Scalable computation of energy functions for nonlinear balanced truncation
| dc.contributor.author | Kramer, Boris | en |
| dc.contributor.author | Gugercin, Serkan | en |
| dc.contributor.author | Borggaard, Jeff | en |
| dc.contributor.author | Balicki, Linus | en |
| dc.date.accessioned | 2025-02-04T13:28:43Z | en |
| dc.date.available | 2025-02-04T13:28:43Z | en |
| dc.date.issued | 2024-07-01 | en |
| dc.description.abstract | Nonlinear balanced truncation is a model order reduction technique that reduces the dimension of nonlinear systems in a manner that accounts for either open- or closed-loop observability and controllability aspects of the system. A computational challenges that has so far prevented its deployment on large-scale systems is that the energy functions required for characterization of controllability and observability are solutions of various high-dimensional Hamilton-Jacobi-(Bellman) equations, which are computationally intractable in high dimensions. This work proposes a unifying and scalable approach to this challenge by considering a Taylor-series-based approximation to solve a class of parametrized Hamilton-Jacobi-Bellman equations that are at the core of nonlinear balancing. The value of a formulation parameter provides either openloop balancing or a variety of closed-loop balancing options. To solve for the coefficients of Taylor-series approximations to the energy functions, the presented method derives a linear tensor system and heavily utilizes it to numerically solve structured linear systems with billions of unknowns. The strength and scalability of the algorithm is demonstrated on two semi-discretized partial differential equations, namely the Burgers and the Kuramoto-Sivashinsky equations. | en |
| dc.description.version | Published version | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.doi | https://doi.org/10.1016/j.cma.2024.117011 | en |
| dc.identifier.issue | 117011 | en |
| dc.identifier.orcid | Gugercin, Serkan [0000-0003-4564-5999] | en |
| dc.identifier.orcid | Borggaard, Jeffrey [0000-0002-4023-7841] | en |
| dc.identifier.uri | https://hdl.handle.net/10919/124478 | en |
| dc.identifier.volume | 427 | en |
| dc.language.iso | en | en |
| dc.rights | Creative Commons Attribution 4.0 International | en |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | en |
| dc.title | Scalable computation of energy functions for nonlinear balanced truncation | en |
| dc.title.serial | Computer Methods in Applied Mechanics and Engineering | en |
| dc.type | Article - Refereed | en |
| dc.type.dcmitype | Text | en |
| dc.type.other | Article | en |
| pubs.organisational-group | Virginia Tech | en |
| pubs.organisational-group | Virginia Tech/Science | en |
| pubs.organisational-group | Virginia Tech/Science/Mathematics | en |
| pubs.organisational-group | Virginia Tech/All T&R Faculty | en |
| pubs.organisational-group | Virginia Tech/Science/COS T&R Faculty | en |