论文标题
操作员推断与滚动的推断以学习稀缺和低质量数据的减少模型
Operator inference with roll outs for learning reduced models from scarce and low-quality data
论文作者
论文摘要
数据驱动的建模已成为计算科学和工程学的关键基础。但是，科学和工程中可用的数据通常很少，经常受到噪音的污染，并受到测量错误和其他扰动的影响，这使得学习系统充满挑战的动态。在这项工作中，我们建议通过操作员推断将数据驱动的建模与通过神经普通微分方程的滚动进行动态训练相结合。运营商推断滚动的推断继承了传统操作员推断的可解释性，可伸缩性和结构保存，同时通过多个时间步骤利用动态训练，以提高稳定性和鲁棒性，从而从低质量和嘈杂的数据中学习。描述浅水波和表面准地斑动力学的数据的数值实验表明，即使数据在及时稀少并以高达10％的噪声污染的数据中，具有训练轨迹的操作员的推理也可以提供训练轨迹的预测模型。
Data-driven modeling has become a key building block in computational science and engineering. However, data that are available in science and engineering are typically scarce, often polluted with noise and affected by measurement errors and other perturbations, which makes learning the dynamics of systems challenging. In this work, we propose to combine data-driven modeling via operator inference with the dynamic training via roll outs of neural ordinary differential equations. Operator inference with roll outs inherits interpretability, scalability, and structure preservation of traditional operator inference while leveraging the dynamic training via roll outs over multiple time steps to increase stability and robustness for learning from low-quality and noisy data. Numerical experiments with data describing shallow water waves and surface quasi-geostrophic dynamics demonstrate that operator inference with roll outs provides predictive models from training trajectories even if data are sampled sparsely in time and polluted with noise of up to 10%.
