  We propose a neural network-based model for nonlinear dynamics in continuous
time that can impose inductive biases on decay rates and/or frequencies.
Inductive biases are helpful for training neural networks especially when
training data are small. The proposed model is based on the Koopman operator
theory, where the decay rate and frequency information is used by restricting
the eigenvalues of the Koopman operator that describe linear evolution in a
Koopman space. We use neural networks to find an appropriate Koopman space,
which are trained by minimizing multi-step forecasting and backcasting errors
using irregularly sampled time-series data. Experiments on various time-series
datasets demonstrate that the proposed method achieves higher forecasting
performance given a single short training sequence than the existing methods.
