Hierarchical Implicit Neural Emulators

Xiao Zhang (University of Chicago) · Rebecca Willett (U Chicago) · Ruoxi Jiang (Fudan University, The University of Chicago) · Karan Jakhar (University of Chicago) · Peter Y. Lu (Tufts University) · Pedram Hassanzadeh (University of Chicago) · Michael Maire (University of Chicago)

autoregressive baselinescomputational overheaddynamics across granularitieserror accumulationlong-range temporal coherencelong-term prediction accuracylong-term stable forecastslower-dimensional future state representationsmultiscale implicit neural emulatorneural pde solversnext-timestep refinementsnumerical implicit time-steppingphysical consistencyshort-term accuracytemporal downsampling ratiosturbulent fluid dynamics

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.