Reconstructing Nonlinear Dynamical Systems from Multi-Modal Time Series
This work addresses the challenge of integrating multiple data modalities for dynamical system reconstruction, which is incremental as it extends existing single-modality methods to multi-modal contexts.
The authors tackled the problem of reconstructing nonlinear dynamical systems from multi-modal time series, proposing a framework that uses recurrent neural networks and modality-specific decoders, and demonstrated it can compensate for noisy or missing data in one channel by leveraging others, with applications in neuroscience benchmarks.
Empirically observed time series in physics, biology, or medicine, are commonly generated by some underlying dynamical system (DS) which is the target of scientific interest. There is an increasing interest to harvest machine learning methods to reconstruct this latent DS in a data-driven, unsupervised way. In many areas of science it is common to sample time series observations from many data modalities simultaneously, e.g. electrophysiological and behavioral time series in a typical neuroscience experiment. However, current machine learning tools for reconstructing DSs usually focus on just one data modality. Here we propose a general framework for multi-modal data integration for the purpose of nonlinear DS reconstruction and the analysis of cross-modal relations. This framework is based on dynamically interpretable recurrent neural networks as general approximators of nonlinear DSs, coupled to sets of modality-specific decoder models from the class of generalized linear models. Both an expectation-maximization and a variational inference algorithm for model training are advanced and compared. We show on nonlinear DS benchmarks that our algorithms can efficiently compensate for too noisy or missing information in one data channel by exploiting other channels, and demonstrate on experimental neuroscience data how the algorithm learns to link different data domains to the underlying dynamics.