用于数据同化增强型参数估计的量子优化框架
A Quantum Optimization Framework for Data-Assimilation-Augmented Parameter Estimation
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中文总结 AI 辅助
本研究提出混合经典-量子框架，将数据同化增强型参数估计转化为组合优化任务，经实验可从多类动力系统的部分观测中准确恢复参数，为量子优化应用于相关问题提供可行路径。
中文摘要 AI 辅助
参数估计是常微分方程（ODE）模型校准中的基础挑战，重复数值积分会导致高计算成本。本研究探讨是否可利用量子算法辅助非线性动力系统的参数估计，开发了一种混合经典-量子框架，将数据同化增强型参数估计问题重新表述为组合优化任务。模型动力学与数据同化完全在经典侧执行，所得参数估计代价泛函被离散化并近似为二次无约束二元优化（QUBO）代理模型，该代理模型被映射为伊辛哈密顿量，量子优化器用于搜索对应候选参数估计的低能构型。将该框架应用于SIS、SIR流行病模型、混沌Lorenz-63系统及高维两层Lorenz-96系统，用于从稳态、混沌及高维多尺度动力系统的部分状态观测中恢复经典系统参数。合成数据的数值实验表明，所提方法可准确恢复参数，且仅需在规定粗网格上求解数据同化问题；该框架避免了量子态层析，为将量子优化整合至非线性动力系统的数据驱动参数估计提供了可行路径。
英文摘要
Parameter estimation is a fundamental challenge in the calibration of ordinary differential equation (ODE) models, where repeated numerical integration can lead to high computational cost. In this work, we investigate whether quantum algorithms can be leveraged to assist parameter estimation in nonlinear dynamical systems. We develop a hybrid classical-quantum framework that reformulates a data-assimilation-augmented parameter estimation problem as a combinatorial optimization task. Model dynamics and data assimilation are enforced entirely on the classical side, while the resulting parameter estimation cost functional is discretized and approximated by a quadratic unconstrained binary optimization (QUBO) surrogate. This surrogate is mapped to an Ising Hamiltonian, and quantum optimizers are used to search for low-energy configurations corresponding to candidate parameter estimates. We apply the framework to SIS and SIR epidemic models, the chaotic Lorenz-63 system, and a high-dimensional two-layer Lorenz-96 system. In this setting, the method is used to recover classical system parameters from partial state observations across steady-state, chaotic, and high-dimensional multiscale dynamical systems. Numerical experiments with synthetic data show that the proposed approach accurately recovers parameters while requiring data-assimilation solves only on a prescribed coarse grid. The framework avoids quantum state tomography, illustrating a viable pathway for integrating quantum optimization into data-driven parameter estimation for nonlinear dynamical systems.
