1714 Advances in scientific machine learning for high dimensional many-query problems

  • Thomas O'Leary-Roseberry, UT Austin Oden Institute
  • Peng Chen, UT Austin Oden Institute
  • Omar Ghattas, UT Austin Oden Institute

Inverse, optimal design, optimal control, and uncertainty quantification problems -- so-called many-query problems - have often been out of reach in cases where the parameter dimension is high or the parametric map is governed by expensive-to-solve partial differential equations. Recent developments in scientific machine learning (SciML) are creating new opportunities to construct surrogates that approximate the PDE-based parametric maps underlying many-query problems, thereby avoiding the solution of PDEs in the online phase. While traditional techniques for construction of reliable surrogates do not scale to very high dimensions and expensive PDEs, recent advances in deep learning and nonlinear dimension reduction offer hope that the twin curses of dimensionality and model expense can be overcome. SciML methods are being developed that are capable of providing cheap-to-evaluate surrogates with certified accuracy and scalability to high dimensions. This minisymposium brings together leading experts in scientific machine learning for many-query problems to discuss recent theoretical and algorithmic advances, with applications to a broad spectrum of scientific and engineering problems.

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