Title: An Adaptive Framework for Autoregressive Forecasting in CFD Using Hybrid Modal Decomposition and Deep Learning Show Chinese title

Title: 基于混合模态分解与深度学习的CFD自回归预测自适应框架

Abstract: 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. Show Chinese abstract

Abstract: 本文工作，在作者们所知的范围内，首次提出了一个可泛化的完全数据驱动的自适应框架，旨在稳定深度学习（DL）自回归预测模型在长时间范围内的表现，目的是减少计算流体力学（CFD）模拟所需的计算成本。所提出的方法在两个阶段之间交替进行：(i) 使用训练好的DL模型预测选定时间间隔内流场的演变，以及(ii) 当稳定性下降时，用新生成的CFD数据更新模型，从而保持长期预测的准确性。 这种自适应再训练策略确保了鲁棒性，同时避免了自回归模型中常见的预测误差累积问题。 该框架在三个复杂程度逐渐增加的流动条件下进行了验证，从层流到湍流，展示了30%到95%的计算成本降低，且未损害物理一致性或准确性。 其完全数据驱动的本质使其易于适应各种时间相关的仿真问题。 实现该方法的代码作为开源发布，并将集成到即将发布的ModelFLOWs-app版本中。