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

By Elizabeth Qian, Boris Kramer, Benjamin Peherstorfer, Karen E. Willcox. Physica A: Statistical Mechanics and its Applications, 2019

316 citations recorded by the source corpus.

Abstract 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.

View Paper: https://www.semanticscholar.org/paper/45723daf7af37074a286064cc04e2a445c1d7708

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Citations in the corpus

Enhancing computational fluid dynamics with machine learning (2021, methodology): “The operator-inference approach is closely related to Galerkin projection, where a neighboring operator is learned from data [115–117].”