Dynamic data-driven model reduction: adapting reduced models from incomplete data

Benjamin Peherstorfer, Karen Willcox

Research output: Contribution to journalArticlepeer-review


This work presents a data-driven online adaptive model reduction approach for systems that undergo dynamic changes. Classical model reduction constructs a reduced model of a large-scale system in an offline phase and then keeps the reduced model unchanged during the evaluations in an online phase; however, if the system changes online, the reduced model may fail to predict the behavior of the changed system. Rebuilding the reduced model from scratch is often too expensive in time-critical and real-time environments. We introduce a dynamic data-driven adaptation approach that adapts the reduced model from incomplete sensor data obtained from the system during the online computations. The updates to the reduced models are derived directly from the incomplete data, without recourse to the full model. Our adaptivity approach approximates the missing values in the incomplete sensor data with gappy proper orthogonal decomposition. These approximate data are then used to derive low-rank updates to the reduced basis and the reduced operators. In our numerical examples, incomplete data with 30–40 % known values are sufficient to recover the reduced model that would be obtained via rebuilding from scratch.

Original languageEnglish (US)
Article number11
JournalAdvanced Modeling and Simulation in Engineering Sciences
Issue number1
StatePublished - Dec 1 2016


  • Dynamic data-driven application systems
  • Dynamic data-driven reduced models
  • Gappy proper orthogonal decomposition
  • Incomplete sensor data
  • Model reduction
  • Online adaptivity

ASJC Scopus subject areas

  • Modeling and Simulation
  • Engineering (miscellaneous)
  • Computer Science Applications
  • Applied Mathematics


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