This paper presents a new architecture for unsupervised hybrid machine
learning, called a Rayleigh Ritz Autoencoder (RRAE). It is suitable for
applications in instrumentation and measurement where the system being
observed by multiple sensors is well modelled as a boundary value problem.
The embedding of the admissible functions in the decoder implements a truly
physics-informed machine learning architecture. The RRAE provides an exact
fulfilment of Neumann, Cauchy, Dirichlet or periodic constraints. Only the
encoder needs to be trained; consequently, the RRAE is numerically more
efficient during training than traditional autoencoders.

The new Rayleigh-Ritz Autoencoder has been applied to an instrumentation
and measurement problem in structural monitoring. It involves the fusion
of data from multiple sensors and the solution of a boundary value problem.
A 1-norm minimization has been chosen to minimize the effects of
non-Gaussian perturbations and to demonstrate the non-linear abilities of
the RRAE. The results from the tunnel monitoring application over months of
work are presented in detail."