arXiv Machine Learning By Yanjun Ji, Dennis Willsch, Orkun \c{S}ensebat, Priyanka Arkalgud Ganeshamurthy, Zhi Pei, M. Sahnawaz Alam, Ivelina Stoyanova, Frank K. Wilhelm, Bo Zhao, Chao Wang, Kristel Michielsen

Repairability of Inexact Solvers in Recursive State Estimation with Machine Learning

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The paper investigates how approximate numerical solvers used in recursive state estimation can be repaired using bounded corrections, characterizing when such corrections meet local admissibility tolerances and how they influence finite‑horizon covariance. It derives error identities that separate solve error from gain drift, revealing quartic and sixth‑order contributions to the covariance response. The framework is applied to a power‑grid tolerance study, showing that learned corrections reduce the required conjugate‑gradient iterations, and it demonstrates a unified interface for classical, quantum, and hybrid solvers.

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