Improving Long-term Autoregressive Spatiotemporal Predictions: A Proof of Concept with Fluid Dynamics

Abstract: Data-driven methods are emerging as efficient alternatives to traditional numerical forecasting, offering fast inference and lower computational cost. Yet, for complex systems, long-term accuracy often deteriorates due to error accumulation, and autoregressive training (though effective) demands large GPU memory and may sacrifice short-term performance. We propose the Stochastic PushForward (SPF) framework, which retains one-step-ahead training while enabling multi-step learning. SPF builds a supplementary dataset from model predictions and combines it with ground truth via a stochastic acquisition strategy, balancing short- and long-term performance while reducing overfitting. Multi-step predictions are precomputed between epochs, keeping memory usage stable without storing full unrolled sequences. Experiments on the Burgers' equation and the Shallow Water benchmark show that SPF achieves higher long-term accuracy than autoregressive methods while lowering memory requirements, making it promising for resource-limited and complex simulations.