Beijing Institute of Mathematical Sciences and Applications

Yi Zhu

Haijun Yu

Thursday, April 14, 2022 10:00 AM - 11:30 AM

Tencent 836 6547 4971 ()

With recent advancements in machine learning and growing availability of data, there is an increasing focus on developing machine-learning-based methods for building dynamical models from observations of natural processes. However, existing machine learning methods usually lead to black-box models, the learned mathematical models may lack a theoretical guarantee of long time stability. We propose a systematic method (OnsagerNet) for learning stable and interpretable low-dimensional dynamical models based on a generalized Onsager principle. The learned dynamics are autonomous ordinary differential equations parameterized by neural networks that retain clear physical structure information. The deep neural networks with rectified power units(RePU) are used to ensure the smoothness of learned dynamics and good approximation capability. For high dimensional problems with a low dimensional slow manifold, an autoencoder with isometric regularization is proposed to find generalized coordinates on which we learn the generalized Onsager dynamics. The method exhibits clear advantages in several benchmark problems for learning ordinary differential equations. We also applied this method as a model reduction tool to learn Lorenz-like low-dimensional models for the Rayleigh-Benard convection problem and derive moment-closure models for the Fokker-Planck equation of liquid crystal polymer dynamics. In those applications, both qualitative and quantitative properties of the underlying dynamics are captured.

于海军，中国科学院数学与系统科学研究院 研究员。分别于2002年,2007年获得北京大学学士学位和博士学位。2007-2010年曾先后在美国普林斯顿大学和普渡大学从事博士后研究。主要研究方向为高精度数值方法. 在复杂流体的数学建模和计算, 高维偏微分方程稀疏网格谱方法，非梯度系统的相变路径高精度计算等方面取得多项重要成果。先后获得过中科院陈景润之星人才项目, 基金委重大研究计划和国际合作项目等资助。现任北京市计算数学学会理事, 中国工业与应用数学学会大数据与人工智能专委会委员.