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

Modeling Nonlinear Dynamics in Continuous Time with Inductive Biases on Decay Rates and/or Frequencies