2025/06/05 by Ruoxi Jiang, Xiao Zhang, Jiang, Ruoxi +11 · 2 citations
Computer Science · Physics and Astronomy · #FOS: Computer and information sciences #Generative Adversarial Networks and Image Synthesis #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Neural Networks and Reservoir Computing
paper · pdf · doi:10.48550/arxiv.2506.04528
openalex publication_date 2025/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Neural PDE solvers offer a powerful tool for modeling complex dynamical systems, but often struggle with error accumulation over long time horizons and maintaining stability and physical consistency. We introduce a multiscale implicit neural emulator that enhances long-term prediction accuracy by conditioning on a hierarchy of lower-dimensional future state representations. Drawing inspiration from the stability properties of numerical implicit time-stepping methods, our approach leverages predictions several steps ahead in time at increasing compression rates for next-timestep refinements. By actively adjusting the temporal downsampling ratios, our design enables the model to capture dynamics across multiple granularities and enforce long-range temporal coherence. Experiments on turbulent fluid dynamics show that our method achieves high short-term accuracy and produces long-term stable forecasts, significantly outperforming autoregressive baselines while adding minimal computational overhead.