Work

Reconstructing fluid velocity fields from sparse sensors using a variational quantum algorithm

Year: 2026

Type: preprint

Abstract: 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.09268

Authors: Nguyen, Nhat-Quang, Akash, Mohammad Mehedi Hasan, Shoele, Kourosh, Chen, Yanzhu, Wu, Huixuan

Institutions: Florida State University, Florida A&M University - Florida State University College of Engineering, Florida Agricultural and Mechanical University

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: Florida State University, Air Force Office of Scientific Research

Award: G1523888516

OpenAlex ID: W7212137538

Cites: 7

Cited by:

Related to: 10