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

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.

HydroGym: A Reinforcement Learning Platform for Fluid Dynamics

Modeling and controlling fluid flows is critical for several fields of science and engineering, including transportation, energy, and medicine. Effective flow control can lead to, e.g., lift increase, drag reduction, mixing enhancement, and noise reduction. However, controlling a fluid faces several significant challenges, including high-dimensional, nonlinear, and multiscale interactions in space and time. Reinforcement learning (RL) has recently shown great success in complex domains, such as robotics and protein folding, but its application to flow control is hindered by a lack of standardized benchmark platforms and the computational demands of fluid simulations. To address these challenges, we introduce HydroGym, a solver-independent RL platform for flow control research. HydroGym integrates sophisticated flow control benchmarks, scalable runtime infrastructure, and state-of-the-art RL algorithms. Our platform includes 42 validated environments spanning from canonical laminar flows to complex three-dimensional turbulent scenarios, validated over a wide range of Reynolds numbers. We provide non-differentiable solvers for traditional RL and differentiable solvers that dramatically improve sample efficiency through gradient-enhanced optimization. Comprehensive evaluation reveals that RL agents consistently discover robust control principles across configurations, such as boundary layer manipulation, acoustic feedback disruption, and wake reorganization. Transfer learning studies demonstrate that controllers learned at one Reynolds number or geometry adapt efficiently to new conditions, requiring approximately 50% fewer training episodes. The HydroGym platform is highly extensible and scalable, providing a framework for researchers in fluid dynamics, machine learning, and control to add environments, surrogate models, and control algorithms to advance science and technology.