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The problem of a stabilisation system synthesis for the motion of a control object along a given spatial trajectory is considered. The complexity of the problem is that the preset trajectory is defined in the state subspace and not in time. This paper describes a stabilisation system synthesis for motion along a trajectory specified in time and along a trajectory specified in the form of a manifold in a state space. In order to construct a stabilisation system, it is necessary to determine a distance between an object and the given trajectory at each moment in time. For trajectories that are not given in time, the determination of this distance can be ambiguous. An object may be exactly on a trajectory but at a different time. This paper proposes some approaches to solve the problem. One of the approaches is to transform a given trajectory in a state subspace into a trajectory given in time. A description of a universal method to perform this transformation is presented. In order to solve the synthesis problem automatically, without having to analyse the mathematical model of the control object, it is suggested that machine learning control by symbolic regression is used. In computational experiments, examples of stabilisation system syntheses for quadcopter motion along a given spatial trajectory are presented. [ABSTRACT FROM AUTHOR]

The rapidly advancing fields of machine learning and mathematical modeling, greatly enhanced by the recent growth in artificial intelligence, are the focus of this special issue. This issue compiles extensively revised and improved versions of the top papers from the workshop on Mathematical Modeling and Problem Solving at PDPTA'23, the 29th International Conference on Parallel and Distributed Processing Techniques and Applications. Covering fundamental research in matrix operations and heuristic searches to real-world applications in computer vision and drug discovery, the issue underscores the crucial role of supercomputing and parallel and distributed computing infrastructure in research. Featuring nine key studies, this issue pushes forward computational technologies in mathematical modeling, refines techniques for analyzing images and time-series data, and introduces new methods in pharmaceutical and materials science, making significant contributions to these areas. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel approach to solving theorem proving problems without relying on any deduction method. We transform logical formulas into numbers, vectors and matrices, and feed the corresponding data into various machine learning algorithms to predict their satisfiability. Here, we introduce ProverX, a novel theorem prover that utilizes various binary classification algorithms, ranging from traditional machine learning to deep learning, to tackle the satisfiability (SAT) problem of propositional logic. Empirical experiments were conducted to evaluate the performance of ProverX using datasets we generated. ProverX achieved accuracy rates ranging from 81.8% to 98.7%, demonstrating a remarkable speedup of almost 180 times compared to CTL-RP, a highly efficient prover. These results demonstrate the feasibility of replacing deduction with learning in theorem proving, opening promising avenues for further exploration in more complex logics, e.g., Modal Logic, Coalition Logic, Propositional Linear-Time Temporal Logic, Computation Tree Logic, etc., provided that their resolution methods exist. We also present a detailed analysis of the best-performing machine learning approaches for this task and introduce a new algorithm, IPDA, which has the potential to further enhance performance. [ABSTRACT FROM AUTHOR]

Many methods exist for solving the problem of evaluating efficiency in different processes. They are divided into two basic groups, parametric and non-parametric methods, which can have significant differences in the results. In this study, the authors consider the process of assessing the business climate depending on realized foreign investments. Due to the expected difference in efficiency assessment using different approaches, the goal of this paper is to create an optimization model of an ensemble for efficiency assessment that uses both types of methods with the aim of creating a symmetrical approach that achieves better results than each type of method individually. The proposed solution simultaneously analyzes the impact of different factors on foreign investments in order to determine the most important factors and thus enable each local government to ensure the best possible efficiency in this process. The innovative idea of this study is in the inclusion of classification and feature selection methods of machine learning to fulfill the set goal. Our research, focused on a specific case study in various cities across the Republic of Serbia, evaluated the effectiveness of that process. This study extends previous research and confirms the published results, highlighting the advantages of the newly proposed model. [ABSTRACT FROM AUTHOR]

In numerous scientific disciplines and practical applications, addressing optimization challenges is a common imperative. Nature-inspired optimization algorithms represent a highly valuable and pragmatic approach to tackling these complexities. This paper introduces Dendritic Growth Optimization (DGO), a novel algorithm inspired by natural branching patterns. DGO offers a novel solution for intricate optimization problems and demonstrates its efficiency in exploring diverse solution spaces. The algorithm has been extensively tested with a suite of machine learning algorithms, deep learning algorithms, and metaheuristic algorithms, and the results, both before and after optimization, unequivocally support the proposed algorithm's feasibility, effectiveness, and generalizability. Through empirical validation using established datasets like diabetes and breast cancer, the algorithm consistently enhances model performance across various domains. Beyond its working and experimental analysis, DGO's wide-ranging applications in machine learning, logistics, and engineering for solving real-world problems have been highlighted. The study also considers the challenges and practical implications of implementing DGO in multiple scenarios. As optimization remains crucial in research and industry, DGO emerges as a promising avenue for innovation and problem solving. [ABSTRACT FROM AUTHOR]

This paper investigates the output feedback (OPFB) tracking control problem for discrete-time linear (DTL) systems with unknown dynamics. To solve this problem, we use an augmented system approach, which first transforms the tracking control problem into a regulation problem with a discounted performance function. The solution to this problem is derived using a Bellman equation, based on the Q-function. In order to overcome the challenges of unmeasurable system state variables, we employ a multistep Q-learning algorithm that surpasses the advantages of the policy iteration (PI) and value iteration (VI) techniques and state reconstruction methods for output feedback control. As such, the requirement for an initial stabilizing control policy for the PI method is removed and the convergence speed of the learning algorithm is improved. Finally, we demonstrate the effectiveness of the proposed scheme using a simulation example. [ABSTRACT FROM AUTHOR]

It is an enormous challenge for imbalanced data learning in the field of machine learning. To construct balanced datasets, oversampling techniques have been studied extensively. However, many oversampling methods suffer from introducing noisy samples and blurring classification boundaries, leading to overfitting. To solve this problem, this paper proposes a new oversampling method, namely CS-SMOTE, for synthesizing minority class samples by three-point interpolation. CS-SMOTE is mainly based on the center offset factor and a synthesis strategy. First, the CS-SMOTE method removes noise samples, calculates the center offset factor, and selects sparsely distributed minority class samples by using the K-distance graph technique. Next, new samples are generated based on sparse minority samples, random minority samples, and sub-cluster centers located in the same sub-cluster samples. Finally, multiple comparative experiments on 18 well-known datasets demonstrate the effectiveness and general applicability of the proposed CS-SMOTE method for the imbalanced data classification. The experiments show that CS-SMOTE outperforms other competitors in terms of classification accuracy, while avoiding the issue of overfitting. [ABSTRACT FROM AUTHOR]

"Open world" environments are those in which novel objects, agents, events, and more can appear and contradict previous understandings of the environment. This runs counter to the "closed world" assumption used in most AI research, where the environment is assumed to be fully understood and unchanging. The types of environments AI agents can be deployed in are limited by the inability to handle the novelties that occur in open world environments. This paper presents a novel cognitive architecture framework to handle open-world novelties. This framework combines symbolic planning, counterfactual reasoning, reinforcement learning, and deep computer vision to detect and accommodate novelties. We introduce general algorithms for exploring open worlds using inference and machine learning methodologies to facilitate novelty accommodation. The ability to detect and accommodate novelties allows agents built on this framework to successfully complete tasks despite a variety of novel changes to the world. Both the framework components and the entire system are evaluated in Minecraft-like simulated environments. Our results indicate that agents are able to efficiently complete tasks while accommodating "concealed novelties" not shared with the architecture development team. [ABSTRACT FROM AUTHOR]

We present a novel methodology based on Physics-Informed Neural Networks (PINNs) for solving systems of partial differential equations admitting discontinuous solutions. Our method, called Gradient-Annihilated PINNs (GA-PINNs), introduces a modified loss function that forces the model to partially ignore high-gradients in the physical variables, achieved by introducing a suitable weighting function. The method relies on a set of hyperparameters that control how gradients are treated in the physical loss. The performance of our methodology is demonstrated by solving Riemann problems in special relativistic hydrodynamics, extending earlier studies with PINNs in the context of the classical Euler equations. The solutions obtained with the GA-PINN model correctly describe the propagation speeds of discontinuities and sharply capture the associated jumps. We use the relative l 2 error to compare our results with the exact solution of special relativistic Riemann problems, used as the reference "ground truth", and with the corresponding error obtained with a second-order, central, shock-capturing scheme. In all problems investigated, the accuracy reached by the GA-PINN model is comparable to that obtained with a shock-capturing scheme, achieving a performance superior to that of the baseline PINN algorithm in general. An additional benefit worth stressing is that our PINN-based approach sidesteps the costly recovery of the primitive variables from the state vector of conserved variables, a well-known drawback of grid-based solutions of the relativistic hydrodynamics equations. Due to its inherent generality and its ability to handle steep gradients, the GA-PINN methodology discussed in this paper could be a valuable tool to model relativistic flows in astrophysics and particle physics, characterized by the prevalence of discontinuous solutions. [ABSTRACT FROM AUTHOR]