A physics-data combined neural network-based finite volume parametric reduced order model

A novel physics-data combined finite volume parametric reduced order model (ROM) for incompressible flows is presented in this paper. The novelty lies in that the semi-implicit method for pressure-linked equations (SIMPLE) is embedded into our previously developed physics-data combined machine learning based parametric ROM framework. It is a finite volume physics-data combined neural network-based parametric ROM. It uses proper orthogonal decomposition (POD) to extract a low-dimensional basis from high-fidelity simulations across varying parameters (e.g., Reynolds number), and trains a neural network to predict the corresponding modal coefficients. But unlike pure data-driven “black-box” ROM, we enforce mass conservation at the reduced manifold space by incorporating a finite volume informed loss: the discrete continuity residual arising from the momentum–pressure coupling is projected onto the POD subspace and penalized during training. This “SIMPLE algorithm projection residual loss” ensures the velocity field in the reduced manifold space remains divergence-free. Three test cases are demonstrated to show the capabilities of this newly presented physics-data combined finite volume parametric ROM, such as lid-driven cavity, thermally driven channel, and backward-facing step configurations. The results show that the proposed finite volume ROMs achieve high accuracy in steady-state predictions for incompressible flows and exhibit excellent stability and generalization ability across parameter regimes.