A Hybrid Reduced-Order Modeling Framework for Accelerating Physics-Informed Neural Networks in Modeling Flow Instabilities

Kelvin-Helmholtz (KH) and Holmboe (H) instabilities are key to mixing in stratified shear flows but require computationally intensive simulations like Large Eddy Simulations (LES) to resolve across broad parameter spaces defined by the Richardson number (J) and scale ratio (R), the latter denoting the ratio of shear to stratification layer thickness. While Physics-Informed Neural Networks (PINNs) offer a physics-guided alternative, they suffer from spectral bias, require extensive hyperparameter tuning, and converge slowly. To overcome these limitations, we propose a hybrid framework that integrates reduced-order modeling (ROM) with PINNs for efficient and accurate prediction of these instabilities. LES-generated buoyancy and vorticity fields across a range of (J, R) values were compressed using a convolutional autoencoder (CAE) and evolved temporally using an LSTM network. To improve spatial fidelity, we implemented a multiscale CAE with Butterworth-filtered bands and enhanced fine-scale reconstruction using a U-Net with transposed convolutions. The trained U-Net ROM serves as an effective initial guess for PINNs, accelerating convergence and improving accuracy. Our framework achieves R² > 95% across test cases, enabling fast, robust modeling of nonlinear flow dynamics and instability transitions.