JAWS：通过空间自适应雅可比正则化增强神经算子的长期推广

Data-driven surrogate models enhance the efficiency of simulating continuous dynamical systems; however, their autoregressive rollouts are often constrained by instability and spectral blow-up. While global regularization techniques can enforce contractive dynamics, they uniformly dampen high-frequency features, leading to a contraction-dissipation dilemma. Additionally, long-horizon trajectory optimization methods that explicitly correct drift face bottlenecks due to memory constraints. JAWS (Jacobian-Adaptive Weighting for Stability) is proposed as a probabilistic regularization strategy to address these limitations. By framing operator learning as Maximum A Posteriori (MAP) estimation with spatially heteroscedastic uncertainty, JAWS offers a novel solution to enhance stability and efficiency over extended time horizons.