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.
翻译:这项工作引入了一种非侵入性模型减少方法,用于从部分观测到的高维动态系统的状态轨迹中学习减少的模型,从部分观测到的高维动态系统轨迹中学习部分观测到的国家轨迹;拟议方法通过建立非马尔科维亚减少的模型弥补了由于部分观测到的状态而导致信息丢失的情况,这些模型根据减少的状态的历史作出未来国家的预测,而传统的马尔科维亚减少的模型则依赖目前缩小的状态单靠预测下一个状态来预测下一个状态。这项工作的核心贡献是数据抽样计划,从高维维动力系统中抽取部分观测到的状态;此外,在数字实验中,拟议方法从数据中学习了非马尔科维亚减少的模型,从只有20 % 所观察到的精确度的传统模型恢复到20 % 所观察到的正确度。