Interpretable and flexible non-intrusive reduced-order models using reproducing kernel Hilbert spaces

Abstract

This paper develops an interpretable, non-intrusive reduced-order modeling technique using regularized kernel interpolation. Existing non-intrusive approaches approximate the dynamics of a reduced-order model (ROM) by solving a data-driven least-squares regression problem for low-dimensional matrix operators. Our approach instead leverages regularized kernel interpolation, which yields an optimal approximation of the ROM dynamics from a user-defined reproducing kernel Hilbert space. We show that our kernel-based approach can produce interpretable ROMs whose structure mirrors full-order model structure by embedding judiciously chosen feature maps into the kernel. The approach is flexible and allows a combination of informed structure through feature maps and closure terms via more general nonlinear terms in the kernel. We also derive a computable a posteriori error bound that combines standard error estimates for intrusive projection-based ROMs and kernel interpolants. The approach is demonstrated in several numerical experiments that include comparisons to operator inference using both proper orthogonal decomposition and quadratic manifold dimension reduction.

References in corpus (18)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition
• On Dynamic Mode Decomposition: Theory and Applications
• Koopman invariant subspaces and finite linear representations of nonlinear dynamical systems for control
• Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders
• Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems
• A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder
• An artificial neural network framework for reduced order modeling of transient flows
• A Quadratic Manifold for Model Order Reduction of Nonlinear Structural Dynamics
• Data-driven reduced-order models via regularized operator inference for a single-injector combustion process
• Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms
• Nonlinear Model Order Reduction via Lifting Transformations and Proper Orthogonal Decomposition
• Operator inference for non-intrusive model reduction with quadratic manifolds
• LaSDI: Parametric Latent Space Dynamics Identification
• Kernel Learning for Robust Dynamic Mode Decomposition: Linear and Nonlinear Disambiguation Optimization (LANDO)
• gLaSDI: Parametric Physics-informed Greedy Latent Space Dynamics Identification
• GPLaSDI: Gaussian Process-based Interpretable Latent Space Dynamics Identification through Deep Autoencoder
• A fast and accurate domain-decomposition nonlinear manifold reduced order model