Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems

Qian, Elizabeth; Kramer, Boris; Peherstorfer, Benjamin; Willcox, Karen

doi:10.1016/j.physd.2020.132401

Title: Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems

Journal Article · Wed Feb 19 00:00:00 EST 2020 · Physica. D, Nonlinear Phenomena

DOI:https://doi.org/10.1016/j.physd.2020.132401· OSTI ID:1803677

Qian, Elizabeth ^[1]; Kramer, Boris ^[2]; Peherstorfer, Benjamin ^[3]; Willcox, Karen ^[4]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Univ. of California, San Diego, CA (United States)
New York Univ. (NYU), NY (United States). Courant Institute of Mathematical Sciences
Univ. of Texas, Austin, TX (United States). Oden Institute for Computational Engineering and Sciences

In this work, we present Lift & Learn, a physics-informed method for learning low-dimensional models for large-scale dynamical systems. The method exploits knowledge of a system’s governing equations to identify a coordinate transformation in which the system dynamics have quadratic structure. This transformation is called a lifting map because it often adds auxiliary variables to the system state. The lifting map is applied to data obtained by evaluating a model for the original nonlinear system. This lifted data is projected onto its leading principal components, and low-dimensional linear and quadratic matrix operators are fit to the lifted reduced data using a least-squares operator inference procedure. Analysis of our method shows that the Lift & Learn models are able to capture the system physics in the lifted coordinates at least as accurately as traditional intrusive model reduction approaches. This preservation of system physics makes the Lift & Learn models robust to changes in inputs. Numerical experiments on the FitzHugh–Nagumo neuron activation model and the compressible Euler equations demonstrate the generalizability of our model.

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Research Organization:: Univ. of Texas, Austin, TX (United States); New York Univ. (NYU), NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC); US Air Force Office of Scientific Research (AFOSR)

Grant/Contract Number:: SC0019303; SC0019334; FA9550-17-1-0195; FA9550-15-1-0038; FA9550-18-1-0023

OSTI ID:: 1803677

Alternate ID(s):: OSTI ID: 1603700

Journal Information:: Physica. D, Nonlinear Phenomena, Vol. 406, Issue C; ISSN 0167-2789

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 95 works

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