An Adaptive Framework for Autoregressive Forecasting in CFD Using Hybrid Modal Decomposition and Deep Learning

This work presents, to the best of the authors' knowledge, the first generalizable and fully data-driven adaptive framework designed to stabilize deep learning (DL) autoregressive forecasting models over long time horizons, with the goal of reducing the computational cost required in computational fluid dynamics (CFD) simulations.The proposed methodology alternates between two phases: (i) predicting the evolution of the flow field over a selected time interval using a trained DL model, and (ii) updating the model with newly generated CFD data when stability degrades, thus maintaining accurate long-term forecasting. This adaptive retraining strategy ensures robustness while avoiding the accumulation of predictive errors typical in autoregressive models. The framework is validated across three increasingly complex flow regimes, from laminar to turbulent, demonstrating from 30 % to 95 % reduction in computational cost without compromising physical consistency or accuracy. Its entirely data-driven nature makes it easily adaptable to a wide range of time-dependent simulation problems. The code implementing this methodology is available as open-source and it will be integrated into the upcoming release of the ModelFLOWs-app.