DRESO: An Adaptive Complementary Spectral Neural Operator for Robust Autoregressive Prediction

Neural operators learn mappings between function spaces and provide fast surrogates for partial differential equations (PDEs), but accurate one-step prediction does not guarantee stable autoregressive rollouts. DRIFT-Net combines a spectral branch for global low-frequency structure with an image branch for local details and nonstationary patterns. The two branches are fused through lightweight bandwise weighting (Li & Salim, 2026). However, DRIFT-Net’s hard spectral partition does not support direct gradient-based optimization of the cutoff, while its bandwise energy summary provides limited information about the spectral structure within each region. To address these limitations, we propose DRESO, a dual-region evidence-guided spectral operator, which consists of a learnable complementary filter (LCF) and an adaptive gain controller (AGC). First, LCF designs a smooth Gaussian low-pass filter with a learnable cutoff and its complementary high-pass filter. This design enables each spectral layer to adaptively learn its low–high frequency allocation during training. Then, based on the low- and high-frequency regions provided by LCF, AGC extracts ten spectral descriptors from each region, converts their normalized comparisons into sample–channel-specific gains, and uses these gains to recombine the independently transformed regional spectra before the inverse FFT. These descriptors provide richer regional spectral information for adaptive routing than raw features or low-dimensional spectral summaries. On the six CamLab-ETHZ tasks, DRESO-L achieves the lowest error on all six one-step problems. DRESO-B ranks second in each comparison and outperforms DRIFT-Net with 32.9% fewer parameters. DRESO-B also uses 44.0% fewer parameters than NESTOR-Small, the strongest competing baseline. Code is available at anonymous code repository.