SC Seminar Nathaniel Trask (Sandia)

Structure preserving deep learning architectures for convergent and stable data-driven modeling
  • What Scientific Computing English
  • When 29-04-2021 from 16:15 to 17:15 (Europe/Amsterdam / UTC200)
  • Where online
  • Contact Name
  • Add event to calendar iCal

Join Zoom Meeting
https://cwi-nl.zoom.us/j/82098750344?pwd=V1RwN0MyMnJCdWlCaW1tY1pBaDBTQT09

Meeting ID: 820 9875 0344
Passcode: 051962

Nathaniel Trask (Sandia), Structure preserving deep learning architectures for convergent and stable data-driven modeling

The unique approximation properties of deep architectures have attracted attention in recent years as a foundation for data-driven modeling in scientific machine learning (SciML) applications. The "black-box" nature of DNNs however require large amounts of data that generalize poorly in traditional engineering settings where available data is relatively small, and it is generally difficult to provide a priori guarantees about the accuracy and stability of extracted models. We adopt the perspective that tools from mimetic discretization of PDEs may be adapted to SciML settings, developing architectures and fast optimizers tailored to the specific needs of SciML. In particular, we focus on: realizing convergence competitive with FEM, preserving topological structure fundamental to conservation and multiphysics, and providing stability guarantees. In this talk we introduce some motivating applications at Sandia spanning shock magnetohydrodynamics and semiconductor physics before providing an overview of the mathematics underpinning these efforts.