从部分观测状态轨迹学习降阶模型的非马尔可夫项算子推断
Operator inference of non-Markovian terms for learning reduced models from partially observed state trajectories
摘要：
本文介绍了一种非侵入性的模型降阶方法，用于从高维动力系统的部分观测状态轨迹中学习降阶模型。所提出的方法补偿信息的损失，由于部分观察到的状态，通过构建非马尔可夫简化模型，使未来状态的预测的基础上，历史的减少状态，在传统的马尔可夫简化模型，仅依赖于当前的减少状态来预测下一个状态。这项工作的核心贡献是一个数据采样计划，部分观察到的状态从高维动力系统和一个回归问题的制定，以适应非马尔可夫减少条款的采样状态。在一定条件下，所提出的方法从数据中恢复非常相同的非马尔可夫条款，一个获得的侵入式方法，需要的高维动力系统的控制方程和离散算子。数值结果表明，所提出的方法导致非马尔可夫减少模型的预测远远超出了训练制度。此外，在数值实验中，所提出的方法从只有20%观测状态分量的轨迹中学习非马尔可夫简化模型，其精度与传统的马尔可夫简化模型拟合到具有99%观测分量的轨迹一样。
英文摘要：
This work introduces a non-intrusive model reduction approach for learning reduced models from partially observed state trajectories of high-dimensional dynamical systems. The proposed approach compensates for the loss of information due to the partially observed states by constructing non-Markovian reduced models that make future-state predictions based on a history of reduced states, in contrast to traditional Markovian reduced models that rely on the current reduced state alone to predict the next state. The core contributions of this work are a data sampling scheme to sample partially observed states from high-dimensional dynamical systems and a formulation of a regression problem to fit the non-Markovian reduced terms to the sampled states. Under certain conditions, the proposed approach recovers from data the very same non-Markovian terms that one obtains with intrusive methods that require the governing equations and discrete operators of the high-dimensional dynamical system. Numerical results demonstrate that the proposed approach leads to non-Markovian reduced models that are predictive far beyond the training regime. Additionally, in the numerical experiments, the proposed approach learns non-Markovian reduced models from trajectories with only 20% observed state components that are about as accurate as traditional Markovian reduced models fitted to trajectories with 99% observed components.
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。
