Development and research of data generation algorithms based on mathematical remodelling

Mathematical remodeling is a modern approach in the field of mathematical modeling, the essence of which is the transformation of an existing model of one class into a new model belonging to a different, often simpler or computationally more efficient class. Unlike the classical modeling process, where a model is created "from scratch" based on primary data, remodeling starts from the premise that there already exists some adequate initial model f1 that describes an object or process accurately enough. However, this model may be too complex for practical application, require significant computational resources, or be presented in a form that is inconvenient for further use, for example, in real-time systems or on devices with limited performance. The key task in the remodeling process is the generation of a representative training dataset on which the new model f2 will be built. The accuracy and adequacy of the newly obtained model directly depend on the quality and structure of this synthesized dataset. Traditional generation methods, such as uniform random distribution of points in a given domain or using design of experiments methods, often prove to be ineffective: they either do not account for the behavioral features of the original function or become computationally infeasible in high-dimensional problems. Consequently, there is a need to develop intelligent algorithms for adaptive data generation that could purposefully place points in those regions of the input variable space where the original function f1 demonstrates the greatest variability and nonlinearity. This work is devoted to the development and research of precisely such an approach, based on the principles of interval analysis and sequential bisection of the domain. This allows for the optimal distribution of a limited volume of generated data and significantly improves the accuracy of mathematical remodeling.

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