Solving ordinary differential equations using genetic algorithms and the Taylor series matrix method

Gutierrez-Navarro, Daniel; López-Aguayo, Servando

doi:10.1088/2399-6528/aaedd2

Cited by 12 publications

(4 citation statements)

References 11 publications

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“…Unlike real evolutionary-genetic transformations, GA does not solve the problem of the "survival" of the population as a whole and are aimed at optimizing certain moments in its vital activity, but "... it would be rash to see in optimization the key to understanding how populations and individuals survive" [22]. Both GA and EANN can be quite effective for solving differential equations (including evolutionary ones) and systems of such equations [23][24][25][26]. However, using evolutionary computational methods, it is impossible to predict abrupt transitions in the evolution of a complex open system from a state of chaos to a qualitatively new state, since genetic operators alone are not enough to model evolutionunderstanding the nature of the collective forces of interaction between "individuals" that lead to irreversible and indeterminacy of the phase trajectories of such systems is needed.…”

Section: Artificial Intelligence Techniquesmentioning

confidence: 99%

Model of Self-organizing Knowledge Representation and Organizational Knowledge Transformation

Moroz¹

2020

AJAI

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The purpose of the paper is development of a conceptual model for the representation of knowledge as an active intellectual substance and, on this basis, study of metaphysics of knowledge transformation process being produced both individually and collectively in the practice of organizations. The first principle of knowledge engineering, as Edward Albert Feigenbaum noted, says that the power in solving problems that an intellectual subject (person or machine) manifests in the process of activity depends primarily on its knowledge base, and only secondly on the methods of inference used. Strength is hidden in knowledge. The process of producing knowledge is permanent and does not depend on whether an individual is going to use this knowledge or not. Knowledge constantly produces new knowledge regardless of the owner's desire. Besides that, knowledge can't arise from nothing, but always -from some knowledge obtained earlier. As well as the intelligence, knowledge is an emergent instance arising from the collective interaction of a lot of intellectual atomic elements of knowledge (knowledge quanta). Idiosyncrasy of this interaction is expressed precisely in the creation of new knowledge. Due to postulating the knowledge self-organizing, the hierarchical knowledge structures in memory and the process of thinking as a kind of syntax for the procedure of new knowledge generation are described. This is an effort towards understanding the memory mechanisms, the process of thinking, the sources of heuristic knowledge just through the inner nature of knowledge. Also, based on the knowledge self-organization principle, an archetype of the appropriate knowledge-based system architecture is presented too. As an implementation of the concept, the perceptual act model is described, and on its base, a possible scenario for the behavior of a robot meeting an obstacle in its path is considered. As the mutual transformation of tacit and explicit knowledge makes new knowledge, the impact of the self-organization of knowledge on the transformation process as well as conditions of self-organization of both individual knowledge and organizational knowledge are analyzed in detail. Finally, modification of the known model of knowledge dimensions by Nonaka and Takeuchi is proposed. Because of the native activity of knowledge, it is impossible to build a knowledge management system without considering the internal structure of knowledge and its emergent ability to self-organize. Ensuring the natural process of knowledge development at all ontological levels in an organization is an essential prerequisite for the evolution of values in this organization.

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Section: Artificial Intelligence Techniquesmentioning

confidence: 99%

Model of Self-organizing Knowledge Representation and Organizational Knowledge Transformation

Moroz¹

2020

AJAI

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“…With the help of this technique, one may define the concept of a Taylor series matrix, which turns a differential equation into an optimization problem. The coefficients of a series expansion make up the objective function in this problem [3].…”

Section: Introductionmentioning

confidence: 99%

Analysis of applications for Taylor series expansion: Evidence from machine learning, mathematics and engineering

2023

TNS

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Contemporarily, the Taylor series expansion is a common mathematical approach that is widely applied in various fields. This study provides a comprehensive overview of the Taylor expansion, a powerful mathematical tool used to represent continuous and differentiable functions as an infinite sum of terms around a specific point. This paper delves into the historical context and the fundamental concepts of the Taylor expansion, followed by its applications in machine learning, mathematics, and engineering. Furthermore, the research highlights the advantages and disadvantages of using the Taylor expansion in different scenarios. According to the analysis, it also discusses recent advancements in utilizing the Taylor expansion to improve computational efficiency and problem-solving across these three fields. In conclusion, despite its limitations, the Taylor expansion has significantly contributed to scientific advancements and will continue to play a vital role in diverse research areas. Overall, these results shed light on guiding further exploration of the Taylor expansion.

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“…The idea of GA optimization is effectively applied to nonlinear differential equations for optimized solutions [13][14][15][16]. Through reviewing the literature, it can be seen that collocation method has not been applied to the Troesch's equation.…”

Section: Introductionmentioning

confidence: 99%

Computational heuristics for Troesch’s Problem in Plasma Physics

2023

IJANSER

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Exponential Collocation Genetic Algorithm (ECGA) approach has been developed and analyzed for fast computation of hyperbolic sine nonlinear Troesch's problem which arises in the confinement of plasma. The governing equation is converted to an optimization problem by formulating the Fitness function in terms of an exponential basis. The problem is solved for three scenarios of Troesch's parameters of 0.5, 1, and 2 respectively. The stability of the solutions has been investigated for multiple independent runs. The results obtained in this work are in good agreement with the already published with enhanced stability and fast convergence. The developed technique is a simple and reliable method for the solution of hyperbolic sine nonlinear Troesch's problem.

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Solving ordinary differential equations using genetic algorithms and the Taylor series matrix method

Cited by 12 publications

References 11 publications

Model of Self-organizing Knowledge Representation and Organizational Knowledge Transformation

Model of Self-organizing Knowledge Representation and Organizational Knowledge Transformation

Analysis of applications for Taylor series expansion: Evidence from machine learning, mathematics and engineering

Computational heuristics for Troesch’s Problem in Plasma Physics

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