# Balanced Truncation Model Reduction for Lifted Nonlinear Systems

arXiv: https://arxiv.org/abs/1907.12084 · HTML: https://mlsanity.com/paper/1907.12084/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jul 2019.

## Built on by (most cited first, 5 of 5)

- [Reduced operator inference for nonlinear partial differential equations](https://mlsanity.com/paper/2102.00083/) (2021)
- [Learning Nonlinear Projections for Reduced-Order Modeling of Dynamical Systems using Constrained Autoencoders](https://mlsanity.com/paper/2307.15288/) (2023)
- [Canonical and Noncanonical Hamiltonian Operator Inference](https://mlsanity.com/paper/2304.06262/) (2023)
- [Nonlinear energy-preserving model reduction with lifting transformations that quadratize the energy](https://mlsanity.com/paper/2503.02273/) (2025)
- [Structure-preserving Lift & Learn: Scientific machine learning for nonlinear conservative partial differential equations](https://mlsanity.com/paper/2507.00301/) (2025)

## Abstract (arXiv)

We present a balanced truncation model reduction approach for a class of nonlinear systems with time-varying and uncertain inputs. First, our approach brings the nonlinear system into quadratic-bilinear~(QB) form via a process called lifting, which introduces transformations via auxiliary variables to achieve the specified model form. Second, we extend a recently developed QB balanced truncation method to be applicable to such lifted QB systems that share the common feature of having a system matrix with zero eigenvalues. We illustrate this framework and the multi-stage lifting transformation on a tubular reactor model. In the numerical results we show that our proposed approach can obtain reduced-order models that are more accurate than proper orthogonal decomposition reduced-order models in situations where the latter are sensitive to the choice of training data.