Stability Guided Neural Network For Hybrid Eulerian-Lagrangian Solvers

A Self Supervised Proof of Concept for Neural Network Enabled Predictive Blow Up Detection in 2D Hybrid Solvers

Abstract

Solver coupling induced instabilities is the primary problem faced by hybrid Eulerian-Langrangian solvers in vortex dominated flows. Current ML CFD methods target accuracy or speed, but numerical stability is handled by traditional correction methods which are typically threshold based or apply continuous corrections. This project proposes a Sta bility Guided Neural Network, a lightweight LSTM controller trained only on native solver failure trajectories, requiring no external DNS reference data. The SGNN monitors a 12-scalar diagnostic feature vector over a rolling 10-step window and predicts imminent numerical blow-up, enabling preemptive and intermittent application of classical stabilisation techniques only when necessary. Trained across four 2D periodic flow topologies (Kelvin–Helmholtz, Kolmogorov, Tay lor–Green, and random vortex blobs), the controller achieves 0.98 AUC in blow-up prediction and extends stable simu lation time by 1.56× to 2.24× across Reynolds numbers from 10,000 to 30,000, where the uncontrolled baseline solver fails deterministically. Because corrections are applied only when a risk threshold is crossed, the hybrid solver’s con servation properties and spectral cascade are preserved during all stable phases. This proof-of-concept demonstrates that prediction of solver-specific instabilities is a tractable and computationally lightweight objective, complementary to existing accuracy-focused ML-CFD methods.