Hierarchical Implicit Neural Emulators
This work addresses the challenge of maintaining stability and physical consistency in neural PDE solvers for complex dynamical systems, representing an incremental improvement over existing methods.
The paper tackles the problem of error accumulation and instability in neural PDE solvers for long-term predictions by introducing a multiscale implicit neural emulator that conditions on hierarchical future state representations, achieving high short-term accuracy and stable long-term forecasts in turbulent fluid dynamics while outperforming autoregressive baselines with minimal computational overhead.
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.