Leveraging arbitrary mobile sensor trajectories with shallow recurrent
  decoder networks for full-state reconstruction
Megan R. Ebers Jan P. Williams Katherine M. Steele J. Nathan Kutz
Sensing is one of the most fundamental tasks for the monitoring, forecasting
and control of complex, spatio-temporal systems. In many applications, a
limited number of sensors are mobile and move with the dynamics, with examples
including wearable technology, ocean monitoring buoys, and weather balloons. In
these dynamic systems (without regions of statistical-independence), the
measurement time history encodes a significant amount of information that can
be extracted for critical tasks. Most model-free sensing paradigms aim to map
current sparse sensor measurements to the high-dimensional state space,
ignoring the time-history all together. Using modern deep learning
architectures, we show that a sequence-to-vector model, such as an LSTM (long,
short-term memory) network, with a decoder network, dynamic trajectory
information can be mapped to full state-space estimates. Indeed, we demonstrate
that by leveraging mobile sensor trajectories with shallow recurrent decoder
networks, we can train the network (i) to accurately reconstruct the full state
space using arbitrary dynamical trajectories of the sensors, (ii) the
architecture reduces the variance of the mean-square error of the
reconstruction error in comparison with immobile sensors, and (iii) the
architecture also allows for rapid generalization (parameterization of
dynamics) for data outside the training set. Moreover, the path of the sensor
can be chosen arbitrarily, provided training data for the spatial trajectory of
the sensor is available. The exceptional performance of the network
architecture is demonstrated on three applications: turbulent flows, global
sea-surface temperature data, and human movement biomechanics.