{"ID":2866051,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.21196","arxiv_id":"2509.21196","title":"Differential-Integral Neural Operator for Long-Term Turbulence Forecasting","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.","short_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, suf...","url_abs":"https://arxiv.org/abs/2509.21196","url_pdf":"https://arxiv.org/pdf/2509.21196v3","authors":"[\"Hao Wu\",\"Yuan Gao\",\"Fan Xu\",\"Fan Zhang\",\"Qingsong Wen\",\"Kun Wang\",\"Xiaomeng Huang\",\"Xian Wu\"]","published":"2025-09-25T14:08:26Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.CV\"]","methods":"[\"Transformer\"]","has_code":false}