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arXiv · 2506.04528

Hierarchical Implicit Neural Emulators

Ruoxi Jiang·Xiao Zhang·Karan Jakhar·Peter Y. Lu·Pedram Hassanzadeh·Michael Maire·Rebecca Willett
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Abstract

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.

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Ruoxi Jiang, Xiao Zhang, Karan Jakhar, Peter Y. Lu, Pedram Hassanzadeh, Michael Maire, Rebecca Willett. 2025-06-05. Hierarchical Implicit Neural Emulators. https://arxiv.org/abs/2506.04528

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