Kramer, BorisGugercin, SerkanBorggaard, JeffBalicki, Linus2025-02-042025-02-042024-07-01https://hdl.handle.net/10919/124478Nonlinear 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.application/pdfenCreative Commons Attribution 4.0 InternationalArticle - Refereedhttps://doi.org/10.1016/j.cma.2024.117011427117011Gugercin, Serkan [0000-0003-4564-5999]Borggaard, Jeffrey [0000-0002-4023-7841]