Gradient-Preserving Hyper-Reduction of Nonlinear Dynamical Systems via Discrete Empirical Interpolation

We present a framework for learning Hamiltonian systems using data. This work is based on a lifting hypothesis, which posits that nonlinear Hamiltonian systems can be written as nonlinear systems with cubic Hamiltonians. By leveraging this, we obtain quadratic dynamics that are Hamiltonian in a transformed coordinate system. To that end, for given generalized position and momentum data, we propose a methodology to learn quadratic dynamical systems, enforcing the Hamiltonian structure in combination with a weakly-enforced symplectic autoencoder. The obtained Hamiltonian structure exhibits long-term stability of the system, while the cubic Hamiltonian function provides relatively low model complexity. For low-dimensional data, we determine a higher-dimensional transformed coordinate system, whereas for high-dimensional data, we find a lower-dimensional coordinate system with the desired properties. We demonstrate the proposed methodology by means of both lowdimensional and high-dimensional nonlinear Hamiltonian systems.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Gradient-Preserving Hyper-Reduction of Nonlinear Dynamical Systems via Discrete Empirical Interpolation

Cited by 3 publications

References 25 publications

Gradient preserving Operator Inference: Data-driven reduced-order models for equations with gradient structure

Gradient preserving Operator Inference: Data-driven reduced-order models for equations with gradient structure

Energy-conserving hyper-reduction and temporal localization for reduced order models of the incompressible Navier-Stokes equations

Data-Driven Identification of Quadratic Representations for Nonlinear Hamiltonian Systems Using Weakly Symplectic Liftings

Contact Info

Product

Resources

About