控制瞬态放大提高长周期展开
Controlling Transient Amplification Improves Long-horizon Rollouts
AI总结：
本文通过分析发现瞬态放大是导致长周期展开误差的原因，提出交换性正则化方法，通过减少雅可比矩阵的正常性和交换子范数来提升模型的长周期展开能力。
摘要：
自回归神经模拟器现在在短周期物理系统预测上能与经典求解器相媲美，但其在长周期展开时准确性迅速下降。本文识别出在展开轨迹周围扰动的瞬态放大是导致展开误差的结构机制。通过线性化分析，我们发现当自回归轨迹上的雅可比矩阵非正交且非交换时，模型会瞬态放大误差，即使整体系统渐近稳定。基于此分析，我们提出交换性正则化：一种结合两种惩罚项的方法，旨在减少单个雅可比矩阵的非正交缺陷和跨步雅可比矩阵的交换子范数。惩罚项通过雅可比-向量积估计，无推理时间成本。我们展示了一个传播界，量化在近似交换性和正交性下的展开误差。我们评估了带有交换性正则化的UNet和FNO变体，在合成和真实1D和2D时空数据上实现了数千步的长周期展开。此外，我们展示该方法在ERA5数据上改进FourCastNet气候预测，无需使用任何新数据。增益在分布外情况最显著：训练在几百步轨迹上，正则化模型在初始条件上可维持数千步的展开，而基线模型则发散。
英文摘要：
Autoregressive neural simulators now match classical solvers on short-horizon prediction of physical systems, yet their accuracy degrades rapidly when rolled out over long horizons. In this work, we identify transient amplification of perturbations around rollout trajectories as a structural mechanism driving rollout error. Using a linearization analysis we show that when the Jacobians along an autoregressive trajectory are non-normal and non-commuting, the model amplifies errors transiently, resulting in model rollout drift even when the overall system is asymptotically stable. Building on the analysis, we propose commutativity regularization: a combination of two penalties designed to reduce the normality defect of individual Jacobians and the commutator norm of Jacobians across steps. The penalties are estimated with Jacobian-vector products and have no inference-time cost. We show a propagator bound that quantifies rollout error under approximate commutativity and normality. We evaluate UNet and FNO variants with commutativity regularization on 1D and 2D spatio-temporal data in synthetic and real settings, showing successful long-horizon rollouts over thousands of steps. Further, we show that the method improves FourCastNet climate forecasts on ERA5 without using any new data. The gain is most pronounced out-of-distribution: trained on trajectories of a few hundred steps, regularized models remain in-distribution for thousands of rollout steps on initial conditions where baselines diverge.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
