Solution of Incompressible Flow Equations with Physics and Equality Constrained Artificial Neural Networks

arXiv — cs.LGTuesday, November 25, 2025 at 5:00:00 AM
  • A novel meshless method has been introduced for solving incompressible Navier-Stokes equations in advection-dominated scenarios, utilizing physics- and equality-constrained artificial neural networks alongside a conditionally adaptive augmented Lagrangian formulation. This approach allows for the simultaneous parameterization of velocity and pressure fields, trained without labeled data, relying solely on governing equations and constraints.
  • This development is significant as it enhances the accuracy of simulations in fluid dynamics, particularly in complex flow scenarios. By employing a single neural network to address both velocity and pressure, it streamlines the computational process and potentially reduces the need for extensive labeled datasets, which are often challenging to obtain.
  • The introduction of this method aligns with ongoing advancements in artificial intelligence applications within computational fluid dynamics. It reflects a broader trend of integrating machine learning techniques to improve the efficiency and accuracy of numerical simulations, addressing challenges such as non-IID sampling and spatial complexity in physical systems, which are critical for advancing predictive modeling in various engineering fields.
— via World Pulse Now AI Editorial System

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