Abstract
This paper describes the transition from neural network architecture to ordinary differential equations and initial value problem. Two neural network architectures are compared: classical RNN and ODERNN, which uses neural ordinary differential equations. The paper proposes a new architecture of p-ODE-RNN, which allows you to achieve a quality comparable to ODE-RNN, but is trained much faster. Furthermore, the derivation of the proposed architecture in terms of random process theory is discussed.
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