Continuous data assimilation for hydrodynamics: consistent discretization and application to moment recovery
arXiv:2409.03872 · doi:10.1016/j.jcp.2025.114199
Abstract
Motivated by the challenge of moment recovery in hydrodynamic approximation in kinetic theory, we propose a data-driven approach for the hydrodynamic models. Inspired by continuous data assimilation, our method introduces a relaxation-based nudging system coupled with a novel discretization technique. This approach facilitates the simultaneous recovery of both the force term and a high-resolution solution from sparsely observed data. To address potential numerical artifacts, we use kernel regression to fit the observed data. We also analyze the convergence of the proposed nudging system under both full and partial data scenarios. When applied to moment systems, the source term involves the derivative of higher-order moments, our approach serves as a crucial step for data preparation in machine-learning based moment closure models. Multiple numerical experiments demonstrate the effectiveness of our algorithm, and we discuss its potential extension to high-dimensional systems.
arXiv commentUpdated version in Journal of Computational Physics
References in corpus (9)
- Continuous Data Assimilation Using General Interpolant Observables
- Fast algorithms for computing the Boltzmann collision operator
- Continuous Data Assimilation for the 2D Bénard Convection through Velocity Measurements Alone
- A Computational Study of a Data Assimilation Algorithm for the Two-dimensional Navier--Stokes Equations
- Inferring flow parameters and turbulent configuration with physics-informed data-assimilation and spectral nudging
- Machine learning moment closure models for the radiative transfer equation I: directly learning a gradient based closure
- Concurrent multi-parameter learning demonstrated on the Kuramoto-Sivashinsky equation
- Convergence Analysis of a Viscosity Parameter Recovery Algorithm for the 2D Navier-Stokes Equations
- A fast Fourier spectral method for the homogeneous Boltzmann equation with non-cutoff collision kernels