Hierarchical Implicit Neural Emulators

2025-06-05

AI Summary

Neural PDE solvers suffer from error accumulation, poor long-term stability, and physical inconsistency in extended-time forecasting. To address these limitations, this work proposes the Multi-scale Implicit Neural Simulator (MINS). MINS introduces a hierarchical implicit conditioning mechanism that dynamically adjusts temporal downsampling rates to jointly model multi-granularity dynamics; it guides fine-grained one-step predictions using hierarchically compressed future-state representations and embeds implicit time-stepping stability—previously unexplored in neural PDE architectures—directly into the model design. The framework integrates implicit neural networks, multi-scale temporal compression, hierarchical conditional prediction, and physics-guided self-supervised training. On turbulent flow simulation, MINS achieves an 18% improvement in short-term accuracy, reduces hundred-step prediction error by 3.2×, preserves physically stable long-term trajectories, and incurs less than 5% additional computational overhead.

Technology Category

• Machine Learning: Neuro-Symbolic Learning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Multiagent Systems: Multiagent Learning

Application Category

• Web Mining and Content Analysis: Web data generation and simulation
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• Enhances long-term prediction accuracy in neural PDE solvers
• Addresses error accumulation and stability in dynamical systems
• Improves temporal coherence across multiple granularities in forecasts

Innovation

• Multiscale implicit neural emulator enhances prediction
• Leverages ahead predictions at increasing compression
• Adjusts temporal ratios for multi-granularity dynamics