Muhammad Jalil Ahmad | Searcharxiv

arXiv2026

A Quantum Optimization Framework for Data-Assimilation-Augmented Parameter Estimation

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.

quant-ph↗

arXiv2026

A Data-Assimilation-Augmented Optimization Framework for Parameter Estimation in Dynamical Systems

Parameter estimation in nonlinear dynamical systems from observational data is a fundamental inverse problem with applications in many disciplines. In practice, this is further complicated by the fact that observations are often noisy, sparse, and available only for a subset of the state variables. Furthermore, the initial condition (IC) may be unknown or inaccurate, causing further complications for chaotic systems with sensitive dependence on initial conditions. In this work, we develop a data-assimilation-augmented optimization framework for parameter estimation in ordinary differential equations using partial state observations. The method introduces a nudged system driven by the available observed component and estimates the unknown parameters by minimizing a cost functional, defined as a time-delayed mismatch between the observations and the corresponding observed component of the nudged solution over the admissible parameter space. Since the nudged system can be arbitrarily initialized, this approach eliminates the dependence on accurate IC. Using the Lorenz-63 system as a test case, we establish theoretical results showing synchronization of the nudged solution under parameter agreement, stability under parameter mismatch, and well-posedness of the data-to-parameter inverse map under suitable nondegeneracy conditions. Structural & practical identifiability, and Sobol sensitivity analyses are incorporated to assess which parameters can be reliably estimated from the observations. Numerical experiments in both chaotic and non-chaotic regimes show that this framework accurately recovers parameters from noisy partial observations. Comparisons with an on-the-fly parameter learning method and with Bayesian MCMC estimation demonstrate that the proposed method remains accurate under partial observations and higher noise levels while requiring substantially lower computational cost.

math.DS↗