Non-intrusive Nonlinear Model Reduction via Machine Learning Approximations to Low-dimensional Operators
This addresses the limitation of broad adoption for ROMs in applications like PDE simulations by making them non-intrusive, though it is incremental as it builds on existing ROM frameworks.
The paper tackles the problem of intrusiveness in projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems by proposing a non-intrusive method that approximates low-dimensional operators using machine learning, achieving up to 1000× reduction in run time.
Although projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing such a reduced-order model typically requires significant modifications to the underlying simulation code. To address this, we propose a method that enables traditionally intrusive reduced-order models to be accurately approximated in a non-intrusive manner. Specifically, the approach approximates the low-dimensional operators associated with projection-based reduced-order models (ROMs) using modern machine-learning regression techniques. The only requirement of the simulation code is the ability to export the velocity given the state and parameters as this functionality is used to train the approximated low-dimensional operators. In addition to enabling nonintrusivity, we demonstrate that the approach also leads to very low computational complexity, achieving up to $1000\times$ reduction in run time. We demonstrate the effectiveness of the proposed technique on two types of PDEs.