论文标题
在中等模型不确定性下预测错误的通用上限估计值
Universal Upper Estimate for Prediction Errors under Moderate Model Uncertainty
论文作者
论文摘要
我们在中等但未知的模型不确定性下得出了模型预测误差的通用上限估计。我们的估计值给出了沿模型轨迹的领先顺序轨迹 - 不确定性的上限，仅作为模型已知Cauchy-Green应变张量不变的功能。我们的界限原来是最佳的，这意味着对于通用系统无法改进它们。与模型不确定性相关的领先轨迹不确定性的数量是模型敏感性，我们认为这是快速全局评估对相空间各个域中建模不确定性的影响的有用工具。研究有限时间Lyapunov指数捕获对建模错误的敏感性的期望，我们表明这通常不遵循。但是，我们发现MS字段中FTLE的某些重要特征持续存在。
We derive universal upper estimates for model-prediction error under moderate but otherwise unknown model uncertainty. Our estimates give upper bounds on the leading order trajectory-uncertainty arising along model trajectories, solely as functions of the invariants of the known Cauchy-Green strain tensor of the model. Our bounds turn out to be optimal, which means that they cannot be improved for general systems. The quantity relating the leading-order trajectory-uncertainty to the model uncertainty is the Model Sensitivity, which we find to be a useful tool for a quick global assessment of the impact of modeling uncertainties in various domains of the phase space. Examining the expectation that Finite-Time Lyapunov Exponents capture sensitivity to modeling errors, we show that this does not generally follow. However, we find that certain important features of the FTLE persist in the MS field.
