  Most machine learning methods are used as a black box for modelling. We may
try to extract some knowledge from physics-based training methods, such as
neural ODE (ordinary differential equation). Neural ODE has advantages like a
possibly higher class of represented functions, the extended interpretability
compared to black-box machine learning models, ability to describe both trend
and local behaviour. Such advantages are especially critical for time series
with complicated trends. However, the known drawback is the high training time
compared to the autoregressive models and long-short term memory (LSTM)
networks widely used for data-driven time series modelling. Therefore, we
should be able to balance interpretability and training time to apply neural
ODE in practice. The paper shows that modern neural ODE cannot be reduced to
simpler models for time-series modelling applications. The complexity of neural
ODE is compared to or exceeds the conventional time-series modelling tools. The
only interpretation that could be extracted is the eigenspace of the operator,
which is an ill-posed problem for a large system. Spectra could be extracted
using different classical analysis methods that do not have the drawback of
extended time. Consequently, we reduce the neural ODE to a simpler linear form
and propose a new view on time-series modelling using combined neural networks
and an ODE system approach.
