Fault-tolerant shallow recurrent decoders for sparse sensing with missing sensor measurements

Matteo Romilio Pasqual, Matteo Tomasetto, J. Nathan Kutz, Andrea Manzoni

Real-world sensing systems are inherently imperfect: sensors may fail, intermittently disconnect, operate with asynchronous sampling rates, and be subject to noise, leading to measurement streams that are irregular, incomplete, and heterogeneous. Nevertheless, sensing strategies for real-time state reconstruction typically assume synchronous and continuously active sensors, a constraint that substantially limits their applicability in operational environments. In this work, we introduce fault-tolerant sparse sensing strategies in the context of shallow recurrent decoders (SHRED) to enable high-dimensional state estimation from sparse, asynchronous, and missing sensor measurements. Specifically, we consider naive imputation strategies, fault-tolerant recurrent temporal encoders, and we introduce four different transformer-based masking mechanisms to make SHRED explicitly aware of sensor availability through the binary data-availability mask. Moreover, we further introduce a multi-step decoding training objective for SHRED, resulting in smoother latent trajectories and more robust predictions. Throughout a synthetic benchmark and three real-world problems in hydrodynamic and ocean…