SC Seminar John Harlim (Penn state)

Machine learning of missing dynamical systems
  • What Scientific Computing English Not a Seminar Seminars
  • When 21-05-2021 from 16:00 to 17:00 (Europe/Amsterdam / UTC200)
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Meeting ID: 863 2656 5885
Passcode: 931873

John Harlim (Penn State), Machine learning of missing dynamical systems

In the talk, I will discuss a general closure framework to compensate for the model error arising from missing dynamical systems. The proposed framework reformulates the model error problem into a supervised learning task to estimate a very high-dimensional closure model, deduced from the Mori-Zwanzig representation of a projected dynamical system with projection operator chosen based on Takens embedding theory. Besides theoretical convergence, this connection provides a systematic framework for closure modeling using available machine learning algorithms. I will demonstrate numerical results using a kernel-based linear estimator as well as neural network-based nonlinear estimators. If time permits, I will also discuss error bounds and mathematical conditions that allow for the estimated model to reproduce the underlying stationary statistics, such as one-point statistical moments and auto-correlation functions, in the context of learning Ito diffusions.