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arXiv 2107.09256cs.LGcs.NAmath.NA
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从噪声数据中学习低维动态系统模型的主动算子推理

Active operator inference for learning low-dimensional dynamical-system models from noisy data

Courant Institute of Mathematical Sciences, New York University(纽约大学柯朗数学科学研究所)

Wayne Isaac Tan Uy, Yuepeng Wang, Yuxiao Wen, Benjamin Peherstorfer

摘要:

噪声对学习动态系统模型提出了挑战,因为已经很小的变化可以扭曲轨迹数据所描述的动态。这项工作建立在科学机器学习的算子推理基础上,从被噪声污染的高维状态轨迹中推断出低维模型。分析表明,在一定条件下,推断的运营商是良好的研究基于投影的约简算子从传统的模型约简无偏估计。此外,操作员推理和基于投影的模型简化之间的连接使得能够限制使用学习模型相对于传统简化模型进行的预测的均方误差。该分析还激发了一个积极的运营商的推理方法,明智地采样高维轨迹的目的是通过减少噪声的影响,实现低均方误差。高维线性和非线性状态动力学的数值实验表明,主动算子推理得到的预测具有数量级较低的均方误差比传统的,等距采样的轨迹数据的算子推理。

英文摘要:

Noise poses a challenge for learning dynamical-system models because already small variations can distort the dynamics described by trajectory data. This work builds on operator inference from scientific machine learning to infer low-dimensional models from high-dimensional state trajectories polluted with noise. The presented analysis shows that, under certain conditions, the inferred operators are unbiased estimators of the well-studied projection-based reduced operators from traditional model reduction. Furthermore, the connection between operator inference and projection-based model reduction enables bounding the mean-squared errors of predictions made with the learned models with respect to traditional reduced models. The analysis also motivates an active operator inference approach that judiciously samples high-dimensional trajectories with the aim of achieving a low mean-squared error by reducing the effect of noise. Numerical experiments with high-dimensional linear and nonlinear state dynamics demonstrate that predictions obtained with active operator inference have orders of magnitude lower mean-squared errors than operator inference with traditional, equidistantly sampled trajectory data.

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。

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