下一代储层计算的不确定性量化及其在记忆驱动动力系统中的应用
Uncertainty Quantification of Next Generation Reservoir Computing with Applications to Memory-Driven Dynamical Systems
- Cornell University（康奈尔大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究针对下一代储层计算（NGRC）的不确定性量化，分析贝叶斯岭回归与共形预测区间的差异，揭示维度、正则化及残差分布的影响，为储层预测提供选择与解释不确定性方法的理论框架。
AI中文摘要：
具有记忆的非线性动力系统广泛存在于科学和工程领域，然而对于诸如下一代储层计算（NGRC）等高效预测方法的不确定性量化仍发展不足。我们研究了NGRC的贝叶斯岭回归和共形预测区间，并刻画了它们的不确定性估计何时一致或不同。在低维情况下，它们的渐近宽度由残差分布的不同汇总统计量决定，因此一致性取决于残差形状而非仅维度。在高维情况下，正则化在估计方差、收缩偏差和后验不确定性之间引入了进一步的权衡，导致贝叶斯区间比共形区间更宽或更窄的机制之间存在明确的转变。我们将这些结果推广到二次NGRC特征映射，并给出了将分析迁移到时间依赖预测窗口的充分条件。模拟和真实数据实验支持理论预测，并展示了残差分布、正则化、维度和分布偏移如何影响区间校准和效率。这些结果为在基于储层的预测中选择和解释不确定性量化方法提供了一个原则性框架。
英文摘要：
Nonlinear dynamical systems with memory arise across science and engineering, yet uncertainty quantification for efficient forecasting methods such as Next Generation Reservoir Computing (NGRC) remains underdeveloped. We study Bayesian ridge and conformal prediction intervals for NGRC and characterize when their uncertainty estimates agree or differ. In low dimensions, their asymptotic widths are governed by different summaries of the residual distribution, so agreement depends on residual shape rather than dimensionality alone. In high dimensions, regularization introduces a further tradeoff between estimation variance, shrinkage bias, and posterior uncertainty, leading to an explicit transition between regimes where Bayesian intervals are wider or narrower than conformal intervals. We extend these results to quadratic NGRC feature maps and give sufficient conditions for transferring the analysis to temporally dependent forecast windows. Simulations and real-data experiments support the theoretical predictions and illustrate how residual distribution, regularization, dimensionality, and distribution shift affect interval calibration and efficiency. These results provide a principled framework for choosing and interpreting uncertainty quantification methods in reservoir-based forecasting.
