Benchmarking Long Roll-outs of Auto-regressive Neural Operators for the Compressible Navier-Stokes Equations with Conserved Quantity Correction

2026-01-30

AI Summary

This work addresses the instability of autoregressive neural operators in long-term simulations, which arises from error accumulation and violations of physical conservation laws. To mitigate this, the authors propose a model-agnostic conservation correction mechanism that explicitly embeds physical conservation constraints during inference, significantly enhancing the long-term stability of simulations for the compressible Navier–Stokes equations. Through spectral analysis, the study reveals the inadequacy of existing neural operators in modeling high-frequency components and demonstrates the critical role of conservation constraints in turbulent flow simulation. The proposed method is compatible with various neural operator architectures and improves both physical consistency and long-term predictive accuracy without requiring modifications to the underlying model structure.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Multiagent Systems: Adversarial Agents
• Search and Optimization: Non-convex Optimization

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• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
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Abstract

Deep learning has been proposed as an efficient alternative for the numerical approximation of PDE solutions, offering fast, iterative simulation of PDEs through the approximation of solution operators. However, deep learning solutions have struggle to perform well over long prediction durations due to the accumulation of auto-regressive error, which is compounded by the inability of models to conserve physical quantities. In this work, we present conserved quantity correction, a model-agnostic technique for incorporation physical conservation criteria within deep learning models. Our results demonstrate consistent improvement in the long-term stability of auto-regressive neural operator models, regardless of the model architecture. Furthermore, we analyze the performance of neural operators from the spectral domain, highlighting significant limitations of present architectures. These results highlight the need for future work to consider architectures that place specific emphasis on high frequency components, which are integral to the understanding and modeling of turbulent flows.

Problem

• long roll-outs
• auto-regressive error
• conserved quantities
• neural operators
• compressible Navier-Stokes equations

Innovation

• conserved quantity correction
• auto-regressive neural operators
• long roll-outs
• spectral analysis
• compressible Navier-Stokes equations