A Rayleigh-Ritz Autoencoder

Anika Terbuch, Paul O'Leary, Dimitar Ninevski, Elias Jan Hagendorfer, Elke Schlager, Andreas Windisch, Christoph Schweimer

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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."
Original languageEnglish
Title of host publication2023 IEEE International Instrumentation and Measurement Technology Conference (I2MTC) (I2MTC 2023)
Place of PublicationKuala Lumpur, Malaysia
PublisherInstitute of Electrical and Electronics Engineers
Publication statusPublished - 2023
Event2023 IEEE International Instrumentation and Measurement Technology
Conference (I2MTC) (I2MTC 2023): nstrumentation and Measurement: Rising Above Covid-19
- Kuala Lumpur, Malaysia
Duration: 22 May 202325 May 2023


Conference2023 IEEE International Instrumentation and Measurement Technology
Conference (I2MTC) (I2MTC 2023)
Abbreviated titleI2MTC 2023
CityKuala Lumpur
Internet address


  • Physics informed machine learning
  • Rayleigh-Ritz
  • Structural monitoring

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