Nonlinear balanced truncation model reduction through scalable Taylor series

The theory of nonlinear balanced truncation provides a system-theoretic framework for model reduction that preserves important properties such as stability, controllability, and observability. We present a scalable algorithm for computing reduced-order models based on the nonlinear balancing theory. The approach is based on polynomial approximations using the Kronecker product representation, building on recent numerical linear algebra advancements to enable scalability. We derive polynomial approximations for the balancing transformation and the explicit balanced realization of the full-order model, which yields true nonlinear reduced-order models upon truncation of redundant state components. The proposed tools are tested on various examples, demonstrating a nuanced perspective of the benefits and limitations of nonlinear balancing not shown in the existing literature.