Sensing with shallow recurrent decoder networks

Sensing is a universal task in science and engineering. Downstream tasks from sensing include inferring full-state estimates of a system (system identification), control decisions and forecasting. We propose a shallow recurrent decoder (SHRED) neural network structure for sensing, which incorporates (i) a recurrent neural network to learn a latent representation of the temporal dynamics of the sensors and (ii) a shallow decoder that learns a mapping between this latent representation and the high-dimensional state space. SHRED enables accurate reconstructions with far fewer sensors, outperforms existing techniques when more measurements are available and is more robust to random sensor placements. In the example cases explored, complex spatio-temporal dynamics are characterized by exceedingly limited sensors that can be randomly placed with minimal loss of performance.