AIMS Lab Seminar - Mohammad Farazmand - Data-driven prediction of multistable systems from partial observations
Title: Data-driven prediction of multistable systems from partial observations
Abstract: Direct numerical simulation of spatiotemporal dynamics using a PDE model requires the initial condition to be known on a dense spatial grid. In practice, however, such detailed measurements of the initial condition are often infeasible. I argue that many scientific questions can be addressed (at least partially) without such detailed simulations. In particular, I will introduce a data-driven method, based on semi-supervised classification, to predict the asymptotic state of multistable systems when only sparse spatial measurements of the system are feasible. Our method predicts the asymptotic behavior of an observed state by quantifying its proximity to the states in a precomputed library of data. To quantify this proximity, we introduce a sparsity promoting metric-learning (SPML) optimization, which learns a metric directly from the precomputed data. The resulting metric has two important properties: (i) It is compatible with the precomputed library, and (ii) It is computable from sparse measurements. I demonstrate the application of this method on a multistable reaction-diffusion equation which has four asymptotically stable steady states.
Date/Time: Monday November 23, 11:30am - 12:20pm
Join Zoom Meeting
Meeting ID: 910 5698 2661