Weak Dominant Balance for Robust Identification of Dynamically Consistent Fluid Flow Structure
arXiv:2606.29047v1 Announce Type: cross 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 frame
The proliferation of complex spatiotemporal data in physics, biology, and engineering necessitates improved methods for extracting interpretable physical mechanisms, a challenge previously limited by numerical differentiation techniques.
This development allows for robust, derivative-free identification of fluid flow structures, overcoming key obstacles that previously limited the application of advanced analysis to noisy real-world data and irregular geometries.
The ability to accurately extract physical mechanisms from complex, noisy real-world data without relying on problematic numerical differentiation opens new avenues for AI application in scientific discovery and engineering design.
- · AI/ML researchers
- · Fluid dynamics engineers
- · Scientific computing
- · Material science
- · Traditional numerical differentiation methods
- · Early-stage physics-informed AI models
More accurate and interpretable AI models for physical systems, especially for complex fluid dynamics, will emerge.
This methodology could accelerate discovery in fields relying on spatiotemporal data, such as climate modeling, aerospace, and medical imaging.
The principle of weak dominant balance might generalize to other complex systems beyond fluid dynamics, enabling new forms of AI-driven scientific inquiry across diverse disciplines.
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Read at arXiv cs.LG