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Data-driven Implementations of Various Generalizations of Balanced Truncation
arXiv:2506.23204v2 Announce Type: replace
Abstract: There exist two main approaches for non-intrusive implementations of approximate balanced truncation within the Loewner framework: the quadrature-based method [1] and the Alternating Direction Implicit (ADI)-based method [2]. Both approaches rely solely on samples of the transfer function to construct truncated balanced models, eliminating the need for access to the original model's statespace realization. Recently, the quadrature-based approach has been extended to various generalizations of balanced truncation, including positive-real balanced truncation, bounded-real balanced truncation, and balanced stochastic truncation. While this extension [3] is theoretically non-intrusive-meaning it does not require the original state-space realization-it depends on samples of spectral factorizations of the transfer function. Since practical methods for obtaining such samples are currently unavailable, this extension remains largely a theoretical contribution. In this work, we present a non-intrusive ADI-type framework for these generalized balanced truncation methods that requires only samples of the original transfer function for implementation.
Abstract: There exist two main approaches for non-intrusive implementations of approximate balanced truncation within the Loewner framework: the quadrature-based method [1] and the Alternating Direction Implicit (ADI)-based method [2]. Both approaches rely solely on samples of the transfer function to construct truncated balanced models, eliminating the need for access to the original model's statespace realization. Recently, the quadrature-based approach has been extended to various generalizations of balanced truncation, including positive-real balanced truncation, bounded-real balanced truncation, and balanced stochastic truncation. While this extension [3] is theoretically non-intrusive-meaning it does not require the original state-space realization-it depends on samples of spectral factorizations of the transfer function. Since practical methods for obtaining such samples are currently unavailable, this extension remains largely a theoretical contribution. In this work, we present a non-intrusive ADI-type framework for these generalized balanced truncation methods that requires only samples of the original transfer function for implementation.
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