用于从稀缺和低质量数据中学习简化模型的操作员推理
Operator inference with roll outs for learning reduced models from scarce and low-quality data
摘要：
数据驱动建模已经成为计算科学和工程中的关键构件。然而，科学和工程领域的可用数据通常很少，经常受到噪声污染，并受到测量误差和其他扰动的影响，这使得学习系统的动态具有挑战性。在这项工作中，我们建议通过操作员推理将数据驱动的建模与通过神经常微分方程的推出进行动态训练相结合。具有推出的操作员推理继承了传统操作员推理的可解释性，可扩展性和结构保留，同时利用多个时间步长上通过推出的动态训练来提高从低质量和噪声数据中学习的稳定性和鲁棒性。用描述浅水波和表面准地转动力学的数据进行的数值实验表明，即使数据在时间上被稀疏采样并且被高达10%的噪声污染，操作员对滚动的推断也可以从训练轨迹提供预测模型。
英文摘要：
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%.
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。
