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.
@article{arxiv.2506.04528,
title = {Hierarchical Implicit Neural Emulators},
author = {Ruoxi Jiang and Xiao Zhang and Karan Jakhar and Peter Y. Lu and Pedram Hassanzadeh and Michael Maire and Rebecca Willett},
journal= {arXiv preprint arXiv:2506.04528},
year = {2025}
}