A Robust SINDy Approach by Combining Neural Networks and an Integral Form

The discovery of governing equations from data has been an active field of research for decades. One widely used methodology for this purpose is sparse regression for nonlinear dynamics, known as SINDy. Despite several attempts, noisy and scarce data still pose a severe challenge to the success of the SINDy approach. In this work, we discuss a robust method to discover nonlinear governing equations from noisy and scarce data. To do this, we make use of neural networks to learn an implicit representation based on measurement data so that not only it produces the output in the vicinity of the measurements but also the time-evolution of output can be described by a dynamical system. Additionally, we learn such a dynamic system in the spirit of the SINDy framework. Leveraging the implicit representation using neural networks, we obtain the derivative information -- required for SINDy -- using an automatic differentiation tool. To enhance the robustness of our methodology, we further incorporate an integral condition on the output of the implicit networks. Furthermore, we extend our methodology to handle data collected from multiple initial conditions. We demonstrate the efficiency of the proposed methodology to discover governing equations under noisy and scarce data regimes by means of several examples and compare its performance with existing methods

Performance prediction based on employees' job engagement mediated by ethical leadership

Background: Education has a great impact on the social, economic and cultural progress of society. This study's goal was to develop a thorough model for performance prediction that was based on employee job engagement and was mediated by moral leadership. Methods: This study was applied and a descriptive-correlational. The statistical population was included 341 people from employees and managers of the education department in Kerman province. They were chosen at random by a stratified sample. Information was gathered using questionnaires created by the researcher, including a work performance questionnaire with 28 questions, a job engagement questionnaire with 34 questions, and a questionnaire on ethical leadership with 46 questions. Assessing the validity of the components by the Delphi method by surveying 30 experts and the results of fit of the components obtained with AMOS software were determined. The Cronbach's alpha coefficient of the variables was more than 0.7, suggesting that the items were internally coordinated and that the reliability was confirmed. Results: With the increase of behavioral involvement such as commitment to time, intensity and seriousness of work, cognitive involvement such as concentration, work attraction and emotional involvement such as enthusiasm and mental flexibility, along with the rise in ethical leadership, the degree of ethical leadership in education grew, the level of performance, the employment of employees increased. Conclusion: The importance of mediating role of ethical leadership in education department employees in predicting performance based on job engagement can be used by managers in the area of learning and education in the country

Transmission scheduling for multi-process multi-sensor remote estimation via approximate dynamic programming

In this paper, we consider a remote estimation problem where multiple dynamical systems are observed by smart sensors, which transmit their local estimates to a remote estimator over channels prone to packet losses. Unlike previous works, we allow multiple sensors to transmit simultaneously even though they can cause interference, thanks to the multi-packet reception capability at the remote estimator. In this setting, the remote estimator can decode multiple sensor transmissions (successful packet arrivals) as long as their signal-to-interference-and-noise ratios (SINR) are above a certain threshold. In this setting, we address the problem of optimal sensor transmission scheduling by minimizing a finite horizon discounted expected estimation error covariance cost across all systems at the remote estimator, subject to an average transmission cost. While this problem can be posed as a stochastic control problem, the optimal solution requires solving a Bellman equation for a dynamic programming (DP) problem, the complexity of which scales exponentially with the number of systems being measured and their state dimensions. In this paper, we resort to a novel Least Squares Temporal Difference (LSTD) Approximate Dynamic Programming (ADP) based approach to approximating the value function. More specifically, an off-policy based LSTD approach, named in short Enhanced-Exploration Greedy LSTD (EG-LSTD), is proposed. We discuss the convergence analysis of the EG-LSTD algorithm and its implementation. A Python based program is developed to implement and analyse the different aspects of the proposed method. Simulation examples are presented to support the results of the proposed approach both for the exact DP and ADP cases

Ethical leadership status and performance health of Education workers

Background: Ethical managers provide mutual trust in the organization by increasing the authority to act, which increases interest in work. This study was conducted with the aim of investigating the Ethical leadership status and performance health of Education workers. Methods: This study was applied, descriptive and by survey method on 341 Education workers in Kerman province, in which the samples were selected by stratified random method and included in the study. Data collection was done on 46 questions and job performance questionnaire including 28 questions. 30 specialists used the Delphi technique to assess the components' dependability, and AMOS software was installed. A Cronbach's alpha coefficient greater than 0.7 revealed the items' internal consistency and verified their dependability. Software called SPSS-22 was utilized to analyze the data. Results: The results show that the status of ethical leadership and its components are favorable among employees, and the status of job performance and its task dimension are not favorable, and this variable was favorable only in the contextual dimension. The components of job enthusiasm (behavioral, cognitive and emotional) which are considered as predictors of job performance, have a significant difference in which there is a relationship between job enthusiasm and ethical leadership of healthcare workers. Conclusion: The results of job enthusiasm with the mediation of moral leadership show the strengthening of employees' performance health. By identifying the influencing factors related to job performance and work enthusiasm, managers can help to better understand the nature of employees' performance and work enthusiasm

Stochastic dynamic programming solution to transmission scheduling: Multi sensor-multi process with wireless noisy channel

We investigate sensor scheduling for remote estimation when multiple smart sensors monitor multiple stochastic dynamical systems. The sensors transmit their measurements to a remote estimator through a noisy wireless communication channel. Such a remote estimator can receive multiple packets simultaneously sent by local sensors. Sensors transmit their measurements if their Signal Interference and Noise Ratio (SINR) is above a threshold. We compute the optimal policy for sensor scheduling by minimizing expected error covariance subject to total signal transmissions from all sensors. We model this problem as Markov Decision Process (MDP) with discounted cost per stage in the finite time horizon framework, then we employ stochastic Dynamic Programming as the optimization method. A novel algorithm based on sampling and machine learning techniques is proposed as the approximation. At each phase of the DP algorithm, samples are collected using a uniform probability distribution. The data is used to feed Neural Network (NN) and Random Forest (RF) models for cost function and policy approximation. The results of the proposed framework are supported by simulation examples comparing RF and NN as Approximate DP (ADP). Note that this idea builds a bridge among the recent advances in the area of data science, Machine Learning, and the ADP

Applying unweighted least-squares based techniques to stochastic dynamic programming: Theory and application

Big data and the curse of dimensionality are common vocabularies that researchers in different communities have recently been dealing with, e.g. dynamic programming (DP) in automatic control system society. A novel unweighted sampled based least square projection approach is proposed in this study to address the issue of the large state space in the DP optimisation problem. The method, in particular, takes into account both contraction mapping and monotonicity properties of the DP algorithm for value function approximation. Specifically, the batch of samples are gathered by uniform probability distribution at first, and an unweighted LS sub-problem in the subspace is solved. As the case study, a new Markov decision process model associated with a resource allocation problem is considered to illustrate the technique and evaluate its effectiveness. It is noted that the approach can be employed for different applications as well. Moreover, a MATLAB based software is developed to implement and examine different parts of the proposed method. Simulation examples are considered to support the results of the approach via developed software. The idea makes a connection between the recent advances in big data analysis and approximate DP as well

A Lyapunov-based version of the value iteration algorithm formulated as a discrete-time switched affine system

In this paper, we analyse the convergence properties of the Dynamic Programming Value Iteration algorithm by exploiting the stability theory of discrete-time switched affine systems. More specifically, by formulating the Value Iteration algorithm as a switched affine system, a Lyapunov-based optimal policy selection strategy is designed to guarantee the practical stabilisation of the resulting system towards an invariant set of attraction containing a given target value function. The switching control algorithm, referred to as Lyapunov-based Value Iteration algorithm, can be regarded as a convergence analysis tool and can be adopted to verify if and how such target value function can be approached by choosing from a subset of suitable stationary policies, at each time slot. The usage of the proposed algorithm in practice is also discussed. Finally, two different applications are provided to further illustrate and examine the key-aspects of the approach presented

Short-term individual residential load forecasting using an enhanced machine learning-based approach based on a feature engineering framework: A comparative study with deep learning methods

Accurate short-term forecasting of the individual residential load is a challenging task due to the nonlinear behavior of the residential customer. Moreover, there are a large number of features that have impact on the energy consumption of the residential load. Recently, deep learning algorithms are widely used for short-term load forecasting (STLF) of residential load. Although deep learning algorithms are capable of achieving promising results due to their ability in feature extraction, machine learning algorithms are also prone to obtain satisfactory results with lower complexity and easier implementation. Identifying the most dominant features which have the highest impact on residential load is a pragmatic measure to boost the accuracy of STLF. But deep learning algorithms use feature extraction, which leads to the loss of data interpretability due to transforming the data. This paper proposes to improve the accuracy of the individual residential STLF using an enhanced machine learning-based approach via a feature-engineering framework. To this end, various datasets and features such as historical load and climate features are collected. Afterward, correlation analysis and outlier detection via the k-nearest neighbor algorithm are deployed to implement outlier detection. In the next stage, feature selection algorithms are used to identify the foremost dominant features. Additionally, this paper conducts a comparative study between the proposed approach and state-of-the-art deep learning architectures. Eventually, the isolation forest algorithm is used to verify the effectiveness of the proposed approach by identifying anomalous samples and comparing the results of the proposed approach with those of deep learning algorithms

Approximate dynamic programming for stochastic resource allocation problems

A stochastic resource allocation model, based on the principles of Markov decision processes (MDPs), is proposed in this paper. In particular, a general-purpose framework is developed, which takes into account resource requests for both instant and future needs. The considered framework can handle two types of reservations (i.e., specified and unspecified time interval reservation requests), and implement an overbooking business strategy to further increase business revenues. The resulting dynamic pricing problems can be regarded as sequential decision-making problems under uncertainty, which is solved by means of stochastic dynamic programming (DP) based algorithms. In this regard, Bellman’s backward principle of optimality is exploited in order to provide all the implementation mechanisms for the proposed reservation pricing algorithm. The curse of dimensionality, as the inevitable issue of the DP both for instant resource requests and future resource reservations, occurs. In particular, an approximate dynamic programming (ADP) technique based on linear function approximations is applied to solve such scalability issues. Several examples are provided to show the effectiveness of the proposed approac

Enhanced Exploration Least-Squares Methods for Optimal Stopping Problems

This letter presents an Approximate Dynamic Programming (ADP) least-squares based approach for solving optimal stopping problems with a large state space. By extending some previous work in the area of optimal stopping problems, it provides a framework for their formulation and resolution. The proposed method uses a combined on/off policy exploration mechanism, where states are generated by means of state transition probability distributions different from the ones dictated by the underlying Markov decision processes. The contraction mapping property of the associated projected Bellman operator is analysed as well as the convergence of the resulting algorithm