  Numerous industrial processes can be defined using distributed parameter
systems (DPSs). This study introduces a two-stage spatial construction approach
for real-time modeling of DPSs in cases of limited sensors. Initially, a
discrete space-completion approach is created to recuperate the spatiotemporal
patterns of non-monitored locations under sparse sensing. The high-dimensional
space construction method is employed to derive continuous spatial basis
functions (SBFs). The identification and adjustment of the nonlinear temporal
model are carried out via the long short-term memory (LSTM) neural network.
Eventually, the amalgamation of the derived SBFs and temporal model results in
a spatially continuous model. The use of a cubic B-spline surface is validated
as an effective solution for optimizing space construction in the sense of
least squares approximation. Experimental tests conducted on a pouch-type
Li-ion battery demonstrate the efficacy of the proposed modeling technique
under sparse sensing. This work highlights the promise of sparse sensors in
real-time full-space modeling for large-scale battery energy storage systems.
