Weak Dominant Balance for Robust Identification of Dynamically Consistent Fluid Flow Structure

2026-06-27

AI Summary

Extracting local physical mechanisms robustly from noisy, irregular real-world flow data remains highly challenging, as conventional approaches rely on numerical differentiation and are thus susceptible to noise amplification and divergence of high-order terms. This work proposes a weak dominant balance framework that projects the governing equations into a weak (integral) form, circumventing direct differentiation of raw data by employing smooth analytical test functions. For the first time, this enables derivative-free, data-driven decomposition of dynamical structures. The method is successfully applied to turbulent pipe flow governed by a third-order partial differential equation, accurately identifying dominant dynamical modes even under strong noise. Consistent mechanism-level physical interpretations are achieved across both direct numerical simulation and particle image velocimetry experimental data.

Abstract

Extracting interpretable, localized physical mechanisms from complex spatiotemporal data is a foundational challenge across physics, biology, and engineering, but has remained out of reach on real measurements. The central obstacle is obtaining high-quality gradients of data via numerical differentiation, which amplifies noise, diverges for high-order equations, and falters on irregular geometries, limiting the scope of existing approaches to clean simulations of low-order systems. Here, we present weak dominant balance, a derivative-free framework that projects governing equations into a weak (integral) formulation, offloading differentiation onto smooth analytical test functions and leaving the data untouched. The method sustains accurate regime identification under severe noise where existing approaches categorically fail, delivers the first data-driven decomposition of a third-order partial differential equation applied to turbulent duct flow, and produces matching decompositions across direct numerical simulation and particle-image velocimetry measurements of a wavy channel flow, uncovering a previously uncharacterized dynamical regime. Weak dominant balance brings mechanism-level analysis out of simulation and onto measured data, and opens complex physical systems to direct, equation-grounded interpretation.

Problem

• interpretable physical mechanisms
• spatiotemporal data
• numerical differentiation
• dynamically consistent fluid flow
• noisy measurements

Innovation

• weak dominant balance
• derivative-free
• weak formulation
• data-driven discovery
• turbulent flow