Multimodal Teacher Forcing for Reconstructing Nonlinear Dynamical Systems

Many, if not most, systems of interest in science are naturally described as nonlinear dynamical systems (DS). Empirically, we commonly access these systems through time series measurements, where often we have time series from different types of data modalities simultaneously. For instance, we may have event counts in addition to some continuous signal. While by now there are many powerful machine learning (ML) tools for integrating different data modalities into predictive models, this has rarely been approached so far from the perspective of uncovering the underlying, data-generating DS (aka DS reconstruction). Recently, sparse teacher forcing (TF) has been suggested as an efficient control-theoretic method for dealing with exploding loss gradients when training ML models on chaotic DS. Here we incorporate this idea into a novel recurrent neural network (RNN) training framework for DS reconstruction based on multimodal variational autoencoders (MVAE). The forcing signal for the RNN is generated by the MVAE which integrates different types of simultaneously given time series data into a joint latent code optimal for DS reconstruction. We show that this training method achieves significantly better reconstructions on multimodal datasets generated from chaotic DS benchmarks than various alternative methods.