DRIFT-Net: A Spectral--Coupled Neural Operator for PDEs Learning
This work addresses the challenge of global consistency in PDE learning for computational science, offering a more efficient and accurate solver, though it is incremental as it builds on existing attention-based methods.
The paper tackles the problem of error accumulation and drift in neural PDE solvers by proposing DRIFT-Net, a dual-branch neural operator that combines spectral and image branches to improve global coupling and local detail preservation, resulting in a 7%–54% reduction in relative L1 error, a 15% decrease in parameters, and higher throughput compared to baselines.
Learning PDE dynamics with neural solvers can significantly improve wall-clock efficiency and accuracy compared with classical numerical solvers. In recent years, foundation models for PDEs have largely adopted multi-scale windowed self-attention, with the scOT backbone in \textsc{Poseidon} serving as a representative example. However, because of their locality, truly globally consistent spectral coupling can only be propagated gradually through deep stacking and window shifting. This weakens global coupling and leads to error accumulation and drift during closed-loop rollouts. To address this, we propose \textbf{DRIFT-Net}. It employs a dual-branch design comprising a spectral branch and an image branch. The spectral branch is responsible for capturing global, large-scale low-frequency information, whereas the image branch focuses on local details and nonstationary structures. Specifically, we first perform controlled, lightweight mixing within the low-frequency range. Then we fuse the spectral and image paths at each layer via bandwise weighting, which avoids the width inflation and training instability caused by naive concatenation. The fused result is transformed back into the spatial domain and added to the image branch, thereby preserving both global structure and high-frequency details across scales. Compared with strong attention-based baselines, DRIFT-Net achieves lower error and higher throughput with fewer parameters under identical training settings and budget. On Navier--Stokes benchmarks, the relative $L_{1}$ error is reduced by 7\%--54\%, the parameter count decreases by about 15\%, and the throughput remains higher than scOT. Ablation studies and theoretical analyses further demonstrate the stability and effectiveness of this design. The code is available at https://github.com/cruiseresearchgroup/DRIFT-Net.