Learning Parameterized Stable Quadratic Governing Equations via a Neural Network

This project trains neural networks to learn stable quadratic models for the incompressible Navier-Stokes equations. The model is parametrized via $u_1$ and $u_2$ affecting boundary conditions, as well as the Reynolds number $Re$.

Data from simulations is projected onto a dominant subspace using SVD. A neural network is then trained on the projected data to capture both steady-state and oscillatory behaviors, while preserving stability. For discretization and simulation model for Navier-Stokes see this paper. For description of stable quadratic models see this paper.

See this notebook for the training and modeling workflow.