TY - JOUR
T1 - Dynamic data-driven model reduction
T2 - adapting reduced models from incomplete data
AU - Peherstorfer, Benjamin
AU - Willcox, Karen
N1 - Funding Information:
This work was supported in part by the AFOSR MURI on multi-information sources of multi-physics systems under Award Number FA9550-15-1-0038, program manager Jean-Luc Cambier, and by the United States Department of Energy Applied Mathematics Program, Awards DE-FG02-08ER2585 and DE-SC0009297, as part of the DiaMonD Multifaceted Mathematics Integrated Capability Center. Some of the numerical examples were computed on the computer cluster of the Munich Centre of Advanced Computing.
Publisher Copyright:
© 2016, The Author(s).
PY - 2016/12/1
Y1 - 2016/12/1
N2 - 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.
AB - 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.
KW - Dynamic data-driven application systems
KW - Dynamic data-driven reduced models
KW - Gappy proper orthogonal decomposition
KW - Incomplete sensor data
KW - Model reduction
KW - Online adaptivity
UR - http://www.scopus.com/inward/record.url?scp=85044298892&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85044298892&partnerID=8YFLogxK
U2 - 10.1186/s40323-016-0064-x
DO - 10.1186/s40323-016-0064-x
M3 - Article
AN - SCOPUS:85044298892
SN - 2213-7467
VL - 3
JO - Advanced Modeling and Simulation in Engineering Sciences
JF - Advanced Modeling and Simulation in Engineering Sciences
IS - 1
M1 - 11
ER -