使用变分量子算法从稀疏传感器重建流体速度场
Reconstructing fluid velocity fields from sparse sensors using a variational quantum algorithm
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中文总结 AI 辅助
本文提出一种变分量子算法，通过将时空解编码为单个量子态并联合优化测量失配与PDE违反项，从稀疏传感器数据重建非线性流体速度场，并在Burgers和Kuramoto-Sivashinsky方程上验证了其有效性。
中文摘要 AI 辅助
从稀疏测量中重建由非线性偏微分方程（PDE）控制的场是一项具有挑战性的任务，因为控制方程是强非线性的，且观测仅在少数位置可用。流体速度场是一个代表性案例。在本文中，我们提出了一种变分量子算法，该算法一次性重建整个时空域上的解。该方法不是在时间上逐步推进，而是将完整的离散时空解编码在单个变分量子态中，从而所有时间点被联合优化。代价函数结合了稀疏测量失配项和基于物理信息的PDE违反项，使数据和控制方程同时约束解。我们通过数值模拟在一维Burgers和Kuramoto-Sivashinsky方程上演示了该方法。结果表明，采用时空编码方案的变分量子算法为重建非线性PDE动力学提供了一种紧凑的框架。
英文摘要
Reconstructing fields governed by nonlinear partial differential equations (PDEs) from sparse measurements is a challenging task because the governing equations are strongly nonlinear and observations are available at only a few locations. Fluid velocity fields are a representative case. In this paper, we propose a variational quantum algorithm that reconstructs the solution over the entire spacetime domain at once. Rather than marching in time, the method encodes the full discrete spacetime solution in a single variational quantum state, so that all time points are optimized jointly. The cost function combines a sparse-measurement mismatch term with a physics-informed PDE violation term, letting data and the governing equation constrain the solution simultaneously. We demonstrate the method on the one-dimensional Burgers and Kuramoto--Sivashinsky equations using numerical simulations. The results suggest that variational quantum algorithms with a spacetime encoding scheme offer a compact framework for reconstructing nonlinear PDE dynamics.
发表机构
- Florida State University（佛罗里达州立大学）
- FAMU-FSU College of Engineering, Florida State University（佛罗里达州立大学 FAMU-FSU 工程学院）
机构由 AI 辅助整理，请以论文原文为准。
