Hierarchical Implicit Neural Emulators

TL;DR

This paper introduces a multiscale implicit neural emulator for PDEs that improves long-term stability and accuracy in modeling complex dynamical systems, especially turbulent fluid flows.

Contribution

It proposes a hierarchical, implicit neural approach inspired by numerical methods, enabling multiscale long-term predictions with active temporal downsampling adjustment.

Findings

Achieves high short-term accuracy in turbulent fluid dynamics

Produces stable long-term forecasts outperforming autoregressive models

Adds minimal computational overhead

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.