递归状态估计中机器学习非精确求解器的可修复性

中文摘要 AI 辅助

递归状态估计通常在反馈回路内执行近似数值求解，其中高度精确的局部步骤并不能保证更好的整体结果。对于固定的线性卡尔曼模型，我们刻画了在指定子空间和范数预算内的修正何时能满足局部容许公差，以及实际执行的缺陷如何影响有限时域协方差响应。将每个缺陷以所实现协方差的精确增益为中心，可将当前求解误差与继承的增益漂移分离开来。扩展精确残差漂移恒等式，揭示了二次响应之外的相反四次贡献：创新协方差膨胀以正项进入，而局部增益再优化以减项进入。在匹配初始条件下，一个绝对六阶余项界（在固定时域上对有界缺陷序列一致成立）给出了二次欠预测或过预测的充分条件。机器学习提出有界修正，而一个与学习器无关的残差证书和经过验证的回退方案在不改变参考估计器的情况下管理经典和量子候选的执行。在电网容差研究中，与相同残差证书下未修正的求解相比，学习修正降低了无需回退即可部署所需的最小共轭梯度迭代次数。从变分量子线性求解器和基于退火的二进制编码中重建的增益，以及在超导硬件上进行的小规模终端测量和在量子退火机上的采样，均通过同一接口执行。通过将局部可修复性与非线性误差传播联系起来，该框架通过独立认证和有限时域响应来评估近似求解器和学习修正，为研究混合量子-经典计算提供了实用基础。

英文摘要

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.

发表机构

• Forschungszentrum Jülich（于利希研究中心）
• FH Aachen University of Applied Sciences（亚琛应用技术大学）
• RWTH Aachen University（亚琛工业大学）
• Shanghai University（上海大学）
• Saarland University（萨尔大学）
• Aalto University（阿尔托大学）

机构由 AI 辅助整理，请以论文原文为准。