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KIAM Preprint № 131, Moscow, 2019
Authors: Chashchin A.V., Botchev M.A., Oseledets I.V., Ovchinnikov G.V.
Predicting dynamical system evolution with residual neural networks
Abstract:
Forecasting time series and time-dependent data is a common problem in many applications. One typical example is solving ordinary differential equation (ODE) systems ẋ = F (x). Oftentimes the right hand side function F (x) is not known explicitly and the ODE system is described by solution samples taken at some time points. Hence, ODE solvers cannot be used. In this paper, a data-driven approach to learning the evolution of dynamical systems is considered. We show how by training neural networks with ResNet-like architecture on the solution samples, models can be developed to predict the ODE system solution further in time. By evaluating the proposed approaches on three test ODE systems, we demonstrate that the neural network models are able to reproduce the main dynamics of the systems qualitatively well. Moreover, the predicted solution remains stable for much longer times than for other currently known models.
Keywords:
dynamical systems, residual networks, deep learning
Publication language: russian,  pages: 26
Research direction:
Mathematical problems and theory of numerical methods
Russian source text:
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About authors:
  • Chashchin Artem Valerievich,  KIAM RAS
  • Botchev Mikhail Aleksandrovich,  orcid.org/0000-0001-5901-7120KIAM RAS
  • Oseledets Ivan Valer'evich,  orcid.org/0000-0003-2071-2163,  Skolkovo Institute of Science and Technology
  • Ovchinnikov Georgiy Victorovich,  ,  Skolkovo Institute of Science and Technology