Origin of the three-sensor requirement in SHRED

Establish whether the requirement for three sensor measurements in the Shallow REcurrent Decoder (SHRED) architecture is due to triangulation of sources and dynamics, and rigorously determine the theoretical basis for this minimum sensor count in the context of full-state reconstruction from limited time-sequence point measurements.

Background

The SHRED architecture combines a recurrent neural network (an LSTM) for temporal encoding with a shallow decoder network for spatial reconstruction, enabling full-state reconstruction and forecasting of coupled plasma fields from limited sensor data. In this work, SHRED demonstrates accurate reconstruction of fourteen spatio-temporal plasma fields with as few as three point sensors measuring the electron number density.

In the conclusion, the authors note a conjecture regarding why three sensors suffice: they suspect a triangulation principle analogous to how three cell towers localize a source. Clarifying and proving the theoretical origin of this three-sensor requirement would solidify the methodological foundations of SHRED and guide sensor selection strategies.