Fitting Regularized Population Dynamics with Neural Differential Equations

Abstract

Neural differential equations (neural DEs) are yet to see success in its application as interpretable autoencoders/descriptors, where they directly model a population of signals with the learned vector field. In this manuscript, we show that there is a threshold to which these models capture the dynamics of a population of signals produced under the same monitoring protocol. This threshold is computed by taking the derivative at each time point and analyzing the variance of its dynamics. In addition, we show that this can be tackled by projecting a highly-variant population to a lower dynamically variant space, where the model is able to capture dynamics, and similarly project the modelled signal back to the original space.