Multiobjective evolutionary discovery of equation-based analytical models for dynamical systems
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- @Article{Maslyaev:2023:itmo,
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author = "Mikhail A. Maslyaev and Alexander A. Hvatov",
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title = "Multiobjective evolutionary discovery of
equation-based analytical models for dynamical
systems",
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journal = "Scientific and Technical Journal of Information
Technologies, Mechanics and Optics",
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year = "2023",
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volume = "23",
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number = "1",
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pages = "97--104",
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keywords = "genetic algorithms, genetic programming, differential
equation discovery, evolutionary optimization,
multi-objective optimization, differential equations
system, symbolic regression",
-
URL = "https://human-competitive.org/sites/default/files/entry_hvatov.txt",
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URL = "https://human-competitive.org/sites/default/files/multiobjective_evolutionary_discovery_of_equation-based_analytical_models_for_dynamical_systems.pdf",
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URL = "https://ntv.ifmo.ru/file/article/21743.pdf",
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DOI = "doi:10.17586/2226-1494-2023-23-1-97-104",
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size = "8 pages",
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abstract = "an approach to modeling dynamical systems in case of
unknown governing physical laws has been introduced.
The systems of differential equations obtained by means
of a data-driven algorithm are taken as the desired
models. In this case, the problem of predicting the
state of the process is solved by integrating the
resulting differential equations. In contrast to
classical data-driven approaches to dynamical systems
representation, based on the general machine learning
methods, the proposed approach is based on the
principles, comparable to the analytical equation-based
modeling. Models in forms of systems of differential
equations, composed as combinations of elementary
functions and operation with the structure, were
determined by adapted multi-objective evolutionary
optimization algorithm. Time-series describing the
state of each element of the dynamic system are used as
input data for the algorithm. To ensure the correct
operation of the algorithm on data characterizing
real-world processes, noise reduction mechanisms are
introduced in the algorithm. The use of multicriteria
optimization, held in the space of complexity and
quality criteria for individual equations of the
differential equation system, makes it possible to
improve the diversity of proposed candidate solutions
and, therefore, to improve the convergence of the
algorithm to a model that best represents the dynamics
of the process. The output of the algorithm is a set of
Pareto-optimal solutions of the optimization problem
where each individual of the set corresponds to one
system of differential equations. In the course of the
work, a library of data-driven modeling of dynamic
systems based on differential equation systems was
created. The behavior of the algorithm was studied on a
synthetic validation dataset describing the state of
the hunter-prey dynamic system given by the
Lotka-Volterra equations. Finally, a toolset based on
the solution of the generated equations was integrated
into the algorithm for predicting future system states.
The method is applicable to data-driven modeling of
arbitrary dynamical systems (e.g. hydrometeorological
systems) in cases where the processes can be described
using differential equations. Models generated by the
algorithm can be used as components of more complex
composite models, or in an ensemble of methods as an
interpretable component.",
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notes = "Entered 2023 HUMIES",
- }
Genetic Programming entries for
Mikhail A Maslyaev
Alexander A Hvatov
Citations