Machine learning improves repair of approximate solvers in state estimation
Repairability of Inexact Solvers in Recursive State Estimation with Machine Learning
Machine Learning
Summary
State estimation methods often use approximate steps that can cause errors to build up unexpectedly. The authors analyze how small corrections within certain limits can reduce these errors over time, and they show how machine learning can help provide these corrections safely. They demonstrate their approach using examples from power grids and quantum computing hardware. Their work offers a way to safely combine classical and quantum methods for improved state estimation.
What this means in practice
- •For power grid operators: Reduce computation steps needed for real-time state estimation by applying learned corrections to approximate solver outputs under strict safety checks.
- •For quantum algorithm developers: Evaluate and safely integrate quantum solver outputs for linear system solutions into classical recursive filters via a certification framework.
Authors
Yanjun Ji, Dennis Willsch, Orkun Şensebat, Priyanka Arkalgud Ganeshamurthy, Zhi Pei, M. Sahnawaz Alam, Ivelina Stoyanova, Frank K. Wilhelm, Bo Zhao, Chao Wang, Kristel Michielsen
Abstract
Recursive state estimation often executes approximate numerical solutions inside a feedback loop, where highly accurate local steps do not guarantee better overall results. For a fixed linear Kalman model, we characterize when a correction within a prescribed subspace and norm budget can meet a local admissibility tolerance, and how the defects actually executed affect the finite-horizon covariance response. Centering each defect on the exact gain for the implemented covariance separates current solve error from inherited gain drift. Expanding the exact residual-drift identity reveals opposing quartic contributions beyond the quadratic response: innovation-covariance inflation enters positively, while local-gain reoptimization enters subtractively. Under matched initialization, an absolute sixth-order remainder bound, uniform over bounded defect sequences at fixed horizon, gives sufficient conditions for quadratic under- or overprediction. Machine learning proposes bounded corrections, while a learner-independent residual certificate and verified fallback govern execution of classical and quantum candidates without changing the reference estimator. In a power-grid tolerance study, learned correction lowers the minimum conjugate-gradient iteration count for deployment without fallback relative to uncorrected solves under the same residual certificate. Gains reconstructed from a variational quantum linear solver and from an annealing-based binary encoding, with small-scale terminal measurements on superconducting hardware and sampling on a quantum annealer, are executed through the same interface. By linking local repairability to nonlinear error propagation, the framework evaluates approximate solvers and learned corrections through independent certification and finite-horizon response, providing a practical basis for studying hybrid quantum--classical computation.