mlsanityData to 7 Oct 2026

Hierarchical Implicit Neural Emulators

arXiv 2506.04528 ↗First posted 5 Jun 2025cs.LGcited by 9

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Abstract (arXiv)

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.

Key facts. Cited by 9 papers in the map (data through 7 Oct 2026). Builds on 32 of its 55 references that are in the map. First posted on arXiv 5 Jun 2025.

Builds on

32 of 55 references.

References · 32

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20 more
  1. 2022Towards Multi-spatiotemporal-scale Generalized PDE Modelingcited by 190
  2. 2023GenCast: Diffusion-based ensemble forecasting for medium-range weathercited by 169
  3. 2023DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecastingcited by 105
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  7. 2018Learning to Predict the Cosmological Structure Formationcited by 38
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  10. 2024Differentiability in Unrolled Training of Neural Physics Simulators on Transient Dynamicscited by 25
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  12. 2025Thermalizer: Stable autoregressive neural emulation of spatiotemporal chaoscited by 21
  13. 2024When are dynamical systems learned from time series data statistically accurate?cited by 14
  14. 2022Field Level Neural Network Emulator for Cosmological N-body Simulationscited by 13
  15. 2023Learning Closed-form Equations for Subgrid-scale Closures from High-fidelity Data: Promises and Challengescited by 9
  16. 2019Multigrid Neural Memorycited by 7
  17. 2024Embed and Emulate: Contrastive representations for simulation-based inferencecited by 3
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  19. 2022Simple lessons from complex learning: what a neural network model learns about cosmic structure formationcited by 2
  20. 2024Nested Diffusion Models Using Hierarchical Latent Priorscited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 2; 2026: 7.

9 papers.

  1. 2025Probing forced responses and causality in data-driven climate emulators: conceptual limitations and the role of reduced-order modelscited by 6
  2. 2025Method of Manufactured Learning for Solver-free Training of Neural Operatorscited by 3
  3. 2026Cheap2Rich: A Multi-Fidelity Framework for Data Assimilation and System Identification of Multiscale Physics -- Rotating Detonation Enginescited by 3
  4. 2026Project and Generate: Divergence-Free Neural Operators for Incompressible Flowscited by 3
  5. 2026SENDAI: A Hierarchical Sparse-measurement, EfficieNt Data AssImilation Frameworkcited by 2
  6. 2026Accelerating PDE Surrogates via RL-Guided Mesh Optimizationcited by 1
  7. 2026Nested Spatio-Temporal Time Series Forecastingcited by 1
  8. 2026Eigenanalysis framework for autoregressive neural emulators of multi-scale chaotic dynamicscited by 0
  9. 2026CasEm: A Cascade Architecture for Long-Horizon Neural Emulationcited by 0