Physics-Informed Neural Network for Solving 2D Steady Incompressible Navier-Stokes Equations: Application to Poiseuille Flow

Peter Anthony, Philibus M Gyuk and Isaac H Daniel
2025-06-18 621 views 34 downloads

 

This study explores the application of Physics-Informed Neural Networks (PINNs) to solve the two-dimensional steady incompressible Navier-Stokes equations, focusing on Poiseuille flow in a rectangular channel. Implemented using the DeepXDE library with a TensorFlow 1.x backend, the PINN embeds the governing partial differential equations and boundary conditions into its loss function. The neural network architecture consists of four hidden layers, each with 64 neurons. A hybrid optimization strategy, combining Adam (10,000 steps) and L-BFGS-B, ensured robust convergence. The composite loss function, comprising seven components (three for momentum and continuity equations, four for boundary conditions), decreased significantly, achieving a total test loss of 8.71×10^(-5) at step 9000. The predicted x-velocity component (u) was evaluated against the analytical Poiseuille solution, yielding an L_2 relative error of 0.0861 (8.61%). Visual comparisons confirm that the PINN accurately captures the parabolic velocity profile characteristic of Poiseuille flow. This work underscores the potential of PINNs as a data-efficient, mesh-free approach for solving fundamental fluid dynamics problems, paving the way for their application to more complex flow scenarios.

 

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