Model-agnostic AI framework with explicit time integration for long-term fluid dynamics prediction

Abstract

The integration of predictive AI into computational design and engineering workflows is often hindered by the challenge of long-term forecasting performance. This study presents a robust framework for AI-accelerated flow simulation, specifically addressing the critical issue of error accumulation in auto-regressive (AR) surrogate models, which is a key bottleneck for their practical use in the design cycle. We introduce the first implementation of the two-step Adams–Bashforth method specifically tailored for data-driven AR prediction, leveraging historical derivative information to enhance numerical stability without additional computational overhead. To validate our approach, we systematically evaluate time integration schemes across canonical two-dimensional partial differential equations (advection, heat, and Burgers’ equations) before extending to complex Navier–Stokes cylinder vortex shedding dynamics. Additionally, we develop three novel adaptive weighting strategies that dynamically adjust the importance of different future time-steps during multi-step rollout training. Our analysis reveals that as physical complexity increases, such sophisticated rollout techniques become essential, with the Adams–Bashforth scheme demonstrating consistent robustness across investigated systems and our best adaptive approach delivering an 89% improvement over conventional fixed-weight methods while maintaining similar computational costs. For the complex Navier–Stokes vortex shedding problem, despite using an extremely lightweight graph neural network with just 1177 trainable parameters and training on only 50 snapshots, our framework accurately predicts 350 future time-steps—a 7:1 prediction-to-training ratio—reducing mean squared error from 0.125 (single-step direct prediction) to 0.002 (Adams–Bashforth with proposed multi-step rollout). Our integrated methodology demonstrates an 83% improvement over standard noise injection techniques and maintains robustness under severe spatial constraints; specifically, when trained on only a partial spatial domain, it still achieves 58% and 27% improvements over direct prediction and forward Euler methods, respectively. Our framework’s model-agnostic design, operating at the fundamental level of AR prediction mechanics, enables direct integration with any neural network architecture without requiring model-specific modifications, introducing a versatile solution for robust long-term spatio-temporal predictions across various engineering disciplines.