves a computationally intensive process of sampling a family of high-dimensional probability distributions and a procedure for computing estimates based on those samples. The variance of the free energy estimate of interest typically depends strongly on how the total computational resources available for sampling are divided among the distributions, but determining an efficient allocation is difficult without sampling the distributions. Here we introduce the Times Square sampling algorithm, a novel on-the-fly estimation method that dynamically allocates resources in such a way as to significantly accelerate the estimation of free energies and other observables, while providing rigorous convergence guarantees for the estimators. We also show that it is possible, surprisingly, for on-the-fly free energy estimation to achieve lower asymptotic variance than the maximum-likelihood estimator MBAR, raising the prospect that on-the-fly estimation could reduce variance in a variety of other statistical applications. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

Developing automatic history matching (AHM) methods to replace the traditional manual history matching (MHM) approach in adjusting the permeability distribution of the reservoir simulation model has been studied by many authors. Because permeability values need to be evaluated at hundreds of thousands of grid cells in a typical reservoir simulation model, it is necessary to apply a reparameterization technique to allow the optimization algorithms to be implemented with fewer variables. In basic reparameterization techniques including zonation and pilot point methods, the calibrations are usually based solely on the production data with no systematic link to the geological and geophysical data, and therefore, the obtained permeability distribution may be not geologically consistent. Several other reparameterization techniques have attempted to preserve geological consistency by incorporating 4D seismic data; however, these techniques cannot be applied to our fractured basement reservoirs (FBRs) as they do not have 4D seismic data. Taking into account these challenges, in this study, an AHM methodology and workflow have been developed using a new reparameterization technique. This approach attempts to minimize the potential for geological nonconsistency of the calibrated results by linking the permeability to geophysical data. The proposed methodology can be applied to fields with only traditional geophysical data (3D seismic and conventional well logs). In the proposed workflow, the spatial distributions of seismic attributes and geomechanical properties were calculated and estimated from 3D seismic data and well logs, respectively. After that, a feed-forward artificial neural network (ANN) model trained by the back-propagation algorithm of the relationship between initial permeability with seismic attributes and geomechanical properties of their grid cell values is developed. Then, the calibration of the permeability distribution is performed by adjustment of the ANN model. Modification of the ANN model is performed using the simultaneous perturbation stochastic approximation (SPSA) algorithm to calibrate transmission coefficients in the ANN model to minimize the discrepancy between the simulated results and observed data. The developed methodology is applied to calibrate the permeability distribution of a simulation model of Bach Ho FBR in Vietnam. The effectiveness of the methodology is evident by comparing the historical matches with an available manually history-matched simulation model. The application shows that the proposed methodology could be considered as a suitable practical approach for adjusting the permeability distribution for FBR reservoir simulation models. [ABSTRACT FROM AUTHOR]

We develop a flexible stochastic approximation framework for analyzing the long-run behavior of learning in games (both continuous and finite). The proposed analysis template incorporates a wide array of popular learning algorithms, including gradient-based methods, the exponential/multiplicative weights algorithm for learning in finite games, optimistic and bandit variants of the above, etc. In addition to providing an integrated view of these algorithms, our framework further allows us to obtain several new convergence results, both asymptotic and in finite time, in both continuous and finite games. Specifically, we provide a range of criteria for identifying classes of Nash equilibria and sets of action profiles that are attracting with high probability, and we also introduce the notion of coherence, a game-theoretic property that includes strict and sharp equilibria, and which leads to convergence in finite time. Importantly, our analysis applies to both oracle-based and bandit, payoff-based methods—that is, when players only observe their realized payoffs. [ABSTRACT FROM AUTHOR]

We consider a class of stochastic optimal control problems with partial observation, and study their approximation by discrete-time control problems. We establish a convergence result by using the weak convergence technique of Kushner and Dupuis [Numerical Methods for Stochastic Control Problems in Continuous Time, Springer, New York], together with the notion of relaxed control rule introduced by El Karoui, Huú Nguyen and Jeanblanc-Picqué [SIAM J. Control Optim., 26 (1988), pp. 1025--1061]. In particular, with a well chosen discrete-time control system, we obtain a first implementable numerical algorithm (with convergence) for the partially observed control problem. Moreover, our discrete-time approximation result would open the door to study convergence of more general numerical approximation methods, such as machine learning based methods. Finally, we illustrate our convergence result by numerical experiments on a partially observed control problem in a linear quadratic setting. [ABSTRACT FROM AUTHOR]

In this study, we consider a class of multiple-drawing opposite-reinforcing urns with time-dependent replacement rules. The class has the symmetric property of a Friedman-type urn. We divide the class into a small-increment regime and a large-increment regime. For small-increment schemes, we prove almost-sure convergence and a central limit theorem for the proportion of white balls by stochastic approximation. For large-increment schemes, by assuming the affinity condition, we show almost-sure convergence of the proportion of white balls by martingale theory and present a way to identify the limit distribution of the proportion of white balls. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this research paper is to recover the autonomous flight performance of a mini unmanned aerial vehicle (UAV) via stochastically optimizing the wing over certain parameters (i.e. wing taper ratio and wing aspect ratio) while there are lower and upper constraints on these redesign parameters. Design/methodology/approach: A mini UAV is produced in the Iskenderun Technical University (ISTE) Unmanned Aerial Vehicle Laboratory. Its complete wing can vary passively before the flight with respect to the result of the stochastic redesign of the wing while maximizing autonomous flight performance. Flight control system (FCS) parameters (i.e. gains of longitudinal and lateral proportional-integral-derivative controllers) and wing redesign parameters mentioned before are simultaneously designed to maximize autonomous flight performance index using a certain stochastic optimization strategy named as simultaneous perturbation stochastic approximation (SPSA). Found results are used while composing UAV flight simulations. Findings: Using stochastic redesign of mini UAV and simultaneously designing mini ISTE UAV over previously mentioned wing parameters and FCS, it obtained a maximum UAV autonomous flight performance. Research limitations/implications: Permission of the directorate general of civil aviation in the Republic of Türkiye is essential for real-time UAV autonomous flights. Practical implications: Stochastic redesign of mini UAV and simultaneously designing mini ISTE UAV wing parameters and FCS approach is very useful for improving any mini UAV autonomous flight performance cost index. Social implications: Stochastic redesign of mini UAV and simultaneously designing mini ISTE UAV wing parameters and FCS approach succeeds confidence, highly improved autonomous flight performance cost index and easy service demands of mini UAV operators. Originality/value: Creating a new approach to recover autonomous flight performance cost index (e.g. satisfying less settling time and less rise time, less overshoot during flight trajectory tracking) of a mini UAV and composing a novel procedure performing simultaneous mini UAV having passively morphing wing over certain parameters while there are upper and lower constraints and FCS design idea. [ABSTRACT FROM AUTHOR]

We present an embedded fragment approach for high-level quantum chemical calculations on local features in periodic systems. The fragment is defined as a set of localized orbitals (occupied and virtual) corresponding to a converged periodic Hartree–Fock solution. These orbitals serve as the basis for the in-fragment post-Hartree–Fock treatment. The embedding field for the fragment, consisting of the Coulomb and exchange potential from the rest of the crystal, is included in the fragment's one-electron Hamiltonian. As an application of the embedded fragment approach, we investigate the performance of full configuration interaction quantum Monte Carlo (FCIQMC) with the adaptive shift. As the orbital choice, we use the natural orbitals from the distinguishable cluster method with singles and doubles. FCIQMC is a stochastic approximation to the full CI method and can be routinely applied to much larger active spaces than the latter. This makes this method especially attractive in the context of open shell defects in crystals, where fragments of adequate size can be rather large. As a test case, we consider dissociation of a fluorine atom from a fluorographane surface. This process poses a challenge for high-level electronic structure models as both the static and dynamic correlations are essential here. Furthermore, the active space for an adequate fragment (32 electrons in 173 orbitals) is already quite large even for FCIQMC. Despite this, FCIQMC delivers accurate dissociation and total energies. [ABSTRACT FROM AUTHOR]

We study a system of M particles with jump dynamics on a network of N sites. The particles can exist in two states, active or inactive. Only the former can jump. The state of each particle depends on its position. A given particle is inactive when it is at a given site, and active when it moves to a change site. Indeed, each sleeping particle activates at a rate λ > 0 , leaves its initial site, and moves for an exponential random time of parameter μ > 0 before uniformly landing at a site and immediately returning to sleep. The behavior of each particle is independent of that of the others. These dynamics conserve the total number of particles; there is no limit on the number of particles at a given site. This system can be represented by a continuous-time Pólya urn with M balls where the colors are the sites, with an additional color to account for particles on the move at a given time t. First, using this Pólya interpretation for fixed M and N, we obtain the average number of particles at each site over time and, therefore, those on the move due to mass conservation. Secondly, we consider a large system in which the number of particles M and the number of sites N grow at the same rate, so that the M / N ratio tends to a scaling constant α > 0 . Using the moment-generating function technique added to some probabilistic arguments, we obtain the long-term distribution of the number of particles at each site. [ABSTRACT FROM AUTHOR]

The Steam Generator (SG) is a crucial component of a Nuclear Power Plant (NPP), generating steam to transfer heat from the primary loop to the secondary loop. The control performance of the Steam Generator Level Control System (SGLCS) plays a crucial role in the normal operation of the SG. To improve the system's performance, the parameters of the control system should be optimized. However, the steam generator and its corresponding control system are highly complex, exhibiting nonlinearity and time-varying properties. Conventional parameter-setting methods mainly rely on engineers' experience, and are laborious and time-intensive. To tackle the aforementioned challenges, a Model-Free Optimization (MFO) method based on Knowledge-informed Historical Gradient-based Simultaneous Perturbation Stochastic Approximation (GK-SPSA) is applied to the performance optimization of the steam generator level control system. The GK-SPSA algorithm is a variant of the traditional SPSA algorithm. The fundamental idea of this revised algorithm is to maximize the utilization of historical gradient information generated during the optimization process of the SPSA algorithm, with the aim of enhancing overall algorithm performance in a model-free optimization context. Based on the effective utilization of historical gradient information, the GK-SPSA algorithm exhibits two improvements over the SPSA algorithm. The first improvement is related to the recognition of the online optimization progress, utilizing the state of the optimization progress to dynamically adjust the optimization step size. The second improvement is related to gradient estimation compensation, employing compensation rules to enhance the accuracy of gradient estimation, thus improving the optimization efficiency. Through simulation experiments, it can be observed that there is not much difference in the final iteration values among the GK-SPSA, IK-SPSA, and SPSA methods. However, the iteration count of GK-SPSA is reduced by about 20% compared to SPSA and by 11.11% compared to Knowledge-informed SPSA (IK-SPSA). The results indicate that this method can significantly improve the efficiency of parameter tuning for the liquid level control system of a steam generator. [ABSTRACT FROM AUTHOR]

In a recent paper, Lanconelli and Scorolli10 extended to the multidimensional case a Wong–Zakai-type approximation for Itô stochastic differential equations (SDEs) proposed by Øksendal and Hu7. The aim of this paper is to extend the latter result to system of SDEs of Itô type driven by fractional Brownian motion (fBm) like those considered by Hu6. This extension is not trivial since the covariance structure of the fBm precludes us from using the same approach as that used by Lanconelli and Scorolli. Instead we employ a truncated Cameron–Martin expansion as the approximation for the fBm. We are naturally led to the investigation of a semilinear hyperbolic system of evolution equations in several space variables that we utilize for constructing a solution of the Wong–Zakai approximated systems. We show that the law of each element of the approximating sequence solves in the sense of distribution a Fokker–Planck equation and that the sequence converges to the solution of the Itô equation, as the number of terms in the expansion goes to infinite. [ABSTRACT FROM AUTHOR]

The recent emergence of reinforcement learning (RL) has created a demand for robust statistical inference methods for the parameter estimates computed using these algorithms. Existing methods for inference in online learning are restricted to settings involving independently sampled observations, while inference methods in RL have so far been limited to the batch setting. The bootstrap is a flexible and efficient approach for statistical inference in online learning algorithms, but its efficacy in settings involving Markov noise, such as RL, has yet to be explored. In this article, we study the use of the online bootstrap method for inference in RL policy evaluation. In particular, we focus on the temporal difference (TD) learning and Gradient TD (GTD) learning algorithms, which are themselves special instances of linear stochastic approximation under Markov noise. The method is shown to be distributionally consistent for statistical inference in policy evaluation, and numerical experiments are included to demonstrate the effectiveness of this algorithm across a range of real RL environments. for this article are available online. [ABSTRACT FROM AUTHOR]

The article summarizes a thesis which examined the theory and application of Monte Carlo methods and variance reduction techniques in structural reliability analysis. The study investigated sampling and change of measure on simplices, batching adaptive variance reduction, dynamic finite-budget allocation of stratified sampling with adaptive variance reduction by strata, adaptive stratified sampling for structural reliability analysis, and adaptive stratified directional importance sampling.

Finite-sum problems appear as the sample average approximation of a stochastic optimization problem and often arise in machine learning applications with large scale data sets. A very popular approach to face finite-sum problems is the stochastic gradient method. It is well known that a proper strategy to select the hyperparameters of this method (i.e. the set of a-priori selected parameters) and, in particular, the learning rate, is needed to guarantee convergence properties and good practical performance. In this paper, we analyse standard and line search based updating rules to fix the learning rate sequence, also in relation to the size of the mini batch chosen to compute the current stochastic gradient. An extensive numerical experimentation is carried out in order to evaluate the effectiveness of the discussed strategies for convex and non-convex finite-sum test problems, highlighting that the line search based methods avoid expensive initial setting of the hyperparameters. The line search based approaches have also been applied to train a Convolutional Neural Network, providing very promising results. [ABSTRACT FROM AUTHOR]

In this paper, we shall prove an L^{p}(p>2) strong convergence rate of the non-adapted Wong-Zakai approximation for stochastic differential equations with path-dependent coefficients under d_{\infty }-Lipschitz conditions. [ABSTRACT FROM AUTHOR]

Tafolecimab, a novel fully human monoclonal antibody targeting PCSK9, has been assessed in Chinese healthy volunteers and patients with hypercholesterolemia. This analysis is to develop and qualify a population pharmacokinetics (PopPKs)/LDL‐C model to characterize tafolecimab PK and LDL‐C profiles, evaluate the impact of potential covariates on tafolecimab, estimate individual predicted exposure, and LDL‐C decreasing, furthermore, explore exposure–response relationship to support clinical use. Data from six clinical trials in China were used to develop the PopPK/LDL‐C model. A Michaelis–Menten approximation of the target‐mediated drug disposition (TMDD) model was used to describe PK data and indirect response (IDR) model was developed to estimate the LDL‐C profile. A stochastic approximation expectation maximization algorithm was applied to estimate PopPK/LDL‐C parameters. The PK/LDL‐C time course data for tafolecimab were well described by TMDD/IDR model. Baseline covariates resulting in statistically significant changes in PK/LDL‐C parameters included: body weight and sex on absorption rate constant; body weight, sex, and unbound PCSK9 on central volume; body weight and sex on clearance; baseline LDL‐C on first‐order rate constants for the removal of an effect); and disease and sex on maximum effect. However, the magnitudes of changes associated with these covariates do not necessitate dose adjustment. Exposure–efficacy relationship indicated that the nadir of LDL‐C reduction achieved with the steady‐state trough plasma concentration (Ctrough) of tafolecimab at 5 μg/mL, and no further LDL‐C decreasing with the increasing Ctrough. There was no exposure dependency observed in exposure‐safety exploration. The PopPK/LDL‐C model was successfully developed, validated, and predicted tafolecimab/LDL‐C concentrations and individual exposures. [ABSTRACT FROM AUTHOR]

In this work, we propose an extension of a semiparametric nonlinear mixed‐effects model for longitudinal data that incorporates more flexibility with penalized splines (P‐splines) as smooth terms. The novelty of the proposed approach consists of the formulation of the model within the stochastic approximation version of the EM algorithm for maximum likelihood, the so‐called SAEM algorithm. The proposed approach takes advantage of the formulation of a P‐spline as a mixed‐effects model and the use of the computational advantages of the existing software for the SAEM algorithm for the estimation of the random effects and the variance components. Additionally, we developed a supervised classification method for these non‐linear mixed models using an adaptive importance sampling scheme. To illustrate our proposal, we consider two studies on pregnant women where two biomarkers are used as indicators of changes during pregnancy. In both studies, information about the women's pregnancy outcomes is known. Our proposal provides a unified framework for the classification of longitudinal profiles that may have important implications for the early detection and monitoring of pregnancy‐related changes and contribute to improved maternal and fetal health outcomes. We show that the proposed models improve the analysis of this type of data compared to previous studies. These improvements are reflected both in the fit of the models and in the classification of the groups. [ABSTRACT FROM AUTHOR]

Emphatic temporal-difference (ETD) learning (Sutton et al. 2016) is a pioneering off-policy reinforcement learning method involving the use of the followon trace. The recently proposed gradient emphasis learning (GEM, Zhang et al. 2020) algorithm is used to fix the problems of unbounded variance and large emphasis approximation error introduced by the followon trace from the perspective of stochastic approximation. In this paper, we rethink GEM and introduce a novel generalized GEM(β ) algorithm to learn the true emphasis. The key to the construction of the generalized GEM(β ) algorithm is introducing a tunable hyperparameter β that is not necessarily the same as the discount factor γ to the GEM operator. We then apply the emphasis estimated by the proposed GEM(β ) algorithm to the value estimation gradient and the policy gradient, respectively, yielding the corresponding ETD variant for off-policy evaluation (OPE) and actor-critic algorithm for off-policy control. Finally, we empirically demonstrate the advantages of the proposed algorithms on the diagnostic linear OPE benchmark as well as classic control tasks with neural network function approximators. [ABSTRACT FROM AUTHOR]

Motivated by the applications in leader-follower multi-agent dynamics, a class of optimal control problems is investigated, where the goal is to influence the behavior of a given population through another controlled one interacting with the first. The evolution of the systems obeys a non-linear Fokker–Planck-type equation as diffusive terms accounting for randomness in the evolution are taken into account. A well-posedness theory under very low regularity of the control vector fields is developed, as well as a rigorous mean-field limit of a stochastic particle approximation. [ABSTRACT FROM AUTHOR]

Background: The use of mixed effect models with a specific functional form such as the Sigmoidal Mixed Model and the Piecewise Mixed Model (or Changepoint Mixed Model) with abrupt or smooth random change allows the interpretation of the defined parameters to understand longitudinal trajectories. Currently, there are no interface R packages that can easily fit the Sigmoidal Mixed Model allowing the inclusion of covariates or incorporating recent developments to fit the Piecewise Mixed Model with random change. Results: To facilitate the modeling of the Sigmoidal Mixed Model, and Piecewise Mixed Model with abrupt or smooth random change, we have created an R package called nlive. All needed pieces such as functions, covariance matrices, and initials generation were programmed. The package was implemented with recent developments such as the polynomial smooth transition of the piecewise mixed model with improved properties over Bacon-Watts, and the stochastic approximation expectation-maximization (SAEM) for efficient estimation. It was designed to help interpretation of the output by providing features such as annotated output, warnings, and graphs. Functionality, including time and convergence, was tested using simulations. We provided a data example to illustrate the package use and output features and interpretation. The package implemented in the R software is available from the Comprehensive R Archive Network (CRAN) at https://CRAN.R-project.org/package=nlive. Conclusions: The nlive package for R fits the Sigmoidal Mixed Model and the Piecewise Mixed: abrupt and smooth. The nlive allows fitting these models with only five mandatory arguments that are intuitive enough to the less sophisticated users. [ABSTRACT FROM AUTHOR]

This paper studies a general class of stochastic population processes in which agents interact with one another over a network. Agents update their behaviors in a random and decentralized manner according to a policy that depends only on the agent's current state and an estimate of the macroscopic population state, given by a weighted average of the neighboring states. When the number of agents is large and the network is a complete graph (has all-to-all information access), the macroscopic behavior of the population can be well-approximated by a set of deterministic differential equations called a mean-field approximation. For incomplete networks such characterizations remained previously unclear, i.e., in general whether a suitable mean-field approximation exists for the macroscopic behavior of the population. The paper addresses this gap by establishing a generic theory describing when various mean-field approximations are accurate for arbitrary interaction structures. Our results are threefold. Letting W be the matrix describing agent interactions, we first show that a simple mean-field approximation that incorrectly assumes a homogeneous interaction structure is accurate provided W has a large spectral gap. Second, we show that a more complex mean-field approximation which takes into account agent interactions is accurate as long as the Frobenius norm of W is small. Finally, we compare the predictions of the two mean-field approximations through simulations, highlighting cases where using mean-field approximations that assume a homogeneous interaction structure can lead to inaccurate qualitative and quantitative predictions. [ABSTRACT FROM AUTHOR]

We introduce a variant of the multiplicative Sewing Lemma in [Gerasimovičs, Hocquet, Nilssen; J. Funct. Anal. 281 (2021)] which yields arbitrary high order weak approximations to stochastic differential equations, extending the cubature approximation on Wiener space introduced by Lyons and Victoir. Our analysis allows to derive stability estimates and explicit weak convergence rates. As a particular example, a cubature approximation for stochastic differential equations driven by continuous Gaussian martingales is given. [ABSTRACT FROM AUTHOR]

When measuring the value of a function to be minimized is not only expensive but also with noise, the popular simultaneous perturbation stochastic approximation (SPSA) algorithm requires only two function values in each iteration. In this paper, we present a method requiring only one function measurement value per iteration in the average sense. We prove the strong convergence and asymptotic normality of the new algorithm. Limited experimental results demonstrate the effectiveness and potential of our algorithm for solving low-dimensional problems. [ABSTRACT FROM AUTHOR]

Eco-labels are a way to benchmark transportation shipments with respect to their environmental impact. In contrast to an eco-labeling of consumer products, emissions in transportation depend on several operational factors like the mode of transportation (e.g., train or truck) or a vehicle's current and potential future capacity utilization when new orders are added for consolidation. Thus, satisfying eco-labels and doing this cost efficiently is a challenging task when dynamically routing orders in an intermodal network. In this paper, we model the problem as a multiobjective sequential decision process and propose a reinforcement learning method: value function approximation (VFA). VFAs frequently simulate trajectories of the problem and store observed values (violated eco-labels and costs) for states aggregated to a set of features. The observations are used for improved decision making in the next trajectory. For our problem, we face two additional challenges when applying a VFA, the multiple objectives and the "delayed" realization of eco-label satisfaction due to future consolidation. For the first, we propose different feature sets dependent on the objective function's focus: costs or eco-labels. For the latter, we propose enhancing the suboptimal decision making and observed pessimistic primal values within the VFA trajectories with optimistic dual decision making when all information of a trajectory is known ex post. This enhancement is a general methodological contribution to the literature of approximate dynamic programming and will likely improve learning for other problems as well. We show the advantages of both components in a comprehensive study for intermodal transport via trains and trucks in Europe. History: This paper has been accepted for the Transportation Science Special Section on 2021 TSL Workshop: Supply and Demand Interplay in Transport and Logistics. Funding: A. Heinold's work is funded by the Deutsche Forschungsgemeinschaft (DFG) [Project 268276815]. M. Ulmer's work is funded by the Emmy Noether Programme of the DFG [Project 444657906]. This support is gratefully acknowledged. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.1164. [ABSTRACT FROM AUTHOR]

Multilateral wells (MLWs) equipped with multiple flow control devices (FCDs) are becoming increasingly favored within the oil sector due to their ability to enhance well-to-reservoir exposure and effectively handle unwanted fluid breakthrough. However, combining various types of FCDs in multilateral wells poses a complex optimization problem with a large number of highly correlated control variables and a computationally expensive objective function. Consequently, standard optimization algorithms, including metaheuristic and gradient-based approaches, may struggle to identify an optimal solution within a limited computational resource. This paper introduces a novel hybrid optimization (HO) framework combining particle swarm optimization (PSO) and Simultaneous Perturbation Stochastic Approximation (SPSA). It is developed to efficiently optimize the completion design of MLWs with various FCDs while overcoming the individual limitations of each optimization algorithm. The proposed framework is further enhanced by employing surrogate modelling and global sensitivity analysis to identify critical parameters (i.e., highly sensitive) that greatly affect the objective function. This allows for a focused optimization effort on these key parameters, ultimately enhancing global optimization performance. The performance of the novel optimization framework is evaluated using the Olympus benchmark reservoir model. The model is developed by three intelligent dual-lateral wells, with inflow control devices (ICDs) installed within the laterals and interval control valves (ICVs) positioned at the lateral junctions. The results show that the proposed hybrid optimization framework outperforms all industry-standard optimization techniques, achieving a Net Present Value of approximately USD 1.94 billion within a limited simulation budget of 2500 simulation runs. This represents a substantial 26% NPV improvement compared to the open-hole case (USD 1.54 billion NPV). This improvement is attributed to more efficient water breakthrough management, leading to a notable 24% reduction in cumulative water production and, consequently, a 26% increase in cumulative oil production. [ABSTRACT FROM AUTHOR]