Hierarchical Implicit Neural Emulators

• URL: http://arxiv.org/abs/2506.04528v1
• Date: Thu, 05 Jun 2025 00:28:26 GMT
• Title: Hierarchical Implicit Neural Emulators
• Authors: Ruoxi Jiang, Xiao Zhang, Karan Jakhar, Peter Y. Lu, Pedram Hassanzadeh, Michael Maire, Rebecca Willett,
• Abstract summary: We introduce a multiscale implicit neural emulator that enhances long-term prediction accuracy.<n>Our approach leverages predictions several steps ahead in time at increasing compression rates for next-timestep refinements.<n> Experiments on turbulent fluid dynamics show that our method achieves high short-term accuracy and produces long-term stable forecasts.
• Score: 20.09615751270837
• License: http://creativecommons.org/licenses/by/4.0/
• 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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