AI 中文总结
研究从轨迹数据恢复二维伊藤生成器的难题，提出结合多种技术的WG-SINDy估计器，在29个合成二维系统上评估，给出多方面实验结果，虽为合成数据诊断，但有一定参考价值。
AI 中文摘要
从轨迹数据中恢复二维伊藤生成器具有挑战性，因为漂移增量的信噪比低、二元弱设计可能病态，且无约束张量估计不一定是半正定的。我们研究了WG-SINDy估计器，它结合了协方差形状的空间核、岭稳定的局部多项式投影、自适应LASSO/STLSQ选择、每个分量样本内可行的对角GLS传递以及PSD投影 - 具有适度各向同性收缩的Cholesky读出。我们在29个合成二维系统上评估了该估计器，给出了具体的实验结果，包括满足恢复合同的数量、中位数中心网格漂移度量、中位数张量误差等。这些结果是合成的、样本内采样区域诊断，未建立通用或实际数据恢复。
英文摘要
Recovering two-dimensional Ito generators from trajectory data is difficult because drift increments have low signal-to-noise, bivariate weak designs can be ill-conditioned, and unconstrained tensor estimates need not be positive semidefinite. We study WG-SINDy estimator combining covariance-shaped spatial kernels, a ridge-stabilized local-polynomial projection, adaptive-LASSO/STLSQ selection, one in-sample per-component feasible diagonal GLS pass, and a PSD projection--Cholesky read-out with mild isotropic shrinkage. The released estimator uses a data-dependent full-cloud smoother and one in-sample per-component feasible diagonal GLS pass; accordingly, we do not claim exact finite-sample martingale cancellation or a feasible-GLS efficiency theorem for the reported implementation. We evaluate the estimator on 29 synthetic two-dimensional systems: 19 meet their declared per-system recovery contracts, eight are retained as named limits, and two remain scoped reviews. Across the 19 PASS rows, the median central-grid drift metric is 0.204 and the median tensor error is 0.0397. Among the six systems with a finite, non-degenerate off-diagonal target, the median $a_{12}$ cosine is 0.997. Positive-semidefinite validity is imposed by construction. These results are synthetic, in-sample sampled-region diagnostics and do not establish universal or real-data recovery.
Comments45 pages
