Differential-Integral Neural Operator for Long-Term Turbulence Forecasting

• URL: http://arxiv.org/abs/2509.21196v2
• Date: Fri, 26 Sep 2025 10:35:12 GMT
• Title: Differential-Integral Neural Operator for Long-Term Turbulence Forecasting
• Authors: Hao Wu, Yuan Gao, Fan Xu, Fan Zhang, Qingsong Wen, Kun Wang, Xiaomeng Huang, Xian Wu,
• Abstract summary: textbfunderlineDifferential-textbfunderlineIntegral textbfunderlineNeural textbfunderlineOperator (method)<n>method explicitly models the turbulent evolution through parallel branches that learn distinct physical operators.<n>It successfully suppresses error accumulation over hundreds of timesteps, maintains high fidelity in both the vorticity fields and energy spectra, and establishes a new benchmark for physically consistent, long-range turbulence forecast.
• Score: 43.04613533979613
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Accurately forecasting the long-term evolution of turbulence represents a grand challenge in scientific computing and is crucial for applications ranging from climate modeling to aerospace engineering. Existing deep learning methods, particularly neural operators, often fail in long-term autoregressive predictions, suffering from catastrophic error accumulation and a loss of physical fidelity. This failure stems from their inability to simultaneously capture the distinct mathematical structures that govern turbulent dynamics: local, dissipative effects and global, non-local interactions. In this paper, we propose the {\textbf{\underline{D}}}ifferential-{\textbf{\underline{I}}}ntegral {\textbf{\underline{N}}}eural {\textbf{\underline{O}}}perator (\method{}), a novel framework designed from a first-principles approach of operator decomposition. \method{} explicitly models the turbulent evolution through parallel branches that learn distinct physical operators: a local differential operator, realized by a constrained convolutional network that provably converges to a derivative, and a global integral operator, captured by a Transformer architecture that learns a data-driven global kernel. This physics-based decomposition endows \method{} with exceptional stability and robustness. Through extensive experiments on the challenging 2D Kolmogorov flow benchmark, we demonstrate that \method{} significantly outperforms state-of-the-art models in long-term forecasting. It successfully suppresses error accumulation over hundreds of timesteps, maintains high fidelity in both the vorticity fields and energy spectra, and establishes a new benchmark for physically consistent, long-range turbulence forecast.

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