[00975] Data-driven methods for learning mathematical models
Session Time & Room : 5D (Aug.25, 15:30-17:10) @G703
Type : Proposal of Minisymposium
Abstract : Mathematical models are important tools helping people understand scientific phenomena in many disciplines. Recent advances in technologies make it easier to collect huge amounts of data, which offers new opportunities on data-driven methods for the identification of mathematical models behind a phenomenon. This minisymposium focuses on learning mathematical models from an observed data set. Topics in this field include identification of governing equations, reconstruction of certain functions in an equation, and learning operators between input and output spaces. Recently, there have been interesting developments in this field, varying from problem formulations, efficient solvers, techniques on improving robustness to theoretical analysis. This minisymposium brings together researchers to discuss recent advances, challenges and applications in this field.
[05503] Recent Advances in Weak Form-Based System Identification
Format : Online Talk on Zoom
Author(s) :
David Bortz (University of Colorado - Boulder)
Daniel Messenger (University of Colorado - Boulder)
Abstract : Recent advances in data-driven modeling approaches have proven highly successful in a wide range of fields in science and engineering. In this talk, I will present our weak form methodology which has proven to have surprising performance properties. After describing our equation learning (WSINDy) and parameter estimation (WENDy) algorithms, I will discuss applications to several benchmark problems to illustrate the computational efficiency, noise robustness, and modest data needs.
[05509] How much can one learn a PDE from its solution?
Format : Online Talk on Zoom
Author(s) :
Yimin Zhong (Auburn University )
Hongkai Zhao (Duke University)
Yuchen He (Shanghai Jiao Tong University)
Abstract : In this work we study a few basic questions for PDE learning from observed solution data. Using various types of PDEs, we show 1) how the approximate dimension (richness) of the data space spanned by all snapshots along a solution trajectory depends on the differential operator and initial data, and 2) identifiability of a differential operator from solution data on local patches. Then we propose a consistent and sparse local regression method (CaSLR) for general PDE identification. Our method is data driven and requires minimal amount of local measurements in space and time from a single solution trajectory by enforcing global consistency and sparsity.
[05502] Identification of variable coefficient PDEs using group projected subspace pursuit
Format : Online Talk on Zoom
Author(s) :
Yuchen He (Shanghai Jiao Tong University)
Sung Ha Kang (Georgia Institute of Techonology)
Wenjing Liao (Georgia Institute of Technology)
Hao Liu (Hong Kong Baptist University)
Yingjie Liu (Georgia Institute of Technology)
Abstract : We propose a novel scheme, GP-IDENT, for identifying variable coefficient PDEs from noisy observations of single solution trajectories. To effectively solve the associated feature selection problems, we designed a group projected subspace pursuit (GPSP) algorithm, which is also suitable for general feature selection problems with group structure. We will provide examples to show that GP-IDENT can successively identify many non-linear high-order PDEs, and its effectiveness is also justified via comparisons with state-of-the-art methods.
[05246] Learning Koopman Operators that Generalize Well
Format : Online Talk on Zoom
Author(s) :
Bethany Lusch (Argonne National Laboratory)
Abstract : The Koopman operator is a way to represent a nonlinear dynamical system as a globally linear system. However, the linear system is infinite-dimensional, and the representation is difficult to find. Much recent research is on data-driven methods to approximate the Koopman operator. However, finding an approximation that generalizes well for a large region without finely sampling the space can be challenging. We explore learning a Koopman operator that can generalize well given limited data.
